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<!DOCTYPE archimedes [

<?xml version="1.0"?>

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

<author>Gassendi, Pierre</author>

<title>De proportione qua gravia decidentia accelerantur</title>

<place>Paris</place>

<cvs_file>gasse_propo_01_la_1646</cvs_file>

<cvs_version></cvs_version>

</info> <text> <front> </front> <body> <chap> <pb/>

<s><emph type="center"/><emph type="italics"/>PETRI GASSENDI<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/>DE PROPORTIONE, <lb/>QVA GRAVIA DECIDENTIA <lb/>ACCELERANTVR.<emph.end type="center"/></s>

<s><emph type="center"/>EPISTOLÆ TRES.<emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Quibus ad totidem Epi&longs;tolas R. P.<emph.end type="italics"/> PETRI CAZRÆ<gap/><lb/><emph type="italics"/>Societatis<emph.end type="italics"/> IESV <emph type="italics"/>Re&longs;pondetur.<emph.end type="italics"/><emph.end type="center"/></s><figure></figure>

<s><emph type="center"/>PARISIIS,<emph.end type="center"/></s>

<s><emph type="center"/>Apud LVDOVICVM DE HEVQVEVILLE, via Iacobæa, <lb/>&longs;ub &longs;igno Pacis.<emph.end type="center"/><lb/><gap desc="hr tag"/></s>

<s><emph type="center"/><emph type="italics"/>CVM PRIVILEGIO REGIS<emph.end type="italics"/><emph.end type="center"/></s><pb/><figure></figure>

<s><emph type="center"/>EPISTOLARVM<emph.end type="center"/></s>

<s><emph type="center"/>SVMMVLÆ.<emph.end type="center"/><lb/><gap desc="hr tag"/></s>

<s><emph type="center"/>EPISTOLÆ PRIMÆ.<emph.end type="center"/></s>

<s>Scribendi Occa&longs;io. </s>

<s><emph type="italics"/>CVm enim ante annos treis Author edidi&longs;&longs;et duas Epi&longs;to<lb/>las<emph.end type="italics"/> De Motu impre&longs;&longs;o à Motore tran&longs;lato <emph type="italics"/>in&longs;crip<lb/>tas, R. P. </s>

<s>Cazræus Societatis<emph.end type="italics"/> IESV <emph type="italics"/>tum Diuionen&longs;is Collegij <lb/>Rector &longs;crip&longs;it ad ip&longs;um <expan abbr="Epi&longs;tolã">Epi&longs;tolam</expan>, qua reprehendit capita varia <lb/>tam circa cætera de Motu con&longs;cripta, quàm circa di&longs;putata &longs;pe<lb/>ciatim de Motu Terra attributo. </s>

<s>Itaque Author ad illum re&longs;<lb/>crip&longs;it eâ Epi&longs;tolâ, quæ heic babetur ordine tertia, quàmque pri<lb/>mam legere &longs;i libet, licet, imò & non <expan abbr="incongru&utilde;">incongruum</expan> e&longs;t. </s>

<s>Quia verò <lb/>R. P. cætera inter obiecerat, non fui&longs;&longs;e Authorem probatu<lb/>rum<emph.end type="italics"/> G<emph type="italics"/>alilei &longs;ententiam circa Proportionem, qua grauia de<lb/>cidentia accelerantur, &longs;i commi&longs;&longs;um à<emph.end type="italics"/> G<emph type="italics"/>alileo Paralogi&longs;mum <lb/>animaduerti&longs;&longs;et; & Author responderat &longs;e nec potui&longs;&longs;e nec<lb/>dum po&longs;&longs;e Paralogi&longs;mum vllum videre; ac optare adeò, <lb/>vt R. P. tum illum retegeret, tum proportionem quam crede<lb/>ret e&longs;&longs;e veriorem manife&longs;taret; idcircò R. P. con&longs;crip&longs;it, edi<lb/>ditque nuper Epistolam aliam hocce Titulo,<emph.end type="italics"/> Phy&longs;ica <pb/>Demon&longs;tratio, qua ratio, men&longs;ura, modus, ac poten<lb/>tia accelerationis motus in naturali de&longs;cen&longs;u grauium <lb/>determinantur; aduer&longs;us nuper excogitatam à <emph type="italics"/>G<emph.end type="italics"/>alileo <lb/>Galilei Florentino Philo&longs;opho, ac Mathe matico de <lb/>eodem motu P&longs;eudo &longs;cientiam. <emph type="italics"/>Hæc ergo Epi&longs;tola e&longs;t, <lb/>ad quam heic primùm Respondetur.<emph.end type="italics"/> A pag. </s>

<s>Status Controuer&longs;iæ. </s>

<s><emph type="italics"/>Quæritur nimirùm, An, cùm lapide, v. </s>

<s>ex alto cadente, <lb/>accipere liceat primum quoddam spatium, vt vnam orgyiam; <lb/>& habe re pro momento, &longs;eu tempore primo illud quod effluit, <lb/>donec lapis per hanc orgyiam decidit: & pro gradu celeritatis <lb/>primo eam celeritatem, quæ in fine primi huius temporis acqui<lb/>&longs;ita e&longs;t: An inquam, acceptis deinceps æqualibus &longs;patijs, tempo<lb/>ribus, & gradibus, cen&longs;eri debeat lapis motu&longs;-ve ip&longs;ius tum <lb/>acqui&longs;u&longs;&longs;e duos celeritatis gradus, cùm e&longs;t &longs;uperata &longs;ecunda <lb/>orgyia, licet &longs;ecundum tempus nondum totum effluxerit, ac <lb/>pari modo treis, cùm tertia, quatuor cum quarta, &c. </s>

<s>adeò vt <lb/>&longs;emper velocitates &longs;e habeant &longs;ieut &longs;patia, quòd R. P. conten<lb/>dit: An potiùs cen&longs;eride beat <expan abbr="t&utilde;">tum</expan> acqui&longs;u&longs;&longs;e duos celeritatis gra<lb/>dus, cùm effluxit &longs;ecundum tempus, licet plura spatia, quàm <lb/>duo &longs;uperata &longs;int: ac pari modo treis, cùm tertium, quatuor, <lb/><gap/>ùm quartum, &c. </s>

<s>adeò vt &longs;emper velocitates &longs;e habeant &longs;icut <lb/>tempora; quæ e&longs;t Galilei &longs;ententia. </s>

<s>Ex qua aliunde &longs;equitur, <lb/>vt temporibus æqualibus &longs;patia &longs;uperentur iuxta numeros ab <lb/>vnitate impareis: ita vt &longs;i primo tempore lapis decidat per <lb/>vnam orgyiam, decidat &longs;ecundo per treis, tertio per quinque, <lb/>quarto per &longs;eptem, &c. </s>

<s>atque idcircò spatia in fine cuiu&longs;que <lb/>temporis à principio v&longs;que aggregata habeant &longs;e &longs;icut quadra<lb/>ta temporum; hoc e&longs;t, vt spatia &longs;uperata &longs;int in fine vnius<emph.end type="italics"/><pb/><emph type="italics"/>temporis vnum, in fine duorum quatuor; in fine trium nouem; <lb/>in fine quatuor &longs;exdecim, &c. </s>

<s>Quæ omnia liceat repræ&longs;entare <lb/>in maiu&longs;culo quodam Triangulo, cuius lateribus, ac ba&longs;i in par<lb/>teis æqualeis diui&longs;is, interducti&longs;que lineis aream di&longs;pe&longs;centibus <lb/>in minores, mutuò æqualeis, &longs;imilei&longs;que triangulos, partes <lb/>vtriu&longs;vis lateris (incipiendo ab apice) habeantur pro tempori<lb/>bus; ba&longs;es triangulorum ip&longs;is respondentium pro gradibus ce<lb/>leritatis; & intercepta triangula, ip&longs;orumve areæ pro spatiis. <lb/></s>

<s>Vide & totius Epi&longs;tolæ &longs;iue Di&longs;&longs;ertationis &longs;eriem.<emph.end type="italics"/> A p. </s>

<s>De Motus æquabiliter <lb/>accelerati definitione. </s>

<s><emph type="italics"/>Definit<emph.end type="italics"/> G<emph type="italics"/>alileus Motum æquabiliter acceleratum (qua<lb/>lis grauibus decidentibus competit) illum,<emph.end type="italics"/> qui à quiete rece<lb/>dens, temporibus æqualibus æqualia celeritatis mo<lb/>menta acquirit. <emph type="italics"/>Jd autem improbans R. P. contendit po<lb/>tiùs definiendum cum vulgari &longs;ententia illum,<emph.end type="italics"/> qui æquali<lb/>bus &longs;patiis æqualia celeritatis augmenta acqu<gap/>it. <emph type="italics"/>Quan<lb/>quam ex Galilei definitione præclarè intelligitur accelerationis <lb/>æquabilitas: prout incre&longs;<gap/>s celeritas &longs;e habet vt linea inter <lb/>latera memorati Trianguli ab apice v&longs;que in ba&longs;im incre&longs;cen<gap/><lb/>& hæc linea ideò incre&longs;cit æquabiliter, quòd &longs;ecundum parteis<lb/>laterum æqualeis (per quas dictum e&longs;t repræ&longs;entari tempora) <lb/>additamenta continuò æqualia acquirat.<emph.end type="italics"/> E<emph type="italics"/>x definitione au<lb/>tem R. </s>

<s>Patri probata, nihil tale potest intelligi: cùm nulla <lb/>facta temporis mentione, & &longs;umptis partibus lateris trianguli <lb/>pro spatiis, & interceptis triangulis pro celeritatis gradibus, <lb/>con&longs;tet, &longs;i totidem &longs;emper addantur triangula, quot lateris par<lb/>tes, creatum iri triangulum totalem, cuius area inæquabili&longs;<lb/>&longs;imè ab apice in ba&longs;im incre&longs;cat.<emph.end type="italics"/> A p. </s>

<s>De Paralogi&longs;mo, <lb/>qui Galileo Definitionem &longs;puriam impugnan<lb/>ti obiicitur. </s>

<s><emph type="italics"/>Impugnat<emph.end type="italics"/> G<emph type="italics"/>alileus definitionem R. </s>

<s>Patri probatam, <lb/>quòd &longs;i velocitates e&longs;&longs;ent, vt emen&longs;a &longs;patia, atque idcircò <lb/>&longs;patium v. </s>

<s>duplum percurreretur velocitate dupla illius, qua <lb/>dimidium: &longs;equeretur duplum, & dimidium, &longs;eu totum, & <lb/>partem, eodem, aut æquali tempore percurri. </s>

<s>Nempe &longs;eu <lb/>motus æquabilis, &longs;eu acceleratus æquabiliter &longs;it, non potest ce<lb/>leritas e&longs;&longs;e dupla per duplum &longs;patij, quin ea ex&longs;i&longs;tente vbique <lb/>dupla, duplæ partes percurrantur quibu&longs;libet temporibus, &longs;ic<lb/>que perueniatur eodem tempore ad dupli, & ad dimidij finem. <lb/></s>

<s>Contendit R. P. committi heic Paralogi&longs;mum: & nullam <lb/>tamen rationem profert, quàm quæ continetur his verbis,<emph.end type="italics"/><lb/>Si graue de&longs;cendens per AB, tempus quodcum<lb/><figure id="fig1"></figure><lb/>que in&longs;umat, putà quadrantem; ac deinde BC <lb/>ip&longs;i AB æquale dimidio quadrante percurrat: <lb/>quis neget in C duplam haberi velocitatem eius, <lb/>quæ fuit in B? & tamen idem graue totam AC, <lb/>& dimidium eius AB non percurreret. <emph type="italics"/>Vbi &longs;anè <lb/>nihil aliud, quàm rem controuer&longs;am &longs;upponit, habetque <lb/>pro principio: videlicet &longs;ecundam partem percurri di<lb/>midio temporis, quo primam. </s>

<s>Atque id quidem præter Incom<lb/>modum ex po&longs;itione hac con&longs;equens, quòd cùm oporteat pari <lb/>modo percurri partem tertiam dimidio temporis, quo &longs;ecun<lb/>dam; quartam, quo tertiam, &c. </s>

<s>debeat cum effluxu temporis <lb/>&longs;ecundi percurri spatium infinitum: quatenus omnia illa di<lb/>midiorum dimidia, &longs;iue fragmenta temporis non po&longs;&longs;unt<emph.end type="italics"/><pb/><emph type="italics"/>æquari vni integro (cuius &longs;emper relinquitur inexhaustum <lb/>aliquid) ni&longs;i priùs omnia, hoc e&longs;t infinita, fuerint numerata.<emph.end type="italics"/><lb/>A. p. </s>

<s>ART. XIII. XIV. XV. XVI. XVII. <lb/>XVIII. </s>

<s>De Po&longs;tulato Galilei circa motum <lb/>&longs;uper æque-altis, non æque-inclinatis planis. </s>

<s><emph type="italics"/>Cùm experientiâ con&longs;tet accelerationem eadem ratione <lb/>fieri, &longs;iue ad perpendiculum graue decidat, &longs;iue &longs;upra planum <lb/>inclinatum delabatur; candidè egit<emph.end type="italics"/> G<emph type="italics"/>alileus, dum a&longs;&longs;umens<emph.end type="italics"/><lb/>Gradus velocitatis eiu&longs;dem mobilis &longs;uper diuer&longs;as pla<lb/>norum inclinationes acqui&longs;itos tum e&longs;&longs;e æqualeis, cùm <lb/>eorumdem planorum eleuationes ponuntur æquales: <lb/><emph type="italics"/>id extulit, non vt demon&longs;tratum (tamet&longs;i Torricellius posteà <lb/>demon&longs;trationem attulerit) &longs;edvt eatenus probabile, quatenus <lb/>deductæ ex eo conclu&longs;iones cum experientia con&longs;entirent. </s>

<s>Id <lb/>tamen R. P. exagitat, vti & confirmationem, non incongruè <lb/>alioquin petitam ex pendulis, quæ longioribus, breuioribu&longs;que <lb/>filis illigata, & ex eadem tamen altitudine vibrari permi&longs;&longs;a, ad <lb/>eandem proximè a&longs;&longs;urgant, &longs;icque debeant omnia parem impe<lb/>tum (&longs;eu velocitatem) de&longs;cendendo acquirere: vtcumque per <lb/>arcus inæqualeis procurrant. </s>

<s>Neque verò etiam R. P. licet <lb/>difficilia obiiciat, proptereà infirmat<emph.end type="italics"/> G<emph type="italics"/>alilei experimenta (qui<lb/>bus Author habet aliqua &longs;imilia) ad probandum grauia tam <lb/>decidentia, quàm delabentia conficere primo tempore vnum &longs;pa<lb/>tium, &longs;ecundo tria, tertio quinque, &c.<emph.end type="italics"/> A p. </s>

<s>De <lb/>Experimento circa ictum, impetumve grauium <lb/>cadentium, ad explorandum impetu&longs;-ne, vt <lb/>&longs;patium incre&longs;cat. </s>

<s><emph type="italics"/>Tamet&longs;i con&longs;tet grauia, quò ex altiore decidunt loco, e<gap/><lb/>maiore impetu e&longs;&longs;e, vehementiu&longs;que percutere, ac tantam e&longs;&longs;e <lb/>velocitatem, quantus impetus, & percußio est: non ideò tamen <lb/>con&longs;tat vllis (qualia R. P. dicit in quolibetgraui clara, facilia, <lb/>indubitata) experimentis, graue decidens ex altitudine dupl<gap/><lb/>duplò fortiùs percutere, triplò ex tripla, quadruplò ex quadru<lb/>pla, &c. </s>

<s>Quin-etiam &longs;unt Experimenta, quæimpetum, per<lb/>cußionemque non e&longs;&longs;e duplò maiorem in&longs;inuant, ni&longs;i ex altitu<lb/>dinequadrupla; triplò, ni&longs;i ex nonupla; quadruplò, ni&longs;i ex &longs;e<lb/>decupla. </s>

<s>Huiu&longs;cemodi &longs;untilla de Aqua cylindrico va&longs;e con<lb/>tenta; cuius duplum non ex&longs;ilit tempore æquali, ni&longs;i altitudo <lb/>quadrupla &longs;it; nec triplum, ni&longs;i nonupla; quadruplum, ni&longs;i &longs;e<lb/>decupla: & de Chorda ten&longs;a, cuius vibratæ itus, reditu&longs;que <lb/>dupli non &longs;unt, ni&longs;i quadruplo pondere tendatur; tripli, ni&longs;i <lb/>nonuplo; quadrupli, ni&longs;i &longs;edecuplo: ac rursùs de Pen&longs;ilibus, <lb/>quorum vibrationes ad perpendiculum peruenientes non acqui<lb/>runt impetum duplum, ni&longs;i altitudo de&longs;cen&longs;us &longs;it quadrupla, <lb/>triplum, ni&longs;i nonupla, quadruplum, ni&longs;i &longs;edecupla, &c.<emph.end type="italics"/><lb/>A p. </s>

<s>ART. XXIII. XXIV. XXV. XXVI. XXVII. <lb/>XXVIII. </s>

<s>De Experimento in Bilance facto, ac <lb/>aliud reuerâ probante, quàm velocitates e&longs;&longs;e <lb/>&longs;icut &longs;patia. </s>

<s><emph type="italics"/>Fuere omnia Experimenta R. P. ad vnum redacta, vt<emph.end type="italics"/><pb/><emph type="italics"/>non modò probaret impetum, atque idcircò velocitatem &longs;icut <lb/>spatium incre&longs;cere; &longs;ed speciatim quoque illud, quod edixit, <lb/>diametrum cuiu&longs;libet globi ita e&longs;&longs;e præci&longs;am impetus illius <lb/>men&longs;uram, vt ex altitudine duarum diametrorum præcisè, per<lb/>cutiat duplò fortiùs: ex altitudine trium triplo: ex altitudine <lb/>quatuor quadruplò, &c. </s>

<s>Iußit autem Experimentum in Bi<lb/>lance peragi, qua ruè &longs;u&longs;pen&longs;a, & alterâ lancium per aërem <lb/>liberâ, alterâ &longs;uffulia, & pondere exæquatâ cum libera, glo<lb/>bóque &longs;imùl, &longs;i deinceps, inquit, dimittatur globus in liberam <lb/>ex vna &longs;ui diametro, is percußionis impetu attollet &longs;uffuliam <lb/>cùm &longs;uper-addito præci è vno &longs;ui pondere; &longs;i ex duabus, cum <lb/>&longs;upper-addito duplo: &longs;i ex tribus, cum triplo: &longs;i ex quatuor, <lb/>cum quadruplo. </s>

<s>Et permirum tamen id Experimentum de<lb/>prehendi fal&longs;um; quatenus dimi&longs;&longs;us globus ex altitudine dia<lb/>metri vnius, non modò attollit cum altera lance (eo, quo dictum <lb/>e&longs;t, modo exæquata) ponderis tantumdem, quanto ip&longs;e e&longs;t, ve<lb/>rùm etiam <expan abbr="dupl&utilde;">duplum</expan>, etiam ad v&longs;que <expan abbr="&longs;eptupl&utilde;">&longs;eptuplum</expan>: & tantum idem <lb/>aliunde attollit non modò ex diametro vna altitudinis, verùm <lb/>etiam ex diametri &longs;emi&longs;&longs;e, imo ex quadrante, imò ex octante, <lb/>imò & ex vncia. </s>

<s>Quin-etiam eius ponderis, quod eleuat &longs;um<lb/>mum ex diametro vna, duplum eleuat non ex diametris dua<lb/>bus, &longs;ed ex quatuor: triplum non ex tribus, &longs;ed ex <lb/>nouem: quadruplum non ex quatuor, &longs;ed ex &longs;edecim: adeò <lb/>proinde vt proprio R. P. experimento eius &longs;ententia euertatur, <lb/>&<emph.end type="italics"/> G<emph type="italics"/>alileana confirmetur. </s>

<s>Adde &, &longs;i velocitatis gradus <lb/>pro ratione diametrorum cre&longs;cerent, euenturum, vt dimißis ex <lb/>eadem altitudine duobus globis ex eadem materia, quorum <lb/>vnus e&longs;&longs;et diametro decies maiore, quàm alius, minor caderet <lb/>decuplo velociùs, ac decuplò citiùs perueniret in terram, quàm <lb/>mator; cùm experientia tamen doceat cadere æque-velociter,<emph.end type="italics"/><pb/><emph type="italics"/>temporéque eodem peruenire in terram: vtcúmque aliunde <lb/>Ari&longs;toteles cen&longs;eat cadere maiorem velociùs, & peruenire <lb/>citiùs.<emph.end type="italics"/> A p 41. in 53. </s>

<s>ART. XXIX. XXX. XXXI XXXII. XXXIII. <lb/></s>

<s>De Tempore, quo R. P. colligit parteis &longs;patij <lb/>&longs;ingulas decur&longs;um non iri. </s>

<s><emph type="italics"/>Origo fuit mali, quòd R. P. & Experimentum fal&longs;um <lb/>(&longs;eu quod nul um e&longs;&longs;et) pro vero habuerit. </s>

<s>& illam Motus <lb/>æquabiliter accelerati definitionem a&longs;&longs;ump&longs;erit, quæ traditur <lb/>nulla temporis mentione: <expan abbr="c&utilde;">cum</expan> impoßibile tamen &longs;it &longs;eu celerita<lb/>tem, &longs;eu accelerationem, maximéque æquabilem, intelligi, &longs;ine <lb/>comparatione ad tempus. </s>

<s>Et quia &longs;upponendo velocitates <lb/>acquiri, vt spatiæ, manife&longs;tè &longs;equitur, vt &longs;ecundum æquale <lb/>spatium decurratur dimidio temporis, quo primum; tertium <lb/>triente, quartum quadrante, &c. (quippe tempore &longs;emper <lb/>ex&longs;i&longs;tente ad velocitatem incre&longs;centem &longs;ubmultiplo) cum heic <lb/>tamen con&longs;equantur incommoda varia, ac illud speciatim, <lb/>quod acceleratio fieret, vt difformiter. </s>

<s>&longs;ic in ratione plu&longs;quam <lb/>tripla: ideò o&longs;tendit quidem R.<emph.end type="italics"/> P. <emph type="italics"/>ex quibu&longs;dam incommodis <lb/>fieri non po&longs;&longs;e vt decurrantur &longs;patia temporibus huiu&longs;modi; <lb/>&longs;ed <expan abbr="o&longs;t&etilde;dit">o&longs;tendit</expan> tamen aduer&longs;us &longs;eip&longs;um, quatenus decurri nec &longs;&longs;ariò <lb/>&longs;equitur ex eapo&longs;itione, quod velocitates &longs;e habeant vt &longs;patia.<emph.end type="italics"/><lb/>A p. </s>

<s>ART. XXXIV. XXXV. XXXVI. XXXVII. <lb/>XXXVIII. </s>

<s>De Tempore, quo R. P. colligit <lb/>&longs;ingulas parteis decur&longs;um iri. </s>

<s><emph type="italics"/>Diui&longs;o ca&longs;us spatio in parteis æqualeis quotcumque,<emph.end type="italics"/><pb/><emph type="italics"/>accipit R. P. punctum infimum primæ partis, & ab ip&longs;o <lb/>&longs;ur&longs;um eiu&longs;dem primæ partis dimiaium, trientem, quauran<lb/>tem, & vniuersè tot fragmenta, quot &longs;unt inferiùs partes <lb/>æquales; ac tum contendit, quanto tempore dimidium inferius <lb/>primæ partis percurritur, tanto deinceps partem &longs;ecundam <lb/>æqualem percurri; quanto triens, tanto tertiam; quanto qua<lb/>drans, tanto quartam, &c. </s>

<s>adeò proinde, vt in inferiore pri<lb/>mæ partis dimidio contineantur &longs;igillatim omnia tempora, qui<lb/>bus omnes &longs;uper&longs;tites æquales partes percurruntur. </s>

<s>Attamen <lb/>abs re, & omninô gratis negligit &longs;uperius dimidium, nullam<lb/>que eius rationem habet; à cuius tamen initio, non fine, motus <lb/>incipit, & per quod iam acceleratur, cùm pauciores parteis, <lb/><expan abbr="quã">quam</expan> inferius nonhabeat. </s>

<s>Gratis <expan abbr="quoq;">quoque</expan> v&longs;urpat inferius, ip&longs;ique <lb/>fata omnium partium inferiorum alligat: nam & quòd vult <lb/>&longs;ecundam partem e&longs;&longs;e huius dimidij duplam, atque ideo e&longs;&longs;e <lb/>velocitatem duplam, & tempus æquale: nihil aliud; quàm <lb/>quæ&longs;itum petit. </s>

<s>Aliunde autem variis argumentis conficitur, <lb/>vt a&longs;&longs;umpto quocumque primo tempore, tam inferius dimidium, <lb/>quàm &longs;ecunda pars tempore breuiore, breuioreque in infinitum <lb/>percurrantur (&longs;ubdiui&longs;o nempe priore dimidio in duo alia, & <lb/>rur&longs;us priore in alia, &c.) vt <expan abbr="it&etilde;">item</expan> tam inferius dimidium, qua <lb/>&longs;ecunda pars percurrantur dimidio temporis, quo integra pri<lb/>ma: vt tempus per &longs;ecundam partem &longs;e&longs;qui alterum &longs;it, non <lb/>duplum ad illud, quo percurritur inferius dimidium: vt tam <lb/>primapars &longs;ola, quàm prima, & &longs;ecunda &longs;imùl, hoc e&longs;t pars, <lb/>& totum eodem, aut æquali percurrantur tempore; atque id <lb/>genus cætera, quæ proportione etiam obiici in trientem, qua<lb/>drantem, fragmentaque alia a&longs;&longs;umptæ primæ partis po&longs;&longs;unt.<emph.end type="italics"/><lb/>A p. </s>

<s>ART. XXXIX. XL. XLI. XLII. <lb/></s>

<s>De Ratione continuò dupla, qua &longs;patia de<lb/>curri temporibus æqualibus R. P. contendit. </s>

<s><emph type="italics"/>Diui&longs;o eodem ca&longs;us &longs;patio in quotcúmque æqualeis parteis, & <lb/>parte prima &longs;ubdiui&longs;a in duo dimidia; a&longs;&longs;umit R. P. illud <expan abbr="t&etilde;pus">tempus</expan>, <lb/>quo inferius <expan abbr="dimidi&utilde;">dimidium</expan> percurritur, pro tempore primo: ac vult <lb/>tempore æquali &longs;ecundo percurri partem &longs;ecundam, quæ est <lb/>nempe dupla illius dimidij: ac tertio parteis tertiam, & quar<lb/>tam, quæ iunctim &longs;unt duplum &longs;ecundæ: & quarto quintam, <lb/>&longs;extam, &longs;eptimam, octauam, quæ iunctim &longs;unt duplum tertiæ, <lb/>& quartæ; & quinto octo &longs;uccedenteis, &longs;exto &longs;equenteis &longs;ex<lb/>decim: atque ita porrò in ratione continuò dupla. </s>

<s>At verò <lb/>heic quoque abs re præteritur primum primæ partis dimidium: <lb/>& maximè cùm requiratur, quæ accelerationis &longs;it ratio non <lb/>à medio v&longs;que primæ partis, &longs;ed ab eius v&longs;que initio. </s>

<s>Peruer<lb/>tit etiam R. P. </s>

<s>Arithmeticam progreßionem, qua &longs;uperiùs <lb/>&longs;tatuens velocitates e&longs;&longs;e, vt &longs;patia, voluit vni parti integræ, non <lb/>eius dimidio competere vnum celeritatis gradum, duobus <lb/>duos, &c. </s>

<s>Conficitur rur&longs;us heic quoque, vt totum, & pars <lb/>eodem tempore percurrantur; vt non ampliùs, quàm triens, & <lb/>quadrans exæquentur toti; vt item &longs;olæ partes quinta, &longs;exta, <lb/>&longs;eptima, octaua; atque ita de reliquis. </s>

<s>Comficitur quoque, vt <lb/>decurrantur &longs;patia non modò in ratione dupla, &longs;ed etiam in <lb/>tripla, quadrupla, &c. </s>

<s>Denique & illud inde &longs;equitur, <lb/>quod iam ante obiectum est; vt primo nimirùm tempore per<lb/>acto, effluere &longs;ecundum æquale non poßit, quin decur&longs;um fuerit <lb/>spatium infinitum.<emph.end type="italics"/> A p. </s>

<s>ART. XLIII. XLIV. </s>

<s>De Tempore, <lb/>quo globum ferreum ca&longs;urum ex Luna in <lb/>Terram contendit. </s>

<s>C<emph type="italics"/>ùm<emph.end type="italics"/> G<emph type="italics"/>alileus &longs;upponendo e&longs;&longs;e à Luna in centrum Ter<lb/>ræ milliaria Jtalica<emph.end type="italics"/> 196000, <emph type="italics"/>deducat ex ob&longs;eruatione, ac <lb/>proportione à &longs;e instituta decur&longs;um iri id spatium à globo fer<lb/>reo è Luna dimi&longs;&longs;o intra horas<emph.end type="italics"/> 3. <emph type="italics"/>minuta<emph.end type="italics"/> 22. <emph type="italics"/>& &longs;ecunda<emph.end type="italics"/> 4. <lb/><emph type="italics"/>deducit R. P. iuxta &longs;uam illam progreßionem in ratione con<lb/>tinuò dupla, decur&longs;um iri id spatium intra minuta non omninò <lb/>duo.<emph.end type="italics"/> I<emph type="italics"/>mmanis &longs;anè pernicitas, & quam refellit etiam ex<lb/>perientia, qua cùm constet globum non conficere amplius vno <lb/>&longs;emi-minuto, quàm milliare vnum altitudinis; & &longs;eruata <lb/>etiam acceleratione in ratione dupla, non poßit &longs;ecundo &longs;emi<lb/>minuto, ni&longs;i duo conficere: tertio, ni&longs;i quatuor: quarto, ni&longs;iocto: <lb/>manife&longs;tum fit ex ijs aggregatis non po&longs;&longs;e intra duo minuta <lb/>confici milliaria plu&longs;quam quindecim. </s>

<s>Quàm ingenti verò <lb/>di&longs;crimine hic numerus abe&longs;t à milliaribus<emph.end type="italics"/> 196000. <emph type="italics"/>&longs;eu ab <lb/>ijs potiùs, quæ ille vult intra duo minuta integra percurri,<emph.end type="italics"/><lb/>1677721<gap/>: <emph type="italics"/>& mira quidem incohærentia, quatenus de<lb/>bent primo &longs;emi-minuto percurri<emph.end type="italics"/> 6, <emph type="italics"/>cum proximè triente: <lb/>&longs;ecundo<emph.end type="italics"/> 403, <emph type="italics"/>cum vna quinta: tertio<emph.end type="italics"/> 25804, <emph type="italics"/>cum quatuor <lb/>quintis: & quarto<emph.end type="italics"/> 1651507, <emph type="italics"/>cum vna quinta?<emph.end type="italics"/> A p. </s>

<s>ART. XLV. XLVI. XLVII. </s>

<s>De Tem<lb/>pore per primas parteis ob&longs;eruatione determi<lb/>nando; pauca de cau&longs;&longs;a Phy&longs;ica, déque lap&longs;u <lb/>circa cam admi&longs;&longs;o. </s>

<s>I<emph type="italics"/>ngenuè quidem R. P. fatetur nonhabere &longs;e vnde tempus<emph.end type="italics"/><pb/><emph type="italics"/>determinet, qua &longs;ecunda pars, quo primæ dimidia &longs;igillatim <lb/>percurruntur: ac alios ideò prouocat, vt rem experiantur in <lb/>turri pedes ducentos alta (vtcumque ip&longs;e præ cæteris videatur <lb/>fui&longs;&longs;e experturus) ac non videtur<emph.end type="italics"/> G<emph type="italics"/>alileum id determinantem <lb/>ex ob&longs;eruatis proprijs &longs;ufficienter refellere: dum ait duntaxat, <lb/>e&longs;&longs;e verendum, ne cùm in alijs magnoperè errauerit, heic quo<lb/>que &longs;it hallucinatus. </s>

<s>Quippe neque o&longs;ten&longs;um e&longs;t erra&longs;&longs;e ip&longs;um <lb/>in alijs, neque heic habet aliquid non experientiæ con&longs;onum, <lb/>maximéque illud effatum,<emph.end type="italics"/> &longs;i à lationis principio duo quæ<lb/>libet &longs;patia &longs;umantur, tempora ip&longs;orum fore inter &longs;e, <lb/>vt alterum eorum ad &longs;patium medium proportionale <lb/>inter ip&longs;a: <emph type="italics"/>iuxta quod quidem promptum e&longs;t, quanto specia<lb/>tim tempore & &longs;ecunda pars, & duo primæ dimidia percur<lb/>rantur, determinare. </s>

<s>Excu&longs;atione, dilationeque v<gap/>ur R. P. <lb/>circa cau&longs;&longs;am Phy&longs;icam, de qua vide batur ip&longs;e titutus feci&longs;&longs;e <lb/>aliquid sperandum. </s>

<s>Circa hanc cau&longs;&longs;am lap&longs;us admi&longs;&longs;us in <lb/>Epistolis<emph.end type="italics"/> de. </s>

<s>Motu impre&longs;&longs;o: <emph type="italics"/>quatenus in ea explicanda ip&longs;i <lb/>gradus velocitatis facti æquales spatijs &longs;unt; & intercepta <lb/>triangula, de quibus &longs;uprà, a&longs;&longs;umpta &longs;unt non modò pro &longs;pa<lb/>tijs, verùm etiam pro gradibus; pro quibus a&longs;&longs;umendæ potiùs <lb/>triangulorum ba&longs;es fuerunt.<emph.end type="italics"/> A. p. </s>

<s><emph type="center"/>ART. XLV. CONCLVSIO.<emph.end type="center"/></s>

<s><emph type="italics"/>Ex præteritione eorum, quæ R. P. anacephalæo&longs;i quadam <lb/>exaggerat; non oblitus etiam quantum condoluerit, habitam ab <lb/>Authore fui&longs;&longs;e<emph.end type="italics"/> G<emph type="italics"/>alilei principijs fidem: neque id &longs;ine &longs;olita <lb/>beneuolentiæ &longs;ignificatione.<emph.end type="italics"/> A p. </s>

<s><emph type="center"/>EPISTOLÆ SECVNDÆ<emph.end type="center"/></s>

<s>Scribendi Occa&longs;io. </s>

<s>Pater vi&longs;o &longs;uperioris Epistolæ autographo, ip&longs;am <lb/>edi non improbauit, &longs;i modò attexeretur alia, quam &longs;ubinde <lb/>&longs;crip&longs;it, in&longs;crip&longs;itque<emph.end type="italics"/> Vindicias Phy&longs;icæ Demon&longs;tratio<lb/>nis. <emph type="italics"/>Qùia verò R. P. profitetur &longs;e&longs;e in ea ignotam Autbori <lb/>veritatem maiori iam luce illu&longs;tratam aperire, & ab errore <lb/>vindicatam exhibere; ac aliunde queritur frequens ea &longs;ibi af<lb/>fingi quæ nec dixerit, nec ex traditis à &longs;e principijs potuerint <lb/>deduci; idcircò &longs;ic edi vi&longs;um e&longs;t Vindicias, vt Exceptio inter<lb/>&longs;eratur, ad explorandum quî fieri poßit, vt veritatem &longs;ic il<lb/>lu&longs;tratam, vindicatamque Author non videat, & ad eluen<lb/>dum labem illam, qua ad&longs;pergi per&longs;en&longs;it &longs;e, ob affictionem to<lb/>ties obiectam.<emph.end type="italics"/> A p. </s>

<s>De Statu Controuer&longs;iæ. </s>

<s><emph type="italics"/>Quòd per&longs;tet R. P. pro Demon&longs;tratione habere eam <lb/>Epi&longs;tolam, in quam &longs;uperior con&longs;cripta e&longs;t; ideò vt Status <lb/>controuer&longs;iæ luculentior fiat, ac &longs;imùl appareat, qualis<emph.end type="italics"/> D<emph type="italics"/>emon<lb/>&longs;tratio hæc &longs;it; placet ip&longs;am eruere ex eius totius Epistolæ textu, <lb/>ac reducere, analy&longs;i facta, in hypotheticum Syllogi&longs;mum, qui <lb/>e&longs;&longs;e poßit huiu&longs;modi.<emph.end type="italics"/></s>

<s><emph type="italics"/>Si in motu accelerato grauium decidentium velocitates <lb/>acqui&longs;itæ &longs;e habent vt emen&longs;a &longs;patia, nece&longs;&longs;e e&longs;t &longs;patia decurri <lb/>temporibus æqualibus in ratione continuò dupla:<emph.end type="italics"/></s>

<s><emph type="italics"/>Atqui in motu accelerato grauium decidentium veloci-<emph.end type="italics"/><pb/><emph type="italics"/>tates acqui&longs;itæ &longs;e habent vt emen&longs;a spatia:<emph.end type="italics"/></s>

<s><emph type="italics"/>Igitur in motu accelerato grauium decidentium nece&longs;&longs;e est <lb/>&longs;patia decurri temporibus æqualibus in ratione continuò <lb/>dupla.<emph.end type="italics"/></s>

<s><emph type="italics"/>Nimirùm, vt ex &longs;erie &longs;uperioris Epi&longs;tolæ patet, factum e&longs;t <lb/>initium ab A&longs;&longs;umptionis confirmatione, dum in<emph.end type="italics"/> G<emph type="italics"/>alileum <lb/>di&longs;putatum e&longs;t; tumgradus ad eiu&longs;dem-met A&longs;&longs;umptionis pro<lb/>bationem factus, dum palmare illud Bilancis Experimentum <lb/>e&longs;t narratum; ac tandem ventum ad probandum con&longs;equutio<lb/>nem Propo&longs;itionis, dum explicitus est conatus circa Rationem <lb/>&longs;patiorum duplam, quæ eadem conclu&longs;io fuit Demon&longs;trationis.<emph.end type="italics"/><lb/>A p 93. in 97. </s>

<s>De Motus <lb/>æquabiliter accelerati Definitione. </s>

<s><emph type="italics"/>Con&longs;tat &longs;emper, quam Galileus Definitionem tradidit. <lb/></s>

<s>Neque enim po&longs;&longs;unt velocitatis gradus per triangulorum re<lb/>præ&longs;entari ba&longs;eis, &longs;i per parteis laterum repræ&longs;ententur &longs;patia, <lb/>vt R. P. vult; tum quòd nulla habita temporis mentione <gap/><lb/>t<gap/>g<gap/> poß<gap/> difformitas mira; tum quòd gradus &longs;emel acqui<lb/>&longs;itus aut perire debeat, aut nihil agere, neque poßit duplum <lb/>illius, qui acquiritur; tum quòd &longs;it futurum vt &longs;ecundo tempo<lb/>re octo penè spatia primo æqualia percurrantur. </s>

<s>Confundit <lb/>R. P. </s>

<s>Vniformitatem cum Proportione, dum progreßiones<emph.end type="italics"/><lb/>G<emph type="italics"/>eometricas non minùs e&longs;&longs;e vniformeis, quàm Arithmeticas <lb/>vult: ac in eadem rursùs incidit Incommoda, dum in difformi <lb/>Triangulo vult iteratò spatia per laterum parteis, potiu&longs;quàm <lb/>per triangulos interceptos repræ&longs;entari.<emph.end type="italics"/> A p. </s>

<s>De Paralogi&longs;mo, <lb/>qui Galileo Definitionem &longs;puriam impugnan<lb/>ti obiicitur. </s>

<s><emph type="italics"/>Magno quidem molimine conatur R. P. </s>

<s>Paralogi&longs;mum <lb/>o&longs;tendere: &longs;ed fru&longs;trà nihilominùs; cùm &longs;eu varios &longs;en&longs;us <lb/>di&longs;tinguat, &longs;eu propo&longs;itiones retexat, &longs;eu con&longs;equutionem ex<lb/>pendat, nihil aliud rursùs, quàm quæ&longs;itum, &longs;eu principium (vt <lb/>fuerat illi <expan abbr="obiect&utilde;">obiectum</expan>) petat; aut in &longs;eip&longs;um etiam, vbi retorquere <lb/>quidpiam vult, mutato nomine, concludat. </s>

<s>Haud iure verò <lb/>conqueritur &longs;ibi affingi, quòd dixerit, &longs;patio in duas parteis <lb/>æqualeis diui&longs;o, po&longs;teriorem percurri dimidio temporis, quo prio<lb/>rem (vnde illatum e&longs;t<emph.end type="italics"/> I<emph type="italics"/>ncommodum de infinito spatio intra <lb/>&longs;ecundum tempus percurrendo) cùm relata ip&longs;ißima illius ver<lb/>ba fuerint (de quadrante nempe, & dimidio quadrantis) ac, vt <lb/>po&longs;&longs;et Paralogi&longs;mi Galileum conuincere, non fuerit alio prin<lb/>cipio v&longs;us. </s>

<s>Denique, &longs;i Paralogi&longs;mus à<emph.end type="italics"/> G<emph type="italics"/>alileo admi&longs;&longs;us &longs;it, <lb/>o&longs;tenditur R. P. alio loco aut nihil conclu&longs;i&longs;&longs;e, aut apertißimè <lb/>in eundem Paralogi&longs;mum incidi&longs;&longs;e.<emph.end type="italics"/> A p. </s>

<s>AD ART. XIII. XIV. XV. XVI. XVII. <lb/>XVIII. </s>

<s>De Po&longs;tulato Galilei circa motum <lb/>&longs;uper æque-altis, non æque-inclinatis planis. </s>

<s>G<emph type="italics"/>alilei ob&longs;eruata ad Po&longs;tulatum hoc confirmandum nul<lb/>lius hactenus fal&longs;itatis conuicta &longs;unt; pote&longs;tque adeò eius do<lb/>ctrina potiore iure cen&longs;eri Scientia, vt quæ experientiæ con<lb/>&longs;entanea &longs;it, quàm ea, quæ à R. P. traditur, vt quæ experien<lb/>tiæ repugnet, ac fundata &longs;it in Experimento, quod fal&longs;um de-<emph.end type="italics"/><pb/><emph type="italics"/>prehen&longs;um e&longs;t. </s>

<s>Si planum, vt minùs decliue, ita etiam prolixius <lb/>&longs;it, potest profectò prolixitas paruitatem incrementorum <lb/>velocitatis &longs;ic compen&longs;are, vt acqui&longs;ita in fine motus veloci<lb/>tas &longs;itnihilo minor. </s>

<s>Quod e&longs;t allatum de pendulis exemplum <lb/>&longs;emper congruit: & ex quatuor pendulis, quæ prolixitate <lb/>&longs;int, primum vnius præcisè pedis, &longs;ecundum quatuor, tertium <lb/>nouem, quartum &longs;edecim: peragit reuerâ, con&longs;tanterque pri<lb/>mum vibrationes quatuor, eodem tempore, quo &longs;ecundum <lb/>peragit treis, & tertium duas, & quartum vnam: &longs;i modò <lb/>quidem <expan abbr="ead&etilde;">eadem</expan> &longs;emper longitudine per&longs;euerent.<emph.end type="italics"/> A p. </s>

<s>De Experimentis circa ictum, impetumve gra<lb/>uium cadentium, ad explorandum, impetu&longs;<lb/>ne, vt &longs;patium incre&longs;cat. </s>

<s><emph type="italics"/>Meritò fuere vno plura requi&longs;ita Experimenta, vbi <lb/>fuit iactatum peragi ea po&longs;&longs;e in grauibus quibu&longs;libet; tamet&longs;i <lb/>ne in vno quidem peragere fuerit conce&longs;&longs;um. </s>

<s>Allata tria ex<lb/>perimenta qua&longs;i &longs;upparia ad &longs;uadendum non incre&longs;cere impe<lb/>tum, velocitatemve &longs;icut spatia, &longs;ed &longs;icut spatiorum radices, <lb/>attinent omninô ad rem; ac illud speciatim de Aqua ef<lb/>fluente ex va&longs;e cylindrico, quatenus &longs;umma aqua in foramen <lb/>decidens, non magis à &longs;ibi &longs;ubiecta, præeunteque impeditur, <lb/>quàm &longs;i per aërem caderet; quòd illa &longs;emper pari cum ip&longs;a <lb/>velocitate &longs;e&longs;e &longs;ubducat, anteceden&longs;que nihil officiat.<emph.end type="italics"/><lb/>A. p. </s>

<s>AD ART. XXIII. XXIV. XXV. XXVI. XXVII. <lb/>XXVIII. </s>

<s>De Experimento in Bilance facto, ac <pb/>aliud reuerâ probante, quàm velocitates e&longs;&longs;e <lb/>&longs;icut &longs;patia. </s>

<s><emph type="italics"/>Quandoquidem iactatum illud tantopere Experimen<lb/>tum fal&longs;itatis conuictum e&longs;t: mirum videri profectò potest, <lb/>quamobrum R. P. venditare pergat pro Demon&longs;tratione ra<lb/>tiocinium, quod fuerit eo Experimento duntaxat &longs;uffultum; ac <lb/>potißimùm prouocando ad vberiorem experientiam, qua con<lb/>trouer&longs;ia dirimatur; qua&longs;i verò &longs;inondum &longs;it dirempta contro<lb/>uer&longs;ia, eius Demon&longs;tratio interim cohæreat? </s>

<s>Fru&longs;trà iam &longs;ol<lb/>licitus e&longs;t de non a&longs;&longs;umendo &longs;upra æquilibrium exce&longs;&longs;u; cùm <lb/>agno&longs;cat iam quàm vanè v&longs;urpet diametrum globi pro men<lb/>&longs;ura præci&longs;a altitudinum, ex quibus totidem pondera at<lb/>tollantur. </s>

<s>Incommodum illud de globo diametri decuplò mi<lb/>noris, & decuplò citius ca&longs;uro ex eadem altitudine, obiectum <lb/>legitimè fuit, & R. P. eximere &longs;e ab illo nequicquam tenta<lb/>uit.<emph.end type="italics"/> A p. </s>

<s>AD ART. XXIX. XXX. XXXI. XXXII. XXXIII. <lb/></s>

<s>De Tempore, quo R.P. colligit parteis &longs;patij <lb/>&longs;ingulas decur&longs;um non iri. </s>

<s><emph type="italics"/>Haud abs re fuere obiecta illa de neglecto tempore in <lb/>tradenda motus æquabiliter accelerati definitione. </s>

<s>Affictum <lb/>nihil fuit R. P. inter vrgendum incommoda; quæ &longs;i variata <lb/>interdum &longs;int, in cau&longs;&longs;a fuit variatio principiorum, quibus <lb/>ille e&longs;t v&longs;us. </s>

<s>Nihil iteratò demon&longs;trat: verum aut ex fal&longs;is <lb/>concludit; aut in<emph.end type="italics"/> D<emph type="italics"/>iallellum incidit, circulum-ve, vt aiunt, <lb/>committit; aut prætereà inuoluit &longs;e multiplici contradictione. <lb/></s>

<s>Quæ&longs;tio ne que e&longs;t, neque fuit, an ostenderit (quod fuit conce&longs;<lb/>&longs;um) non po&longs;&longs;e partem spatij &longs;ecundam decurri dimidio tem-<emph.end type="italics"/><pb/><emph type="italics"/>piris, quo primam, tertiam triente, &c. </s>

<s>&longs;ed an o&longs;tenderit ad<lb/>uer&longs;us &longs;eip&longs;um; vt pote ex cuius principio, po&longs;itioneve illud <lb/>&longs;equatur. </s>

<s>Nequicquam conatur capita ab&longs;urda &longs;ibi obiecta <lb/>retorquere; qua&longs;i &longs;it perinde &longs;eu &longs;patium, &longs;eu tempus cum <lb/>velocitate conferat; & ad hominem cum argumentatur, in <lb/>limine ip&longs;o aberrat, dici vt putà id &longs;upponens, quod minimè <lb/>dicitur, & tempus cum velocitate &longs;ecus conferri, quàm con<lb/>fertur. </s>

<s>Tota gloriatio con&longs;equens nihil habet, quod inuidea<lb/>tur; & dum ait impugnationem &longs;ui ratiocinij, non po&longs;&longs;e, vt <lb/>inanem, ac vanam, inuenire plau&longs;um, ni&longs;i apud minùs peritos; <lb/>&longs;atis e&longs;t prouocare illum vt proferat vel vnicum, cui &longs;uam <lb/>&longs;ententiam per&longs;uadeat, peritum.<emph.end type="italics"/> A p. </s>

<s>ART. XXXIV. XXXV. XXXVI. XXXVII. <lb/>XXXVIII. </s>

<s>De Tempore, quo R.P. colligit <lb/>&longs;ingulas parteis decur&longs;um iri. </s>

<s><emph type="italics"/>Non alia ratione probauit R. P. velocitatem per &longs;ecun<lb/>dam partem e&longs;&longs;e duplam velocitatis per dimidium inferius pri<lb/>mæ, quàm quia &longs;patium, duplum e&longs;t: neque hanc con&longs;equutio<lb/>nem vllo modo probauit; &longs;ed ex eo &longs;olùm &longs;uppo&longs;uit, quod ve<lb/>locitates &longs;icut spatia &longs;int, quæ est iterata principij petitio: cùm <lb/>hoc ip&longs;um &longs;it, quod controuertitur, neque vllatenus inueniatur <lb/>o&longs;ten&longs;um; ni&longs;i ex fal&longs;o illo circa Bilancem experimento. </s>

<s>Ex <lb/>varijs obiectionibus vna est delecta, cui re&longs;ponderetur, propter <lb/>errorem calami, quo in immen&longs;a, importunaque literarum <lb/>farragine litera vna irrep&longs;it pro alia. </s>

<s>Beatus e&longs;t R.<emph.end type="italics"/> P. <emph type="italics"/>cui <lb/>Author e&longs;&longs;e non videatur ingre&longs;&longs;us in controuer&longs;iæ pene tralia, <lb/>quique eum æquè à dictis &longs;uis, atque à natura penitiùs inspi<lb/>ciunda arce at. </s>

<s>Tempus minutorum &longs;ex attributum primæ<emph.end type="italics"/><pb/><emph type="italics"/>parti, non ab Authore fuit delectum, &longs;ed <expan abbr="&longs;uppeditat&utilde;">&longs;uppeditatum</expan> à R. P. <lb/>qui tamet&longs;i alicubi non probet ex ijs &longs;ex minutis quatuor priori <lb/>dimidio, & duo po&longs;teriori attribui: id tamen tum ex varijs <lb/>eius principijs deducitur: tum recipit Author deducturum &longs;e <lb/>eadem, & plura incommoda, ex quacumque alia di&longs;tributione <lb/>eius numeri, aut alterius à R. P. facienda: &longs;i modò &longs;emper <lb/>velocitates habere &longs;e vt spatia &longs;upponat.<emph.end type="italics"/> A p. </s>

<s>ART. XXXIX. XL. XLI. XLII. <lb/></s>

<s>De Ratione continuò dupla, qua &longs;patia de<lb/>curri temporibus æqualibus R. P. contendit. </s>

<s><emph type="italics"/>Mirum, velle adhûc R. P. incipere acceleratum motum <lb/>à primæ partis medio, non ab ip&longs;o eius principio; & maximè <lb/>quidem, cùm aliunde velit velocitates e&longs;&longs;e vt spatia, spatiive <lb/>parteis, quarum vna &longs;it tota prima, non dimidium primæ: ac <lb/>in&longs;ignes prætereà &longs;uboriantur difficultates ex eo, quòd dum <lb/>ad obiecta de &longs;ubdiui&longs;ione prioris dimidij in alia, aliaque dimi<lb/>dia re&longs;pondet, standum ait alicubi, quòd diui&longs;io e&longs;&longs;e in Phy<lb/>&longs;icas parteis infinita non valeat, & ibi tamen standum, vbi <lb/>tot partes adhûc &longs;uper&longs;unt, vt ex ijs ratio accelerati motus <lb/>perfectè intelligatur. </s>

<s>Quippe cùm inter cætera a&longs;&longs;umpto <lb/>ca&longs;u ex Luna, Sole, aut Firmamento, & a&longs;&longs;umpta particula <lb/>prima Phy&longs;icè diuidua, in qua reperiri debeant dimidium <lb/>inferius, ac in ip&longs;o triens, quadrans, & tot fragmenta cætera, <lb/>quot &longs;unt partes ip&longs;i primæ æquales in toto illo &longs;patio, quotque <lb/>etiam di&longs;tingui poßunt in &longs;uperiore dimidio; incredibilis &longs;it <lb/>partium numerus, per quas in priore dimidio contentas opor<lb/>teat motum peragi, priu&longs;quam incipiat accelerari; & in qui<lb/>bus tamen con&longs;i&longs;tendum &longs;it, quòd diui&longs;io vlteriùs fieri in duo<emph.end type="italics"/><pb/><emph type="italics"/>dimidia non valeat, ne ratio motus accelerati non perfectè in<lb/>telligatur. </s>

<s>Quæ&longs;tio heic iterùm non e&longs;t, an velocitas per <lb/>&longs;ecundam partem &longs;it præcisè dupla velocitatis per primam: &longs;ed <lb/>an id &longs;equatur (vt & ab&longs;urda quædam alia) ex R. P. prin<lb/>cipijs. </s>

<s>Refugit R. P. prouocationem ad calculos, nec incom<lb/>moda clariùs pateant, ac illud speciatim, quod obiectum e&longs;t <lb/>ex triente, & quadrante non componi integrum: neque item <lb/>ex partibus quinta, &longs;exta, &longs;eptima, octaua. </s>

<s>Irrito cona<lb/>mine rationem duplam, vt &longs;olam congruam excu&longs;are adniti<lb/>tur, eò quòd ip&longs;a quoque &longs;eip&longs;am euertat, quoties tempora a&longs;<lb/>&longs;umuntur maiora, vel minora dato, quæ &longs;int ip&longs;a quoque inter <lb/>&longs;e æqualia: &longs;iquidem ea quoque deberent in eadem ratione <lb/>respondere spatijs: quod tamen non fit: vt in allato à R. P. <lb/>exemplo de ca&longs;u globi ex Luna mon&longs;tratur.<emph.end type="italics"/> A p. </s>

<s>AD ART. XLIII. XLIV. </s>

<s>De Tempore, <lb/>quo globum ferreum ca&longs;urum ex Luna in <lb/>Terram contendit. </s>

<s><emph type="italics"/>Nihil e&longs;&longs;e heicvidetur addendum ad ea, quæ obiecta &longs;unt<lb/>cùm R. P. fateatur non po&longs;&longs;e illam rapiditatem, quam priùs <lb/>a&longs;&longs;eruerat, in&longs;anam e&longs;&longs;e adeò, vt globus id &longs;patium minutis <lb/>non omninô duobus percurrat: tamet&longs;i lenire rem &longs;tudet, dum <lb/>naturam quidem id exigere, &longs;ed medij tamen conditionem <lb/>obstare ait.<emph.end type="italics"/> A p. </s>

<s>AD ART. XLV. XLVI. XLVII. </s>

<s>De <lb/>quodam lap&longs;u emendando circa cau&longs;&longs;am Phy<lb/>&longs;icam accelerati grauium motus. </s>

<s><emph type="italics"/>Quod R. P. in Vindicijs ad Artic. </s>

<s>XL. de Phy&longs;ica<emph.end type="italics"/><pb/><emph type="italics"/>cau&longs;&longs;a accelerationis di&longs;&longs;erüerit, docendo &longs;olam grauitatem <lb/>e&longs;&longs;e cau&longs;&longs;am initij motus, & &longs;olùm medium, putà aërem e&longs;&longs;e <lb/>cau&longs;&longs;am accelerationis, quatenus à fronte re&longs;iliens, & à tergo <lb/>claudem, graue vrget; cùm alioquin &longs;ola grauitate agente, &longs;i<lb/>bique &longs;imili manente, vt in vacuo, de&longs;cen&longs;us foret vniformis, <lb/>&longs;imili&longs;que &longs;ui per&longs;eueraturus: idcircò an&longs;a & accepta, & in <lb/>hunc locum dimi&longs;&longs;a e&longs;t adiiciendi quidpiam de Phy&longs;ica cau&longs;&longs;a. <lb/></s>

<s>Nam primùm quidem paulò fu&longs;iùs deducitur lap&longs;us indicatus <lb/>ad calcem &longs;uperioris Epistolæ: declarando videlicet, quo pro<lb/>gre&longs;&longs;u tentatum fui&longs;&longs;et in Epi&longs;tolis<emph.end type="italics"/> de Motu impre&longs;&longs;o à <lb/>motore tran&longs;lato <emph type="italics"/>cau&longs;&longs;am dicere, quamobrem grauia acce<lb/>lerentur iuxta progreßionem numerorum imparium ab vnita<lb/>te inc&oelig;ptorum; & quemadmodum talis cau&longs;&longs;a fui&longs;&longs;et agnita <lb/>tum primo momento &longs;ola attractrix Terræ vis, quæ imprime<lb/>ret &longs;ingularem ictum: tum &longs;ecundo, & reliquis tam eadem <lb/>attractrix, quàm aër à tergo &longs;uccedens, in&longs;tan&longs;que, adeò vt <lb/>quolibet momento duo qua&longs;i ictus imprimerentur: &longs;icque & <lb/>primo momento vnus acquireretur velocitatis gradus, quo &longs;u<lb/>peraretur vnum &longs;patium: &longs;equente autem quolibet &longs;uper-ad<lb/>derentur duo, e&longs;&longs;entque proinde tres, quinque, &longs;eptem, &c. <lb/></s>

<s>quibus spatia totidem con&longs;equenter &longs;uperarentur: vnde & <lb/>con&longs;entaneum foret velocitates e&longs;&longs;e, vt spatia, quæ proinde &longs;i<lb/>mul repræ&longs;entari deberent per illas triangulorum areas: quod <lb/>animaduer&longs;um e&longs;t repugnare. </s>

<s>Deinde verò o&longs;tenditur, <lb/>quamobrem cùm cau&longs;&longs;a vnica &longs;ufficiat, iuxta antè expo&longs;ita <lb/>(&longs;upponitur autem videri non e&longs;&longs;e ip&longs;am aliam, quàm ip&longs;am <lb/>vim Terræ tractricem) o&longs;tenditur, inquam, vtramque à<emph.end type="italics"/><lb/>R. P. <emph type="italics"/>aßignatam videri e&longs;&longs;e reiiciendam, quatenus medium, <lb/>putà aër, ad accelerationem nihil confert, quin-etiam potiùs<emph.end type="italics"/><pb/><emph type="italics"/>officit, nec quantum obe&longs;t, tantum iuuat, ac longè e&longs;t adeò, vt <lb/>&longs;olus accelerationis &longs;it cau&longs;&longs;a: grauitas verò, &longs;eu qualitas graui <lb/>in&longs;ita, & ab attractione di&longs;tincta, nulla e&longs;t: neque proinde po<lb/>te&longs;t motum &longs;eu in &longs;patio vacuo, &longs;eu in aëre, (vt &longs;i &longs;olus aër in <lb/>vniuer&longs;o e&longs;&longs;et) præ&longs;tare.<emph.end type="italics"/> A p 209. in 220. </s>

<s>AD ART. XLVIII. </s>

<s>De Re&longs;pon&longs;ionis <lb/>Conclu&longs;ione. </s>

<s><emph type="italics"/>Licitum fuit amicitiæ (&longs;ed &longs;eruata tamen illi reuerentiâ) <lb/>anteponere veritatem. </s>

<s>Fuit in<emph.end type="italics"/> R.P. <emph type="italics"/>vt qua&longs;cumque vellet, duce<lb/>ret lituras, aut etiam rem totam &longs;upprimi iuberet. </s>

<s>Non capitur <lb/>quamobrem cen&longs;eat &longs;e veritatem iam illu&longs;tratam, & ab er<lb/>rore vindicatam exhibere: ac &longs;peret tamen, vt ex correcto <lb/>fal&longs;o &longs;uo Experimento veritas deinceps certiùs inueniatur. </s>

<s>Ip&longs;e <lb/>fuit<emph.end type="italics"/> R.P. <emph type="italics"/>qui Authori alioquin ignotus, prouocauit prior; & <lb/>cui tamen nihil aut re&longs;pon&longs;um, aut oppo&longs;itum &longs;altem, fui&longs;&longs;et, <lb/>&longs;i is fui&longs;&longs;et creditus, qui ip&longs;a rei nouitate, quod iam ait, per<lb/>celleretur, tanquam nemine alio hactenus inuento, qui in eius <lb/>a&longs;&longs;ertionibus, ac decretis pugnam aliquam, contrarietatemque <lb/>aut inuenißet, aut obiecißet. </s>

<s>Quare & e&longs;&longs;e &longs;ecurus pote&longs;t <lb/>iri deinceps nihil inqui&longs;itum in ea, quæ &longs;e dicit habere <lb/>ob&longs;curiora, incertioraque; fore autem, vt &longs;olitum affectum, <lb/>venerationemque &longs;emper experiatur.<emph.end type="italics"/><pb/><gap desc="hr tag"/></s>

<s><emph type="center"/>EPISTOLÆ TERTIÆ.<emph.end type="center"/></s>

<s>Scribendi Occa&longs;io </s>

<s><emph type="italics"/>De hac iam dictum. </s>

<s>Notandum &longs;olùm, Epistolas<emph.end type="italics"/> de <lb/>Motu impre&longs;&longs;o à motore tran&longs;lato, <emph type="italics"/>pro quibus hac fuit <lb/>velut Apologia, ea occa&longs;ione fui&longs;&longs;e con&longs;criptas, quòd fides <lb/>ægrè habita fui&longs;&longs;et Experimentis ab Authore factis, ad&longs;truen<lb/>do illi Theoremati,<emph.end type="italics"/> Si id corpus, cui in&longs;i&longs;timus, trans<lb/>feratur, motus omneis no&longs;tros, rerumque à nobis mo<lb/>bilium, perinde fieri, apparereque, ac &longs;i illud quie&longs;ceret. <lb/><emph type="italics"/>Ea autem fuerant præ cæteris, Quòd naui velocißimè abducta, <lb/>perinde atque quie&longs;cente, proiectus &longs;ursùm lapis &longs;ecundum <lb/>mali longitudinem, tueretur &longs;emper tam a&longs;cendendo, quàm <lb/>ex&longs;cendendo eandem a malo di&longs;tantiam; & dimi&longs;&longs;us è carche<lb/>&longs;io ad pternam, ita caderet, vt neque ex parte puppis de&longs;ere<lb/>retur, neque ex parte proræ attingeretur à malo. </s>

<s>Quòd pi<lb/>la exprora in puppim, expuppi in proram proiecta, pari im<lb/>petu ferri appareret, parque &longs;patium conficeret; & neque tar<lb/>diùs perueniret ad collu&longs;orem, tamet&longs;i aufugientem, qui ad <lb/>proram: neque citiùs ad alium, tamet&longs;i occurrentem, qui ad <lb/>puppim, donec volaret per aërem. </s>

<s>Quòd è curru, aut equo <lb/>citißimè abrepto, perinde ac quie&longs;cente, proiectæ &longs;ursùm res in <lb/>ip&longs;am manum reciderent: dimi&longs;&longs;æ cadere apparerent &longs;ecun<lb/>dum perpendiculum; emi&longs;&longs;æ prorsùm, retror&longs;úmque, nec pro<lb/>piùs, nec longiùs caderent in terram. </s>

<s>Quòd dimi&longs;&longs;a pila <lb/>ab incedente, currenteve per complanatum locum, antro<gap/>m <lb/>&longs;emper procurreret; pari vi antrorsùm, retror&longs;úmque proie<lb/>cta, pariabe&longs;&longs;et, dum à motu ce&longs;&longs;aret, à proiectore di&longs;tantia; &<emph.end type="italics"/><pb/><emph type="italics"/>proiecta &longs;peciatim retrorsùm, nunc aliquantúm excurreret, <lb/>nunc ad perpendiculum caderet, nunc proiectorem etiam &longs;eque<lb/>retur; prout adactio manus retrorsúm e&longs;&longs;et velocior, æquè ve<lb/>lox, aut minùs velox, quàm corporis prorsùm. </s>

<s>Jtaque horum <lb/>aliorumque Experimentorum explicandæ caußæ de&longs;tinata fue<lb/>rat Epi&longs;tola Prior; ac fuerant ideò variæ de Motu attingendæ <lb/>difficultates. </s>

<s>Fuerat & Po&longs;terior speciatim con&longs;cripta decla<lb/>randæ inanitati rationis illius, quæ aduer&longs;us A&longs;&longs;ertores motus <lb/>Telluris peti &longs;oleret ex eo, quòd &longs;agitta &longs;ursùm euibrata è <lb/>puppi, dum nauis moueretur, non in puppim recideret, &longs;ed in <lb/>aquam à tergo puppis, quæ interim &longs;ubducta foret: ac fuerat <lb/>con&longs;equenter o&longs;ten&longs;a imbecillitas aliarum rationum complu<lb/>rium, quæ &longs;olent ij&longs;demobiici. </s>

<s>Præstita, inquam, hæc fue<lb/>rant; cùm R. P. </s>

<s>Epi&longs;tolis vi&longs;is, ea ex vtraque impugnauit, <lb/>quæ potißimùm di&longs;plicuerunt.<emph.end type="italics"/> A p. </s>

<s>Nondum ob&longs;eruatum, <lb/>qui Galileo obiicitur, Paralogi&longs;mum: &, Neu<lb/>tram duarum virium à Motore tran&longs;lato im<lb/>pre&longs;&longs;arum imminui ab alterutra. </s>

<s><emph type="italics"/>Qualem deinceps Paralogi&longs;mum R. P. detexerit, &longs;atis <lb/>est, &longs;uperque in Epi&longs;tolis &longs;uperioribus adnotatum. </s>

<s>Quod &longs;u<lb/>perest: cùm mota, v. </s>

<s>naui, lapis ex ea proiicitur &longs;ursùm; is <lb/>apparet quidem tam proiectori, quàm omnibus, qui in naui <lb/>&longs;unt, a&longs;cendere, de&longs;cenderéque &longs;ecundum perpendiculum: &longs;ed <lb/>reuerâ tamen a&longs;cendit, de&longs;cenditque obliquè (vti & apparet <lb/>quie&longs;centibus in littore) de&longs;cribit nempe lineam curuam, quam <lb/>dicunt parabolicam: cau&longs;&longs;aque e&longs;t, quia manus proiiciens vt<lb/>cumque &longs;ursùm moueri appareat, reuerâ tamen mouetur obli<lb/>què, deflexa nempe à motu nauis, qui illam, dum attollitur,<emph.end type="italics"/><pb/><emph type="italics"/>abducit vnà cum corpore ip&longs;ius proiectoris in latus, &longs;iue &longs;ecun<lb/>dum horizontem. </s>

<s>Et quoniam Author dixerat,<emph.end type="italics"/> Vim im<lb/>pellentem mobile &longs;ursùm, non modò non de&longs;trui, &longs;ed <lb/>ne vlla quidem ratione imminui à vi depellente in la<lb/>tus (<emph type="italics"/>quippe lapis ille neque minùs peruenit aliùm, quàm &longs;i <lb/>pari vi, naui quie&longs;cente, pro: iceretur à manu: vti neque mi<lb/>nùs in latus, quàm &longs;i immota manu veheretur &longs;olo motu nauis) <lb/>Idcircò R. P. i&longs;tud improbans, obiicit, quod e&longs;&longs;e apud peritos <lb/>Effatum ait,<emph.end type="italics"/> Mobile quodcumque duobus motibus in <lb/>diuer&longs;as parteis actis, tantò &longs;egniùs deferri in vnum <lb/>terminum, quantò fortiùs in alterum tendit. <emph type="italics"/>Sed cùm <lb/>hoc e&longs;&longs;e poßit verum, donec mobili iam &longs;eparato à motore &longs;u<lb/>peruenit vis, quæ ip&longs;um deflectat: fal&longs;um e&longs;t tamen, &longs;i nihil <lb/>noui à proiectore v&longs;que interueniat, in quo & vis ip&longs;ius pro<lb/>pria, & vis corporis ip&longs;um transferentis in vnam coïerint, quæ <lb/>tantùm &longs;it alterutrâ fortior, quantùm altera fortis e&longs;t; vt in <lb/>exemplo allato con&longs;tat, in quo quicquid e&longs;t motus &longs;ur&longs;um, à ma<lb/>nu est; quicquid motus prorsùm, à naui; & quod dee&longs;t virtuti <lb/>manus propriæ ad proiiciendum non minus altum &longs;ecundum li<lb/>neam curuam, quàm &longs;ecundum rectam, &longs;uppletur à vi tran&longs;<lb/>latitia nauis; vti & quod deest naui ad adigendum non mi<lb/>nus pror&longs;um &longs;ecundum curua, quàm &longs;ecundum rectam, <lb/>&longs;uppletur à vi proiectitia manus. </s>

<s>Habentur & alia de Ex<lb/>perimentis.<emph.end type="italics"/> A p. </s>

<s>Po&longs;&longs;e varias Sectas <lb/>veritatis &longs;tudio tentari: ac, Po&longs;&longs;e animalis ince&longs;<lb/>&longs;um præ &longs;altatione; & globi volutionem præ <lb/>adactione, dici naturalem. </s>

<s><emph type="italics"/>Quòd Author explicando cau&longs;&longs;as commemoratorum <expan abbr="Ex-perimentor&utilde;">Ex<lb/>perimentorum</expan>, &longs;equutus fuerit alia quædam, quàm Ari&longs;totelea,<emph.end type="italics"/><pb/><emph type="italics"/>& vulgaria principia: id R. P. reprehendit, qua&longs;i &longs;it viris <lb/>eruditis, pij&longs;que minus placiturum: verùm, &longs;alua modò maneat <lb/>pietas, nihil e&longs;t, quod vetet philo&longs;ophari liberè, nullique Sectæ <lb/>addictum e&longs;&longs;e Displicet illi con&longs;equenter dici ince&longs;&longs;um ani<lb/>malis præ &longs;altatione naturalem: &longs;ed non apparet quid &longs;it in<lb/>congruum, quatenus motus naturalis notio e&longs;t, vt sponte, aut <lb/>&longs;ine repugnantia &longs;iat; violenti, vt præter naturam, &longs;eu cum <lb/>aliqua repugnantia. </s>

<s>Displicet & globi volutionem &longs;upræ <lb/>planum dici naturalem præ adactione eiu&longs;dem per aërem: &longs;ed <lb/>con&longs;tat &longs;atis globum e&longs;&longs;e &longs;uapte natura comparatum, vt volua<lb/>tur potiùs &longs;upra planum (quod ni&longs;i aliunde deficeret, euaderet <lb/>motus vt æquabilis, &longs;ic perpetuus) quàm vt per aërem adiga<lb/>tur (per quem aliunde inæquabiliter, & motu &longs;tatim finiendo <lb/>trans fertur.) Vt prætereatur e&longs;&longs;e hæc omnia Ari&longs;toteli con&longs;ona, <lb/>quem coryphæum <expan abbr="eruditor&utilde;">eruditorum</expan> intelligit. </s>

<s>Incredibilem fore <lb/>motus corporum decidentium &longs;egnitiem, &longs;i vt <lb/>incipit, ita pergeret; &, Non &longs;olùm acceleratio<lb/>nem, &longs;ed ip&longs;um quoque initium motus e&longs;&longs;e à <lb/>principio externo. </s>

<s><emph type="italics"/>Displicet rursus<emph.end type="italics"/> R. P. <emph type="italics"/>cen&longs;eri ca&longs;um lapidis violentum <lb/>potiùs, quàm naturalem: nam quamuis accelerationem e&longs;&longs;e <lb/>violentam non deneget: ob de&longs;cen&longs;um tamen, &longs;eu &longs;implicem <lb/>motum, cui illa &longs;uperuenit, contendit e&longs;&longs;e potius dicendum ca<lb/>&longs;umlapidis naturalem. </s>

<s>Sed <expan abbr="prim&utilde;">primum</expan>, quia quicquid in hoc ca&longs;us <lb/>motu &longs;en&longs;ibile e&longs;t, ex acceleratione e&longs;t, ac ne millies quidem <lb/>mille&longs;ima eius pars ad &longs;implicem motum, de&longs;cen&longs;umve &longs;pectat: <lb/>con&longs;tat, &longs;i à potiore parte denominatio facienda &longs;it, dicendum<emph.end type="italics"/><pb/><emph type="italics"/>potius e&longs;&longs;e ca&longs;um ab acceleratione violentum, quàm à &longs;implici <lb/>motu naturalem. </s>

<s>Quàm parùm autem cen&longs;endum &longs;it, quod <lb/>ex &longs;implici motu e&longs;t, ex eo probatur, quòd &longs;i qualis incipit mo<lb/>tus quo momento primo e&longs;t adhûc ab acceleratione liber, talis <lb/>per&longs;eueraret per duarum <expan abbr="orgyiar&utilde;">orgyiarum</expan> altitudinem; ille, a&longs;&longs;umpto <lb/>pro primo momento, vno minuto ex ijs, quæ decima vocant, non<lb/>dum e&longs;&longs;et planè peractus po&longs;t annos<emph.end type="italics"/> 5322380: <emph type="italics"/>neque adeò lapis, <lb/>&longs;i occ&oelig;pi&longs;&longs;et illo motu ab v&longs;que initio Mundi cadere, perfeci&longs;&longs;et <lb/>iam &longs;eptimam vnam digiti partem. </s>

<s>Deinde, cùm illud vio<lb/>lentum dicatur, cuius principium extra e&longs;t; etiam de&longs;cen&longs;us, &longs;eu <lb/>&longs;implex motus e&longs;&longs;e comprobatur à principio externo, nempe à <lb/>virtute attractrice Terræ (credebatur tuncpo&longs;&longs;e quoque aër à <lb/>tergo impellere) tum quia lapis &longs;eu intra vacuum (vbi nihil <lb/>cum Mundo, Terráque adeò communicaret, ac perinde illi fo<lb/>ret, &longs;eu e&longs;&longs;et, &longs;eu non e&longs;&longs;et Mundus) &longs;euintra aërem infinitum <lb/>(&longs;i &longs;olus præter ip&longs;um foret) talem motum nullum haberet: <lb/>tum quia quæ res &longs;unt inten&longs;ionis capaces, à qua cau&longs;&longs;a habent <lb/>gradus reliquos, ab ea nanci&longs;cuntur & primum; atque adeò, <lb/>vti dum calefit aqua, non cæteri gradus ab externo &longs;unt, pri<lb/>mus ab interno principio, &longs;ed omnes ab externo &longs;unt: ita dum <lb/>lapis deorsùm mouetur, non cæteræ motus partes ab externa <lb/>cau&longs;&longs;a, & prima ab interna &longs;unt; verùm &longs;unt omnes ab ex<lb/>terna.<emph.end type="italics"/> A p. </s>

<s>Terram grauia <lb/>attrahere; &, Quid illi contingeret, &longs;i ver&longs;us <lb/>Lunam dimoueretur? </s>

<s>Quid lapidi, &longs;i intra for<lb/>nicem ad centrum Terræ con&longs;titucretur? </s>

<s><emph type="italics"/>Cùm attrahi grauia à Terra videantur, ob cau&longs;&longs;am iam <lb/>expo&longs;itam: Ad illud, quod quærit R. P. quid ip&longs;i Terræ con-<emph.end type="italics"/><pb/><emph type="italics"/>tingeret, &longs;i ver&longs;us Lunam dimoueretur? </s>

<s>Dicitur e&longs;&longs;e probabi<lb/>le, fore, vt vbicumque Terra con&longs;titueretur, illeic quie&longs;ceret<gap/><lb/>eo modo, quo corpus eiu&longs;ce materiæ, vt aquæ &longs;ub pari mole <lb/>æquiponderet, vbicumque in imo, in &longs;ummo, in medio, aut vbi<lb/>uis intra aquam &longs;tatuatur, con&longs;i&longs;tit. </s>

<s>Nimirùm, quòd Terra <lb/>&longs;ecundum &longs;i totam neque grauis &longs;it, neque leuis; & talis affe<lb/>ctio partium propria &longs;it, prout à tota di&longs;trahuntur: quódque in <lb/>Mundo spherico ex&longs;i&longs;tente, medium quidem, & extremum <lb/>&longs;it, non item infimum, & &longs;ummum; ac ta is conditio &longs;it <lb/>Terræ, globorumque Mundi cæterorum propria, propter <lb/>eandem partium di&longs;tractionem, & retractionem, quæ &longs;igillatim <lb/>cum speciali cuiu&longs;que centro comparatur. </s>

<s>Non probatur etiam <lb/>aliunde Terram e&longs;&longs;e in Mundi medio; cùm etiam oppo&longs;itum <lb/>arguant excentrici &longs;iderum motus: neque veri&longs;imile e&longs;t, &longs;i <lb/>Terra abduceretur in verticem Antipodum, vbi &longs;uper<lb/>ficies, cui in&longs;i&longs;timus, excederet punctum, in quo fui&longs;&longs;et centrum, <lb/>nos ibi hæ&longs;uros: aut abreptos vlteriùs, eò auolaturos, &longs;eu po<lb/>tiùs ca&longs;uros. </s>

<s>Ad aliud, quod quærit, quid eueniret lapidi, &longs;i <lb/>intra cauernam in meditullio Terræ excauatam, oppletamque <lb/>aqua, aut aëre constitueretur? </s>

<s>Dicitur probabile e&longs;&longs;e, &longs;i Terra <lb/>quidem qua&longs;i magnes &longs;it, qui &longs;uis qua&longs;i radijs emißis attrahat <lb/>terrena: euenturum, vt lapis ineam cauernæ partem feratur, è <lb/>qua radij plures, confertiore&longs;que affluxerint; &, &longs;i &longs;upponan<lb/>tur ex æquo vndequàque affluere, fore, vtin medio &longs;u&longs;pen&longs;us <lb/><gap/>eneatur. </s>

<s>Vnde &, quod rogat, cur lapis in puteum dimi&longs;&longs;us <lb/>fundum petat, non latera? </s>

<s>Cau&longs;&longs;a e&longs;t in promptu, quòd plu<lb/>res, den&longs;iore&longs;que radij exparte fundi, ad quam e&longs;t tota Terræ <lb/>moles, adueniant, quàm ex parte vlla laterum aduenire <lb/>poßint.<emph.end type="italics"/> A p 247. in 254. </s><pb/>

<s>ART. XV. XVI. XVII. XVIII. XIX. XX. <lb/></s>

<s>Et Magnetem ferrum, & Terram grauia trahe<lb/>reper in&longs;en&longs;ilia organula: &, Cur attractio pro<lb/>pe Terram non &longs;it &longs;en&longs;ibilior, quàm procùl. </s>

<s><emph type="italics"/>Non ridet Author in &longs;inu, vt R. P. ait, dum Magne<lb/>tem non trabere &longs;ine organulis corporeis contendit: neque non <lb/>agit &longs;eriò, dum hamulos, catenula&longs;que, quatenus patitur imbe<lb/>cillitas, fingit. </s>

<s>Dum ait R.<emph.end type="italics"/> P. <emph type="italics"/>non alio modo tractionem fie<lb/>ri, quàm quòd Magnes, & ferrum &longs;ponte naturæ incitata in <lb/>mutuos amplexus accurrant; id eleganter quidem, &longs;ed non ita <lb/>vt res vocibus &longs;ubiecta intelligi poßit: quomodo &longs;cilicet vtrum<lb/>uis, ac &longs;peciatim ferrum inanime, ac inarticulatum, incitet <lb/>&longs;eip&longs;um, & nullare à Magnete emi&longs;&longs;a, diuinet tamen, quando <lb/>e&longs;t propè, & metiatur vireis, ac &longs;patium, è quo ver&longs;us ip&longs;um <lb/>in&longs;iliat. </s>

<s>Neque verò dicere pote&longs;t emitti à Magnete quali<lb/>litatem quandam, quæ &longs;it merum accidens: cùm exinde diffi<lb/>cultatum inextricabilium &longs;eges &longs;ubna&longs;catur. </s>

<s>Quod cau&longs;&longs;atur <lb/><expan abbr="aut&etilde;">autem</expan> organula in&longs;en&longs;ilia dicta: con&longs;tat &longs;atis ea &longs;ic dici, quòd nec <lb/>videri oculis, nec palpari manibus poßint. </s>

<s>Iniuriâ traducit Au<lb/>thorem R. P. qua&longs;i proptereà neget po&longs;&longs;e <expan abbr="De&utilde;">Deum</expan> Magneti talem <lb/>qualitatem, qualem de&longs;cribit imprimere: <expan abbr="c&utilde;">cum</expan> quæ&longs;tio non &longs;it, an <lb/>à Deo &longs;it, quicquid Magneti <expan abbr="impreß&utilde;">impreßum</expan> e&longs;t: &longs;ed quale &longs;it, quod est <lb/>impre&longs;&longs;um. </s>

<s>Quod obiicit verò, vt ferrum à Magnete fortiùs è <lb/>propinquo, quàm, è longinquo trahitur, non &longs;ic ob&longs;eruari <lb/>trahi à terra lapidem, quatenus magis non ponderat, nec ve<lb/>locius initio cadit ad ba&longs;in turris, quàm ad fastigium: Patet <lb/>cau&longs;&longs;am e&longs;&longs;e, non quòd di&longs;crimen aliquod non &longs;it: &longs;ed quòd <lb/>euadere &longs;en&longs;ibile non poßit, quou&longs;que lapis ponderetur, inci<lb/>piatve cadere ex tanta altitudine, quæ non minorem habeat<emph.end type="italics"/><pb/><emph type="italics"/>rationem ad molem Telluris, quàm intercapedo, qua ferrum <lb/>trahitur, ad molem Magnetis.<emph.end type="italics"/> A p. </s>

<s>ART. XXI. XXII. XXIII. XXIV. XXV. <lb/></s>

<s>Non e&longs;&longs;e Atomorum minùs, quàm Ari&longs;toteleæ <lb/>Materiæ tolerabilem in Religione po&longs;itionem. </s>

<s><emph type="italics"/>Haud iure traducit R. P. ea, quæ de ortu, interitu, alte<lb/>ratione, calore, frigore, & cæteris rebus naturalibus iuxtæ <lb/>Atomorum &longs;uppo&longs;itionem dicta &longs;unt, ad &longs;tatum &longs;upernatura<lb/>lem: ac præ&longs;ertim cùm Atomi nihil aliud fint, quàm prima <lb/>Materies, quæ &longs;i prout a&longs;&longs;erta e&longs;t ab Ari&longs;totele, toleretur, a&longs;<lb/>&longs;umendo &longs;olùm, quòd à Deo creata &longs;it: tolerari &longs;anè poßint <lb/>Atomi, prout a&longs;&longs;eruntur non modò ab<emph.end type="italics"/> E<emph type="italics"/>picuro, aut Democrito, <lb/>&longs;ed etiam ab alijs, ac nominatim à Platone (qui cum illi&longs;-ne <lb/>iure ex&longs;ulet, vt R. P. loquitur, à Regno Philo&longs;ophico, con&longs;u<lb/>lendi Patres) a&longs;&longs;umendo &longs;olummodò, fui&longs;&longs;e illas à Deo creatas. <lb/></s>

<s>Satis e&longs;&longs;e vult R. P. &longs;i dicamus halitus calidos, &c. </s>

<s>à corpori<lb/>bus exhalari: at non illi inepti, qui requirunt prætereà ex qui<lb/>bu&longs; nam corpu&longs;culis texantur i&longs;ti halitus, vt modum actionis <lb/>ip&longs;orum condi&longs;cant: quod & Plato po&longs;t alios fecit, & Demo<lb/>critus speciatim &longs;ic e&longs;t ex&longs;equutus, vt ideò Platoni ab Ari&longs;totele <lb/>præ&longs;eratur, & à Cicerone, Plutarcho, alij&longs;que mirè commen<lb/>detur. </s>

<s>Exclamat R. P. conclamatum fore de Formis &longs;ub<lb/>&longs;tantialibus, &longs;iortus, & interitus nihil aliud &longs;int, quàm locales <lb/>quædam Atomorum motiones: exclamat, inquam, vt videtur, <lb/>ob Rationalem animam: cùm tamen, vt generali Effato de for<lb/>mis è materia educibilibus adhibetur exceptio Rationalis ani<lb/>mæ, &longs;ic adhiberi poßit Effato de accidentalibus: ac ip&longs;a Anima <lb/>aliunde &longs;it propriè futura &longs;ubstantia, quatenus &longs;ub&longs;i&longs;tit per<emph.end type="italics"/><pb/><emph type="italics"/>&longs;e, &longs;ecus ac formæ cæteræ, quæ vnde, aut quomodo habeant <lb/>&longs;uam &longs;ub&longs;tantialem entitatem distinctam à materia, dicere <lb/>communis &longs;ententia non poßit. </s>

<s>Quærit & quò &longs;int abitura <lb/>&longs;anctiora Religionis no&longs;træ my&longs;teria: idque, vt videtur, ob <lb/>mysterium augu&longs;tißimum Tran&longs;ub&longs;tantiationis: cùm tamen, <lb/>vt iuxta Ari&longs;toielea &longs;ententiam ex&longs;i&longs;tentia &longs;ub&longs;tantiæ &longs;ine <lb/>accidentibus, aut accidentium &longs;ine &longs;ub&longs;tantia defenditur vir<lb/>tute naturæ impoßibilis, &longs;ed poßibilis virtute diuina: eodem <lb/>modo, ac ij&longs;dem verbis iuxta Democriticam defendatur.<emph.end type="italics"/> A p. </s>

<s>ART. XXVI. XXVII. XXVIII. </s>

<s>Actum <lb/>e&longs;&longs;e de Motu Teriæ, proponendo, non a&longs;&longs;e<lb/>rendo; &, Ferant ne magis Sacræ literæ Ter<lb/>ram in centro, quàm extra centrum circum<lb/>uolui. </s>

<s>C<emph type="italics"/>ùm ex di&longs;putatis in Priore<emph.end type="italics"/> de Motu impre&longs;&longs;o à motore <lb/>tran&longs;lato <emph type="italics"/>Epi&longs;tola, deduci po&longs;&longs;et <expan abbr="null&utilde;">nullum</expan> e&longs;&longs;e, quod aduer&longs;us mo<lb/>tum Telluris petitur vulgò argumentum ex &longs;agitta &longs;ursùm è <lb/>naui emi&longs;&longs;a, neque innauim recidente; nullum, inquam, prout <lb/>&longs;icuti mota naui, omnes motus &longs;iue nautarum, &longs;iue rerum, <lb/>quas ip&longs;i mouent, perinde fiunt, apparentque, ac &longs;i nauis quie&longs;<lb/>ceret, mi&longs;&longs;aque adeò &longs;ursùm &longs;agitta in <expan abbr="eand&etilde;">eandem</expan> nauis, è qua fuerit <lb/>emi&longs;&longs;a, partem recidit: ita &longs;i Terram ver&longs;us ortum moueri <lb/>&longs;uppo&longs;uerimus, omnes motus no&longs;tri, rerumque à nobis mobi<lb/>lium, perinde fient, apparebuntque, ae &longs;i Terra quie&longs;ceret. <lb/></s>

<s>lapisque adeò &longs;ursùm proiectus, in eundem Terræ recidet lo<lb/>cum, è quo proiectus fuerit;<emph.end type="italics"/> S<emph type="italics"/>cilicet<emph.end type="italics"/> T<emph type="italics"/>erra transferens proiecto<lb/>rem, eiu&longs;que manum, &longs;uperaddit, intercedente manu, tantum <lb/>impetus lapidi, quantum oportet, vt &longs;uperet mundanum<emph.end type="italics"/><pb/><emph type="italics"/>&longs;patium æquale illi, quod ea pars Terræ, è qua facta fuerit <lb/>proiectio, interim peruadit; eodem modo, quo nauis transferens <lb/>&longs;uperaddit &longs;agittæ, intercedente arcu, tantum roboris, quantum <lb/>e&longs;t nece&longs;&longs;e, vt &longs;uperet aëreum &longs;patium æquale illi, quod peruadit <lb/>interim eanauis pars, è qua facta emißio: Cùm, inquam, de<lb/>duci id po&longs;&longs;et; Author reipsâ ita deduxit po&longs;teriore Epi&longs;tola, vt <lb/>admonuerit quærendam ergo, ad impugnandum Terræ motum, <lb/>rationem veri&longs;imiliorem. </s>

<s>Et quia poterat responderi alias <lb/>iam multas e&longs;&longs;e inuentas: ideò illas, e&longs;&longs;e o&longs;tendit magna ex parte <lb/>haud magis firmas. </s>

<s>Iam R. P. hoc non fert, ac &longs;uperiore <lb/>ratione euer&longs;a, indignatur fui&longs;&longs;e cæteras convul&longs;as: qua&longs;i aut <lb/>eas expendere præoccupando non licuerit, aut &longs;it, cur magis, <lb/>quàm &longs;uperior vocari in examen non poßint, nec debeant. </s>

<s>Et <lb/>traducit quidem Authorem R. P. qua&longs;i a&longs;&longs;eruerit moueri Ter<lb/>ram non diurna modò reuolutione circa axem proprium, verùm <lb/>etiam annuo motu circa Solem: vnde & ait tolerabilius fui&longs;&longs;e, <lb/>etiam per &longs;acras Literas, &longs;i a&longs;&longs;ertus fui&longs;&longs;et diurnus dumtaxat. <lb/></s>

<s>Attamen, neque a&longs;&longs;erendo, &longs;ed proponendo &longs;olummodò de mo<lb/>tu Terræ actum e&longs;t; neque ea loca Scripturæ &longs;acræ, quæ aduer<lb/>&longs;us motum Terræ obiiciuntur, comperiuntur minùs aduer<lb/>&longs;us diurnum, quàm aduer&longs;us annuum e&longs;&longs;e comparata; neque <lb/>non præclare addit R. P. debere no&longs;tram Philo&longs;ophiam fidei <lb/>Chri&longs;tianæ e&longs;&longs;e con&longs;onam; &longs;ed &longs;upere&longs;t no&longs;&longs;e quid &longs;it di&longs;&longs;onum; <lb/>cùm non statim quicquid videtur repugnare Literis &longs;acris id<lb/>circò reuerà repugnat, vt rectè o&longs;tendit D. </s>

<s>Augu&longs;tinus ad<lb/>uer&longs;us eos, qui dicunt cælum Sphæricum, cùm Scriptura dicat<emph.end type="italics"/><lb/>exten&longs;um, vt pellem. </s>

<s>De Con<lb/>&longs;equutionibus ex Terra Planetis inter&longs;ita <pb/>ductis, déque ignorata Copernicanæ opinionis <lb/>improbatione. </s>

<s>O<emph type="italics"/>biicit R. P. </s>

<s>Si moueri Terram inter Planetas per<lb/>&longs;ua&longs;um &longs;it, creditum quoque iri ip&longs;am e&longs;&longs;e<emph.end type="italics"/> P<emph type="italics"/>lanetam; & e&longs;&longs;e in <lb/>alijs<emph.end type="italics"/> P<emph type="italics"/>lanetis, Stelli&longs;que &longs;uosincolas; ac iri <expan abbr="vocat&utilde;">vocatum</expan> in &longs;u&longs;picio<lb/>nem<emph.end type="italics"/> G<emph type="italics"/>ene&longs;in,<emph.end type="italics"/> I<emph type="italics"/>ncarnationem, Euangelium, fidem<emph.end type="italics"/> C<emph type="italics"/>hri&longs;tia<lb/>nam, quæ docet A&longs;tra non ad hominum, aliarumve rerum ha<lb/>bitationem e&longs;&longs;e facta, &longs;ed vt illuminent, f&oelig;cundentque Terram. <lb/></s>

<s>Verùm legitimas non e&longs;&longs;e huiu&longs;modi con&longs;equutiones, declara<lb/>tur, Tum ex eo, quòd o&longs;tenditur pari ratione deduci ea&longs;dem ex <lb/>placitis alijs, quæ à viris pijs, eruditi&longs;que defenduntur (cuiu&longs;<lb/>modi &longs;unt illa de rotunditate Terræ; de Luna eclip&longs;in patiente <lb/>ob Terram, vt Terrapatitur ob Lunam; déque ip&longs;ius &longs;uperfi<lb/>cie montibus, & conuallibus, terrenæ in&longs;tar interstincta: de <lb/>Terræ exilitate comparatè ad Stellas; aéque Luna adhûc lon<lb/>gè exiliore, quæ præ illis tamen habetur in magnis luminari<lb/>bus, atque ita de cæteris) Tum ex eò, quòd o&longs;tenditur, quàm <lb/>malè cohæreant cum Antecedente, ex quo deducuntur. </s>

<s>Quod <lb/>autem<emph.end type="italics"/> R. P. <emph type="italics"/>opinionem de motu Terræ fui&longs;&longs;e Eccle&longs;iæ &longs;uspe<lb/>ctam ait à<emph.end type="italics"/> C<emph type="italics"/>opernici v&longs;que tempore; id Authori e&longs;t incomper<lb/><gap/>m, & quod iam demùm damnatam ait decreto Ponti&longs;icio, <lb/>profitetur Author &longs;e vel &longs;ola fama, ac non expectata promul<lb/>gatione legitima, ad id complectendum induci.<emph.end type="italics"/> A p. </s>

<s>ART. XXXII. XXXIII. XXXIV. </s>

<s>Sit<lb/>ne ab&longs;urdum reputare Orbem magnum (&longs;eu <lb/>c&oelig;lum Solis) e&longs;&longs;e qua&longs;i punctum comparatum <lb/>ad Firmamentum; & Solem qua&longs;i vnam Fixa-<pb/>rum, Fixas qua&longs;i Soleis totidem habere. </s>

<s><emph type="italics"/>Si Terra moueatur circa<emph.end type="italics"/> S<emph type="italics"/>olem, tantum de&longs;cribet circulum, <lb/>quantum Sol motus circa Terram; atque adeò quantum cælum <lb/>Solis e&longs;t, tantum erit & cælum<emph.end type="italics"/> T<emph type="italics"/>erræ, quod dieunt potiùs<emph.end type="italics"/> O<emph type="italics"/>r<lb/>bem magnum.<emph.end type="italics"/> I<emph type="italics"/>taque R. P. pro ab&longs;urdo habet, quòd<emph.end type="italics"/> C<emph type="italics"/>oper<lb/>nicani a&longs;&longs;umunt tam immanem e&longs;&longs;e Fixarum à nobis di&longs;tan<lb/>tiam, vt &longs;i<emph.end type="italics"/> O<emph type="italics"/>rbis magnus fingatur in earum regionem tran&longs;la<lb/>tus, nobis heic remanentibus, &longs;it appariturus nobis qua&longs;i pun<lb/>ctum: nimirùm ex hoc &longs;equitur,<emph.end type="italics"/> S<emph type="italics"/>tellas, quæ nobis &longs;unt qua<lb/>&longs;i puncta, fore hoc orbe non minores. </s>

<s>Ac Author quidem <lb/>habet diuer&longs;a, quod Stellæ &longs;unt, & quod apparent, vt dicendum <lb/>illicò e&longs;t: interim autem illi re&longs;pondent, cùm ea &longs;it Fixarum <lb/>di&longs;tantia, vt nulla ob&longs;eruatio &longs;it, qua definire illam liceat, & <lb/>ab omnibus merègratis, próque lubitu maior, aut minor a&longs;&longs;u<lb/>matur (nemine putà aliam rationem, quàm propriam &longs;iue opi<lb/>nionem, &longs;iue voluntatem habente) ideò tam po&longs;&longs;e &longs;e maiorem, <lb/>quàm alios minorem eam a&longs;&longs;umere: imò & tantò magis, quantò <lb/>exinde fit commendatior tum concinnitas, tum maiestas operum <lb/>Dei. </s>

<s>Quod ve<gap/>ò R. P. ab&longs;urdum habet cen&longs;eri Solem, qua&longs;i <lb/>vnam quampiam Fixarum, & Fixas e&longs;&longs;e qua&longs;i totidem<emph.end type="italics"/> S<emph type="italics"/>oleis: <lb/>iubent illi attendere, veliuxta ip&longs;am communem &longs;ententiam <lb/>(quæ tam propè admouet Fixas) &longs;i Sol recedat, quantum Fixæ, <lb/>Fixæ accedant, quantum<emph.end type="italics"/> S<emph type="italics"/>ol, fore vt<emph.end type="italics"/> S<emph type="italics"/>ol, qua&longs;i vna Fixarum, <lb/>& vna Fixarum, qua&longs;i<emph.end type="italics"/> S<emph type="italics"/>ol appareat.<emph.end type="italics"/> A p 288. in 293. </s>

<s>ART. XXXIV. XXXV. XXXVI. XXXVII. <lb/></s>

<s>Po&longs;&longs;e Solem è Fixis non minorem, quàm Or<lb/>bem magnum apparere: & veros omnium Stel<lb/>larum di&longs;cos in vnum compo&longs;itos vix apparen<lb/>ti di&longs;co vnius mediocris Stellæ exæquatum iri. </s><pb/>

<s><emph type="italics"/>Vtin lucernæ flammula inter nocturnas tenebras procùl <lb/>vi&longs;a di&longs;tinguere licet di&longs;cum apparentem à vero; cùm ille po&longs;<lb/>&longs;it e&longs;&longs;e pedalis, i&longs;te (hoc e&longs;t flammulæ facies &longs;ecundum diame<lb/>trum tran&longs;uer&longs;am) &longs;emidigitali non maior; ita in<emph.end type="italics"/> S<emph type="italics"/>tellis, quæ <lb/>non videntur, ni&longs;i per tenebras nocturnas, di&longs;tinguendi haud<lb/>dubiè &longs;unt di&longs;ci apparentes à veris. </s>

<s>Itaque, &longs;i apparentes qui<lb/>dem<emph.end type="italics"/> S<emph type="italics"/>tellarum<emph.end type="italics"/> 1022. <emph type="italics"/>di&longs;ci in vnum quemdam compingerentur, <lb/>is triplò maior euaderet, quàm<emph.end type="italics"/> S<emph type="italics"/>olaris vulgò appareat.<emph.end type="italics"/> S<emph type="italics"/>in au<lb/>tem pari modo in vnum di&longs;culi veri coaptarentur, is non maior <lb/>euaderet, quàm vnius<emph.end type="italics"/> S<emph type="italics"/>iellæ magnitudinis quartæ di&longs;cus. </s>

<s>Et <lb/>accepto harum<emph.end type="italics"/> S<emph type="italics"/>tellarum dimidio; qua&longs;i non ampliùs (licet re<lb/>uerâ ampliùs) &longs;upra horizontem appareat; di&longs;ci quidem appa<lb/>rentes conficerent di&longs;cum ad<emph.end type="italics"/> S<emph type="italics"/>olarem, &longs;e&longs;quialterum; at veri <lb/>non <expan abbr="maior&etilde;">maiorem</expan> eo, quo apparet vnica magnitudinis quintæ<emph.end type="italics"/> S<emph type="italics"/>tella. <lb/></s>

<s>Ex quo efficitur, vt mirum non &longs;it, fi<emph.end type="italics"/> S<emph type="italics"/>tellæ tam parùm per <lb/><expan abbr="noct&etilde;">noctem</expan> collu&longs;trent, cùm illu&longs;trent per veros, & non per <expan abbr="appar&etilde;teis">apparenteis</expan> <lb/>di&longs;cos. </s>

<s>Heinc autem responderi pote&longs;t ad id, quod R.<emph.end type="italics"/> P. <emph type="italics"/>obii<lb/>cit de<emph.end type="italics"/> S<emph type="italics"/>ole è Fixis, aut heinc inter Fixas per immen&longs;am illam <lb/>di&longs;tantiam spectato; qua&longs;i nimirùm con&longs;titutus in ip&longs;o<emph.end type="italics"/> O<emph type="italics"/>rbis <lb/>magni centro, aut qua&longs;i centrum eius ex&longs;i&longs;tens, non poßit tantus <lb/>apparere, quantus ip&longs;emet<emph.end type="italics"/> O<emph type="italics"/>rbis e&longs;t.<emph.end type="italics"/> S<emph type="italics"/>cilicet exinde intelligitur, <lb/>futurum, vt<emph.end type="italics"/> S<emph type="italics"/>ole, qua&longs;i<emph.end type="italics"/> S<emph type="italics"/>tellula facto, tamet&longs;i verus illius di&longs;cus <lb/>foret exilißimus, apparens tamen tantus e&longs;&longs;et, qui totum ip&longs;um<emph.end type="italics"/><lb/>O<emph type="italics"/>rbem magnum, aut etiam ampliùs, qua&longs;i compleret: quod de<lb/>claratur pleniùs exemplo flammulæ per noctem conspectæ.<emph.end type="italics"/><lb/>A p. </s>

<s>ART. XXXVIII. XXXIX. </s>

<s>Hùc accom<lb/>modari non potui&longs;&longs;e cau&longs;&longs;am, quæ redditur <lb/>vulgò, quare <expan abbr="flãmæ">flammæ</expan> noctu maiores appareant. </s><pb/>

<s><emph type="italics"/>Quod vulgò dicunt <expan abbr="a&etilde;rem">aerrem</expan>, qui proximè circumftat flam<lb/>mam, ita per parteis halituo&longs;as è flamma procedenteis vehe<lb/>menter illuminari, vt ab oculo computetur in vnam flammam <lb/>continuam: id tum repugnat (quatenus & nullum inter flam<lb/>mam veram, &longs;puriamque apparet di&longs;crimen; &, &longs;ivera flam<lb/>ma occultetur &longs;ola, nulla apparet &longs;puria; &, &longs;i verâ flammâ <lb/>præter foramen visâ, aër occultetur, &longs;puria nibilominùs appa<lb/>ret) tum aliunde accommodari nec Lunæ potest, nec ip&longs;is<emph.end type="italics"/> S<emph type="italics"/>tel<lb/>lis, quarum &longs;pecies noctu magnoperè incre&longs;cit. </s>

<s>Quamobrem <lb/>fuit longè commodiùs repetere cau&longs;&longs;am ex affectione oculi, pu<lb/>pillæ nempe dilatatione, & impreßione retinæ facta, donec ocu<lb/>lus in tenebris degit. </s>

<s>Quippe cau&longs;&longs;a hæc non no&longs;tris modò flam<lb/>mis, & tam Lunæ, quàm<emph.end type="italics"/> S<emph type="italics"/>tellis congruit; &longs;ed congruet etiam <lb/>ip&longs;i<emph.end type="italics"/> S<emph type="italics"/>oli, &longs;i in ip&longs;am Fixarum regionem &longs;upponatur tran&longs;la<lb/>tus. </s>

<s>Videlicet tunc paradoxum non erit, videri noctu<emph.end type="italics"/> S<emph type="italics"/>olem, <lb/>&longs;eu oculum videntem<emph.end type="italics"/> S<emph type="italics"/>olem ver&longs;ari in tenebris;<emph.end type="italics"/> S<emph type="italics"/>ole, vt putá, <lb/>facto, conspectóque qua&longs;i vna quapiam<emph.end type="italics"/> S<emph type="italics"/>tellarum fixarum.<emph.end type="italics"/><lb/>A p. </s>

<s>Qua mente, & qua<lb/>tenus ex motu Terræ æ&longs;tus Maris deductus; &, <lb/>Po&longs;&longs;e exinde explicari varietates, quæ tam per <lb/>Æquinoctia, & Sol&longs;titia, quàm per Nouilunia, <lb/>& Plenilunia contingunt. </s>

<s><emph type="italics"/>Vt de motu Terræ e&longs;t actum proponendo, non a&longs;&longs;erendo: &longs;ic <lb/>& de ip&longs;o Maris æ&longs;tu, quatenus e&longs;t vi&longs;us cum hac motus Ter<lb/>ræ hypothe&longs;i congruere; maximè verò quatenus aqua bis die<lb/>tim fluit, ac refluit, vt bis contingit in motu Terræ inæqualitas, <lb/>propter commi&longs;tionem diurni, & annui, respectu partis eiu&longs;<lb/>dem Terræ, qua, vt va&longs;e, contenta aqua, dum inæquali ductu<emph.end type="italics"/><pb/><emph type="italics"/>mouetur, non pote&longs;t non fluere, ae refluere. </s>

<s>Quòd porrò &longs;icut <lb/>Iupiter &longs;uos &longs;atellites &longs;ibi circumducens, dum interim vnà cum <lb/>ip&longs;is motu duodecenni transfertur per<emph.end type="italics"/> Z<emph type="italics"/>odiacum, cen&longs;etur e&longs;&longs;e <lb/>vnà cum ip&longs;is totale quodam mobile; ita Terra Lunam &longs;ibi <lb/>circumducens, dum interim vnà cum ip&longs;a transfertur motu an<lb/>nuo per Zodiacum, vnum aliquod mobile totale cum ip&longs;a cen<lb/>&longs;eatur:<emph.end type="italics"/> I<emph type="italics"/>deò, &longs;i aliunde &longs;upponatur<emph.end type="italics"/> S<emph type="italics"/>ol, dum &longs;ibi circumuoluitur, <lb/>emittere quo&longs;dam veluti magneticos radios, quibus<emph.end type="italics"/> P<emph type="italics"/>lanetas &longs;i<lb/>bi circumducat, ac &longs;peciatim hoc mobile (Terram videlicet cum <lb/>Luna) Efficietur, vt quia hoc mobile pendebit à<emph.end type="italics"/> S<emph type="italics"/>ole per <expan abbr="radi&utilde;">radium</expan>, <lb/>veluti plumbum à clauo per filum; efficietur, inquam, vt, Quem<lb/>admodum plumbum &longs;egniùs vibratur, &longs;i infra appendatur <lb/><expan abbr="plumbul&utilde;">plumbulum</expan>, quo longius pen&longs;ile euadat; aut ocyùs, &longs;i &longs;upra illige<lb/>tur <expan abbr="plumbul&utilde;">plumbulum</expan>, à quo appetente redire celeriùs, reducatur citiùs: <lb/>Jta Terra per<emph.end type="italics"/> P<emph type="italics"/>lenilunium moueatur aliquantò pigriùs, quòd <lb/>tunc propter Lunam veluti infernè appen&longs;am prolixius euadat <lb/>qua&longs;i pen&longs;ile; & per Nouilunium velociùs, quòd tunc Luna ve<lb/>luti &longs;upernè impendens acceleret nonnihil motum. </s>

<s>Quare & <lb/>exinde &longs;uperuenit quædam tam in<emph.end type="italics"/> P<emph type="italics"/>lenilumo, quàm in Noui<lb/>lunio inæqualitas, ob <expan abbr="quã">quam</expan> tunc mare fluat, ac refluat, quàm per <lb/>quadraturas æ&longs;tuo&longs;iùs. </s>

<s>Quòd autem prætereà hi fluxus, re<lb/>fluxu&longs;que intendantur ip&longs;is Sol&longs;titiorum,<emph.end type="italics"/> Æ<emph type="italics"/>quinoctiorumque <lb/>temporibus; cau&longs;&longs;a e&longs;&longs;e pote&longs;t &longs;uperueniens tertia inæqualitas, <lb/>ob prolixiores, breuiore&longs;que diurni motus arcus (parallelos &longs;em<lb/>per æquatori acceptos) per Zodiacum; atque ita quidem, vt cùm <lb/>in<emph.end type="italics"/> Æ<emph type="italics"/>quinoctiis motus diurnus per ho&longs;ce arcus &longs;it maximè ad<lb/>uer&longs;us motui annuo &longs;ecundum<emph.end type="italics"/> Z<emph type="italics"/>odiacum, efficiatur aliunde, <lb/>vt æstus &longs;int per<emph.end type="italics"/> Æ<emph type="italics"/>quinectia, quam per<emph.end type="italics"/> S<emph type="italics"/>ol&longs;titia vebementiores.<emph.end type="italics"/><lb/>A p. </s>

<s><emph type="center"/>ARTICVL. XLIII. XLIV. XLV.<emph.end type="center"/></s>

<s>Po&longs;&longs;e & varietates alias ad locorum &longs;itus; & <lb/>acce&longs;&longs;us retardationem, quæ dietim fit, ad mo<lb/>tum Lunæ men&longs;truum, quatenus e&longs;t idem cum <lb/>diurno Telluris, referri. </s>

<s><emph type="italics"/>Quæ varietas fluxus in fluminum ripis inæquabilibus ob<lb/>&longs;eruatur, eadem affluxus, & refluxus in litoribus Maris de<lb/>prehenditur; &longs;icque ad varios littorum &longs;itus referri po&longs;&longs;unt di<lb/>uer&longs;itates, quæ mox memoratis generalibus accidentibus &longs;uper<lb/>ueniunt; vt vel exemplo nauiculæ, cui &longs;imiles in&longs;int inæqualita<lb/>tes, intelligi potest. </s>

<s>Quòd autem affluxus ad littora fiat <lb/>diebus &longs;ingulis vnà propò horà (&longs;eu quatuor horæ quintis) tar<lb/>diùs, ex eo e&longs;&longs;e pote&longs;t, quòd cùm, vt iam dictum, Terra, & Lu<lb/>na vnum totale mobile &longs;int, & Terra &longs;uo motu diurno &longs;ic Lu<lb/>nam circum-rapiat, vt Luna tamen non penitùs, ob di&longs;tantiam, <lb/>ob&longs;ecundando, circulum vnum non ab&longs;oluat, ni&longs;i intra men&longs;em; <lb/>ac die bus proinde &longs;ingulis integra propè hora tardiùs ad meri<lb/>dianum perueniat, è quo pridie cum aliqua Terræ parte di&longs;ce&longs;<lb/>&longs;erit, Idcircò affluxus non præcisè redeat, cùm ip&longs;a eadem<emph.end type="italics"/> T<emph type="italics"/>er<lb/>ræpars ad meridianum eumdem redit, &longs;ed cùm redit Luna, quæ <lb/>est mobilis totalis qua&longs;i complementum. </s>

<s>Epistolæ conclu&longs;io.<emph.end type="italics"/><lb/>A p. </s>

<s><emph type="italics"/>Errata in his Summulis.<emph.end type="italics"/> fol. </s>

<s>17. lege <emph type="italics"/>tantumdem.<emph.end type="italics"/> p 2. l. </s>

<s>16. <lb/><emph type="italics"/>heixc.<emph.end type="italics"/> p. </s>

<s>22 XLVIII. fol. </s>

<s>17. <emph type="italics"/>conficere.<emph.end type="italics"/><lb/>p. </s>

<s>2<gap/>. <emph type="italics"/>e<gap/>ruam Omi&longs;&longs;a in i<gap/>xtu.<emph.end type="italics"/> p. </s>

<s>242. 13. <lb/>octingenties. </s>

<s>255. 17. collinees, 256 28. voce non. </s>

<s>270. <lb/>24. An&longs;toteleæ &longs;ententiæ. </s>

<s>285, 2 ad hoc. <emph type="italics"/>In ip&longs;is Errata.<emph.end type="italics"/> l. </s>

<s><emph type="center"/>DE PROPORTIONE, <lb/>QVA GRAVIA DECIDENTIA <lb/>ACCELERANTVR.<emph.end type="center"/></s>

<s><emph type="center"/>EPISTOLA PRIMA.<emph.end type="center"/><lb/><gap desc="hr tag"/></s>

<s><emph type="center"/><emph type="italics"/>ADMODVM REVERENDO, <lb/>& religio&longs;ißimo, doctißimoque Viro,<emph.end type="italics"/> P. <lb/>PETRO CAZRÆO <emph type="italics"/>Societatis<emph.end type="italics"/> IESV, <lb/><emph type="italics"/>Meten&longs;is Collegij Rectori &longs;apientißimo.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/>PETRVS GASSENDVS S.<emph.end type="center"/></s>

<s>PELLEGI, optime Cazræe, quam dig<lb/>natus es ad me dare, ac publici iuris &longs;imul <lb/>facere <emph type="italics"/>Demon&longs;trationem Phy&longs;icam,<emph.end type="italics"/> qua <lb/><emph type="italics"/>Ratio accelerationis in motu rerum grauium <lb/>naturali determinatur.<emph.end type="italics"/></s><s> Agnoui verò imprimis illam &longs;in<lb/>gularem beneuolentiam, qua perrexi&longs;ti ob&longs;tringere <lb/>me, quæque e&longs;t &longs;anè tota ad tuam bonitatis eximiæ <lb/>indolem accepta ferenda. </s>

<s>Promptum deinde fuit <lb/>memini&longs;&longs;e eruditæ Epi&longs;tolæ, qua ante duos annos ea <lb/>&longs;igni&longs;ica&longs;ti, quæ in meis illis, <emph type="italics"/>de Motu impre&longs;&longs;o à motore <lb/>tran&longs;lato,<emph.end type="italics"/> minimè probares; ac illud inter cætera, quòd <pb pagenum="2"/>&longs;en&longs;i&longs;&longs;em cum Galileo, <emph type="italics"/>Motum naturalem rerum deci<lb/>dentium ea ratione accelerari, vt &longs;uperata &longs;patia temporibus <lb/>æqualibus, numerorum imparium progreßionem imitarentur.<emph.end type="italics"/><lb/>Commemini etiam, cùm fui&longs;&longs;em conatus facere &longs;atis <lb/>in cæteris, expetii&longs;&longs;e me, vt quia neque Paralogi&longs;mum, <lb/>quem in Galileo cau&longs;abaris, animaduerti&longs;&longs;em, neque <lb/>experientia, aut ratio mon&longs;tra&longs;&longs;et quidpiam oppo&longs;i<lb/>tum; <gap/>ig<gap/>areris ip&longs;e tum mihi fallaciam Galilei rete<lb/>gere, tum inuentam illam à te progre&longs;&longs;ionem me edo<lb/>cere. </s>

<s>Volui&longs;ti id porrò nunc <expan abbr="dem&utilde;">demum</expan> cumulati&longs;&longs;imè præ<lb/>&longs;tare, ac me vel ex eo deuinxi&longs;ti, quòd euulgare Medi<lb/>tationes de motu præclaras aggre&longs;&longs;us, hanc e&longs;&longs;e pri<lb/>mam volueris, quam non creditori profectò, qualem <lb/>me habes, per&longs;olueres; &longs;ed debitori, qualem me potiùs <lb/>ingenuè fateor, oppignerares. </s>

<s>Heinc e&longs;t, cur licet ni<lb/>hil in me &longs;it, quod qua&longs;i par pari rependam; adnitar <lb/>tamen, quantum licet, te&longs;tari gratitudinem, eandem <lb/>tecum r<gap/>m meditatus, ac eas dubitandi rationes, quæ <lb/>mihi &longs;e&longs;e inter legendum vltrò obtulere, reponens. <lb/></s>

<s>Quippe lógè ab&longs;um abeo, quem tu me e&longs;&longs;e protua illa <lb/>rara comitate volui&longs;ti, dum decreui&longs;ti <expan abbr="Iudic&etilde;">Iudicem</expan> tuæ hu<lb/>ius Demon&longs;trationis. </s>

<s>Is nimirùm &longs;um, qui aliud <lb/>nihil valeam, quàm difficultates qua&longs;dam excitare, ac <lb/>tibimet proponere, qui in hi&longs;ce rebus & diuti&longs;&longs;imè, & <lb/>curio&longs;i&longs;&longs;imè ver&longs;atus, ip&longs;as explanare facillimè po&longs;&longs;is. <lb/></s>

<s>Interim autem non &longs;ubuereor, ne tamet&longs;i videarabs te <lb/>di&longs;&longs;entire, neque illicò manus dare, tu idcircò mihi &longs;u<lb/>cen&longs;eas: cùm ea &longs;is humanitate, eo in veritatem affe<lb/>ctu, vt non po&longs;&longs;is in me candorem, quem ego in te <lb/>probem, improbare. </s><pb pagenum="3"/>

<s><emph type="center"/><emph type="italics"/>Status controuer&longs;iæ.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Principio verò, vt experiar, num rem &longs;atis ca<lb/>piam, de qua agitur; Quæri, ecce, mihi videtur, <emph type="italics"/>Qua <lb/>ratione, &longs;eu proportione celeritas rerum decidentium incre&longs;cæt?<emph.end type="italics"/><lb/>Videlicet &longs;upponimusrem nimis-quàm notam, <expan abbr="mot&utilde;">motum</expan> <lb/><expan abbr="rer&utilde;">rerum</expan> grauium ex alto cadentium e&longs;&longs;e velociorem in fi<lb/>ne, quàm in medio; & in medio, quàm in ip&longs;o princi<lb/>pio. </s>

<s>Supponimus rur&longs;us hanc velocitatem ita conti<lb/>nuò incre&longs;cere, vt ab ip&longs;o v&longs;que in&longs;tanti, quo mobile à <lb/>quiete recedit, illius motus magis, magi&longs;que continen<lb/>ter acceleretur; &longs;eu incrementa velocitatis plura &longs;em<lb/>per, ac plura vniformiter præacqui&longs;itis &longs;uper-addan<lb/>tur. </s>

<s>Supponimus tertiò i&longs;thæc incrementa compa<lb/>rari po&longs;&longs;e aut cum partibus temporis, quæ vno tenore <lb/>&longs;uccedunt, aut cum partibus &longs;patij, quæ plures, plure&longs;<lb/>que continenter per curruntur. </s>

<s>Supponimus quartò <lb/>po&longs;&longs;e accipi, &longs;iue de&longs;ignari primum quoddam tem<lb/>pus, vt minutum horæ &longs;ecundùm, &longs;iue interuallum in<lb/>ter duas pul&longs;ationes arteriæ, cui con&longs;equentia tempora <lb/>æqualia po&longs;&longs;int de&longs;ignari; adeò vt totum illud tem<lb/>pus, quod in decidendo mobile in&longs;umit, in plureis hu<lb/>iu&longs;cemodi æqualeis parteis di&longs;tinguatur. </s>

<s>Supponimus <lb/>quintò po&longs;&longs;e accipi, &longs;iue de&longs;ignari primùm quoddam <lb/>&longs;patium, quod tempore nempe primo percurratur, vt <lb/>putà orgyiam, aut aliam men&longs;uram, cui aliæ æquales <lb/>po&longs;&longs;int accipi, in con&longs;equente &longs;patio, adeò vt totu illud <lb/>&longs;patium, quod à mobili decidente peiuaditur, intelli<lb/>gatur e&longs;&longs;e in plureis huiu&longs;modi parteis diui&longs;um. </s>

<s>Sup<lb/>ponimus demùm po&longs;&longs;e accipi, &longs;iue de&longs;ignari velocita-<pb pagenum="4"/>tem aliquam primam, quæ &longs;cilicet &longs;it acqui&longs;ita in fine <lb/>eiu&longs;dem primi temporis, & cui per con&longs;equentem <lb/>motum æquales aliæ &longs;uper-addantur, vt &longs;olent gra<lb/>dus gradibus in capacibus inten&longs;ionis qualitatibus &longs;u<lb/>per-addi; adeò vt, quæ velocitas in fine motus e&longs;t ac<lb/>qui&longs;ita, ac inten&longs;i&longs;&longs;ima e&longs;t, e&longs;&longs;e coalita cen&longs;eatur ex om<lb/>nibus velocitatibus, &longs;iue gradibus, qui per&longs;euerante <lb/>motu acqui&longs;iti fuerint, ijque inter&longs;e, & <expan abbr="c&utilde;">cum</expan> primo illo <lb/>æquales. </s>

<s>Hi&longs;ce autem &longs;uppo&longs;itis, quia partes tempo<lb/>ris æquales, quæ primæ &longs;uccedunt, pauciores &longs;unt nu<lb/>mero, quàm quæ &longs;patij partes æquales decurruntur <lb/>po&longs;t primam; & qui velocitatis gradus acquiruntur <lb/>po&longs;t primum, ac &longs;unt veluti incrementa &longs;upperaddita, <lb/>comparari po&longs;&longs;unt, vt iam dictum e&longs;t, aut cum parti<lb/>bus æqualibus temporis, aut cum partibus æqualibus <lb/>&longs;patij; ideò difficultas, &longs;eu quæ&longs;tionis &longs;tatus is videtur <lb/>poti&longs;&longs;imùm, <emph type="italics"/>Vtrum gradus velocitatis primo æquales tot <lb/>acquirantur; quot &longs;tuunt partes temporis: an potiùs, quot spa<lb/>tij partes percurruntur?<emph.end type="italics"/> Nempe non alio re&longs;picitur, cùm <lb/>requiritur, <emph type="italics"/>an velocitates &longs;i ut tempora, an &longs;icut spatia &longs;e&longs;e <lb/>habeant?<emph.end type="italics"/></s>

<s>III. <expan abbr="Cæter&utilde;">Cæterum</expan> ea e&longs;t tua opinio, vt velocitates habeant <lb/>&longs;e quemadmodum &longs;patia; &longs;eu, vt tot gradus velocitatis <lb/>æquales primo acquirantur, quot &longs;unt partes æquales <lb/>&longs;patij, quæ po&longs;t primum, primoque gradu &longs;uperatum <lb/>decurruntur. </s>

<s>Siquidem toto &longs;patio diui&longs;o in decem <lb/>v. </s>

<s>orgyias; qualis, quantu&longs;que e&longs;t velocitatis gra<lb/>dus in fine primæ orgviæ acqui&longs;itus, taleis, tanto&longs;que <lb/>vis acqui&longs;itos in fine &longs;ecundæ duos, in fine tertiæ treis, <lb/>in fine quartæ quatuor, & ita deinceps, quov&longs;que in <pb pagenum="5"/>fine decimæ &longs;int decem. </s>

<s>At Galileus vult potiùs &longs;e ve<lb/>locitates habere &longs;icut tempora; &longs;iue gradus velocitatis <lb/>æqualeis primo tot acquiri, quot temporis partes pri<lb/>mæ æquales po&longs;t ip&longs;am fluunt. </s>

<s>Addit verò &longs;patij par<lb/>teis continuò acquiri per parteis temporis æqualeis, ea <lb/>&longs;erie continua, qua numeri impares ab vnitate pro<lb/>grediuntur; adeò vt &longs;i primo momento, &longs;eu prima <lb/>æquali parte temporis mobile deciderit per vnam or<lb/>gyiam, decidat &longs;ecundo per treis, tertio per quinque, <lb/>quarto per &longs;eptem, ac ita deinceps. </s>

<s>Addit rur&longs;us, quia <lb/>numeros &longs;ic progredienteis aggregando, quadrati con<lb/>tinuò numeri creantur; heinc fieri, vt &longs;i primo &longs;patio <lb/>illa continuò aggregentur, quæ æqualia æqualibus <lb/>percurruntur temporibus, &longs;patia tunc &longs;e habeant &longs;icut <lb/>quadrata temporum; hoc e&longs;t, vt quemadmodum pri<lb/>mo tempore e&longs;t &longs;uperatum vnum &longs;patium, &longs;ecundo <lb/>tempore &longs;int &longs;uperata quatuor, tertiò nouem, quaito <lb/>&longs;exdecim, & &longs;ic con&longs;equenter. </s>

<s>Hæc autem melius in<lb/>telligi, declararique non valeant, quàm productis ex <lb/>eodem puncto duabus rectis lineis angulum in ip&longs;o <lb/>creantibus, ac in parteis quotcumque æqualeis diui&longs;is, <lb/>interducti&longs;que rectis lineis tum inter re&longs;pondentia <lb/>&longs;ingula heincinde diui&longs;ionis puncta, tum à quouis hu<lb/>iu&longs;modi in vtraque linea puncto &longs;ecundùm ductum <lb/>alteri lineæ parallelum. </s>

<s>Tale e&longs;t &longs;chema, quod exhi<lb/>bui ad calcem prioris mearum illarum Epi&longs;tolarum, <lb/>quodque &longs;i heic iam repetiero, ac paulò accuratiùs, ob <lb/>factan. </s>

<s>illam, de qua po&longs;teà, æquiuocationem, expo<lb/>&longs;uero, erit forta&longs;&longs;is operæ pretium. </s>

<s>Itaque illud heic apponendo, vides primùm <pb pagenum="6"/>lineas AB, AC, angulum creanteis in A, &longs;ic diui&longs;as e&longs;&longs;e <lb/>heinc inde in parteis æqualeis, ad puncta D, E, F, G, H, <lb/>I, K, L (po&longs;&longs;ent autem in longè plureis continuatæ di<lb/>uidi) vt lineæ ductæ cùm inter ip&longs;a puncta, tùm ex ip&longs;is <lb/>in puncta M, N, O, totum &longs;patium KAL di&longs;pe&longs;cant <lb/>in triangula inter <lb/><figure id="fig2"></figure><lb/>&longs;e &longs;imilia, ac pror<lb/>sù æqualia. </s>

<s>Cùm <lb/>po&longs;&longs;imus porto <lb/>habere punctum <lb/>A pro initio tem<lb/>poris, pro initio <lb/>&longs;patij, pro initio <lb/>velocitatis, quæ <lb/>tria heic in motu <lb/>&longs;pectantur, ac vna <lb/>cùm ip&longs;o inci<lb/>piunt; Po&longs;&longs;umus imprimis habere parteis æqualeis al<lb/>terutrius, aut vtriu&longs;que lineæ AB, AC pro partibus, <lb/>&longs;iue momentis æqualibus temporis ab initio fluentis, <lb/>adeòproinde, vt AE, v. </s>

<s>repræ&longs;entet <expan abbr="prim&utilde;">primum</expan> momen<lb/>tum, EG &longs;ecundum, GI: tertium, IL quartum. <lb/></s>

<s>Po&longs;&longs;umus &longs;ecundò habere æqualia illa triangula pro <lb/>æqualibus &longs;patij partibus, quæ ab initio percurrun<lb/>tur; adeò vt ductâ &longs;eor&longs;im lineâ PQ ca&longs;um refe<lb/>rente per orgyias &longs;exdecim, Triangulum ADE <lb/>repræ&longs;entet primam orgyiam PR, quæ primò mo<lb/>mento percurritur; tria proxima, treis orgyias RS, <lb/>quæ &longs;ecundo; quinque &longs;equentia quinque orgyias <lb/>ST, quæ tertiò; & &longs;eptem &longs;uccedentia &longs;eptem or-<pb pagenum="7"/>gyias TQ, quæ quarto. </s>

<s>Con&longs;tat autem exinde &longs;patia <lb/>aggregata ita &longs;e habere, &longs;icut quadrata tempo<lb/><figure id="fig3"></figure><lb/>rum; quandò ADE triangulum (&longs;patiumve <lb/>PR) e&longs;t vnum; quemadmodum quadratum <lb/>ip&longs;ius AE, hoc e&longs;t temporis vnius, e&longs;t vnum; & <lb/>aggregatum AFG (&longs;eu PS) e&longs;t quatuor; quem<lb/>admodum quadratum AG, duorum, e&longs;t qua<lb/>tuor; & aggregatum AHI (&longs;eu PT) e&longs;t nouem; <lb/>quemadmodum quadratum AI trium, e&longs;t no<lb/>uem; & aggregatum AKL (&longs;eu PQ) e&longs;t &longs;ex<lb/>decim; quemadmodum quadratum AL qua<lb/>tuor, e&longs;t &longs;exdecim. </s>

<s>Po&longs;&longs;umus tertiò habere li<lb/>neam DE, pro primo gradu velocitatis acqui<lb/>&longs;itæ in fine primi temporis: quatenus, vt pri<lb/>mùm tempus AE non e&longs;t indiuiduum, &longs;ed in <lb/>tot in&longs;tantia, &longs;eu temporula pote&longs;t diuidi, quot <lb/>&longs;unt puncta, particulæve in ip&longs;a AE (aut AD) <lb/>ita neque gradus velocitatis indiuiduus e&longs;t, &longs;eu <lb/>vno in&longs;tanti, acqui&longs;itus totus; &longs;ed ab v&longs;que ini<lb/>tio per totum primum tempus incre&longs;cit, ac re<lb/>præ&longs;entari pote&longs;t per tot lineas, quot po&longs;&longs;unt <lb/>parallelæ duci ip&longs;i DE inter puncta linearum <lb/>AD, & AE; adeò vt quemadmodum illæ lineæ <lb/>continuo incre&longs;cunt à puncto A in lineam DE, &longs;ic <lb/>velocitas à principio motus continuò incre&longs;cat, & re<lb/>præ&longs;entata, qualis e&longs;t in interceptis primi temporis in<lb/>&longs;tantibus, per interceptas lineas, repræ&longs;entetur qualis <lb/>e&longs;t in vltimo in&longs;tanti eiu&longs;dem primi temporis, per <lb/>ip&longs;am DE inter vltima ductam puncta. </s>

<s>Et quia ve<lb/>locitas deinceps incre&longs;cere pergens, repræ&longs;entari rur-<pb pagenum="8"/>&longs;us pote&longs;t per lineas maiores, maiore&longs;que continenter <lb/>ductas inter omnia puncta &longs;uccedentia re&longs;iduarum <lb/>linearum DB, & EC, heinc efficitur, vt linea FG re<lb/>præ&longs;entet velocitatem acqui&longs;itam in fine &longs;ecundi mo<lb/>menti: linea HI acqui&longs;itam in fine tertij, & linea KL <lb/>acqui&longs;itam in fine quarti. </s>

<s>Con&longs;tat verò inde, vt ve<lb/>locitates &longs;e habeant &longs;icut tempora; cùm ob triangulos <lb/>anguli communis, & parallelarum ba&longs;ium, notum &longs;it <lb/>e&longs;&longs;e vt DE ad EA, ita FG ad GA, HI ad IA, & KL <lb/>ad LA. </s>

<s>Atque hæc quidem, vt clariùs con&longs;tet, qua <lb/>de re inter nos agatur. </s>

<s>V. Iam, Tu initio argumentum Di&longs;&longs;ertationis ita <lb/>partiris, vt duo præ&longs;tanda tibi proponas. </s>

<s>Vnum, <lb/><emph type="italics"/>vt Galilei hac inre errores, eorumque fonteis aperias; claré<lb/>que demon&longs;tres ea, quæ ab ip&longs;o de acceleratione Motus in na<lb/>turali de&longs;cen&longs;u grauium Libro &longs;ecundo nouæ &longs;cientiæ, & <lb/>toto Dialogo tertio dicta &longs;unt, non modò &longs;u&longs;picionibus meris, <lb/>vixque probabilibus coniecturis niti, &longs;ed ex principijs etiam <lb/>apertè fal&longs;is, euidentibu&longs;que paralogi&longs;mis omnia concludi; ex <lb/>quo con&longs;equens &longs;it, nouam illam &longs;cientiam euane&longs;cere, quam <lb/>ingenio&longs;o quidem, & plau&longs;ibili, &longs;ed inani tamen, & ca&longs;&longs;o <lb/>apparatu nobis<emph.end type="italics"/> G<emph type="italics"/>alileus exhibuerit.<emph.end type="italics"/></s><s> Alterum, <emph type="italics"/>vt reiecta<emph.end type="italics"/><lb/>G<emph type="italics"/>alilei p&longs;eudo-&longs;cientia, veram tu, ac certam in eius locum <lb/>&longs;ubstituas, rationemque, modum, ac men&longs;uram acceleratio<lb/>nis eiu&longs;dem in naturali de&longs;cen&longs;u grauium ex euidentibus, at<lb/>que indubitatis experientiis demonstres.<emph.end type="italics"/></s><s> Circa priùs de<lb/>inde caput, duo &longs;unt, in quibus occuparis; nam impe<lb/>tis <emph type="italics"/>primò<emph.end type="italics"/> definitionem Motus æquabiliter accelerati à <lb/>Galileo traditam: & <emph type="italics"/>&longs;ecundò<emph.end type="italics"/> quod idem ait de gradi<lb/>bus velocitatis, qui acquiruntur à mobili, dùm &longs;uper <pb pagenum="9"/>planis inclinatis mouetur. </s>

<s>Circa po&longs;terius ex&longs;equeris <lb/>tria: Nam <emph type="italics"/>primò<emph.end type="italics"/> declaras quod experimentum, circa <lb/>Bilancem excogita&longs;ti; <emph type="italics"/>&longs;ecundò<emph.end type="italics"/> deducis quam putas ex<lb/>inde accelerationis <expan abbr="ration&etilde;">rationem</expan> haberi; ac <emph type="italics"/>tertiò<emph.end type="italics"/> infers pro<lb/>gre&longs;&longs;ionem, qua &longs;uperantur &longs;patia temporibus æqua<lb/>libus, imitari progre&longs;&longs;ionem non numerorum impa<lb/>rium, &longs;ed rationis continuò duplæ, quam & exprimis <lb/>in de&longs;cen&longs;u globi à Luna v&longs;que in centrum terræ. </s>

<s>Hæc <lb/>e&longs;t igitur Di&longs;&longs;ertationis &longs;umma. </s>

<s><emph type="center"/><emph type="italics"/>De Motus æquabiliter accelerati Definitione.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Vt ordine autem de &longs;ingulis dicam, & à <lb/>Priore capite incipiam, <emph type="italics"/>Primum errorem, & tanquam <lb/>originem cæterorum<emph.end type="italics"/> dicis, quòd <emph type="italics"/>Galileus fal&longs;am hanc ac<lb/>celerati Motus definitionem in&longs;tituerit, Motum æquabiliter <lb/>acceleratum dico eum, qui à quiete recedens temporibus æqua<lb/>libus æqualia celeritatis momenta acquirat.<emph.end type="italics"/></s><s> Rem autem <lb/>putas eius momenti, vt dicas <emph type="italics"/>te contendere huiu&longs;modi <lb/>definitionem adulterinam e&longs;&longs;e, ac fal&longs;am; & quicquid <lb/>toto illo Libro de eodem motu accelerato, &longs;atis alioquin <lb/>ingeniosè<emph.end type="italics"/> G<emph type="italics"/>alileus commentus e&longs;t, nibil veritatis habere.<emph.end type="italics"/><lb/>Improbas &longs;ubinde, quòd <emph type="italics"/>definitionem non experientia <lb/>certa, ac euidenti confirmauerit, &longs;ed ab eius tantum &longs;im<lb/>plicitate motibus naturalibus maximè congruente; à per<lb/>fecta cum demon&longs;tratis à &longs;e theorematibus con&longs;en&longs;ione; & <lb/>ab aperta, vt ip&longs;e quidem fidenter a&longs;&longs;erat, receptæ vulgò <lb/>definitionis ab&longs;urditate.<emph.end type="italics"/></s><s> Tum verò circa &longs;implicitatem <lb/>perpendere &longs;olùm me iubes, an non &longs;implicior &longs;it <lb/>definitio, quæ à cæteris vulgò v&longs;urpatur, dum Mo<lb/>tum æquabiliter acceleratum eum potiùs e&longs;&longs;e a&longs;&longs;e-<pb pagenum="10"/>runt, <emph type="italics"/>Qui æqualibus &longs;patijs æqualia celeritatis augmenta <lb/>acquirit.<emph.end type="italics"/></s><s> Circa con&longs;en&longs;ionem autem &longs;olùm, bucis, <lb/><emph type="italics"/>nouum non e&longs;&longs;e, &longs;i fal&longs;a fal&longs;is ap<gap/>è quandó que, & con<lb/>cinnè cohæreant;<emph.end type="italics"/> ac po&longs;tremò in eo in&longs;iltis, vt probes <lb/>e&longs;&longs;e paralogi&longs;mum, quo ille vulgarem, moxque re<lb/>latam definitionem ab&longs;urditatis apertæ damna<lb/>uit. </s>

<s>VII Ego intereà, optime Vir, neque video De<lb/>&longs;initionem a Galileo in&longs;titutam à te directè impu<lb/>gnari, fal&longs;itati&longs;ve vllius conuinci; neque agno&longs;co quî <lb/>magis vera, congruaque potuerit in&longs;titui. </s>

<s>Quippe <lb/>memini&longs;&longs;e, aut potiùs adnota&longs;&longs;e diligenter oportet <lb/>agi heic de motu æquabiliter accelerato, &longs;iue cuius <lb/>celeritas continenter, vniformiterque incre&longs;cat, ne<lb/>que vllum &longs;it momentum con&longs;equentis temporis, in <lb/>quo motus non &longs;it velocior, quàm in quovis antece<lb/>dente, & in quo non eadem ratione ip&longs;a velocitas <lb/>augeatur. </s>

<s>Fieri id porrò e&longs;t manife&longs;tum ex ijs, quæ <lb/>deducta iam &longs;unt; &longs;i æqualibus temporibus æqualia <lb/>celeritatis momenta, &longs;eu incrementa acquirantur. <lb/></s>

<s>Nam vt repetamus &longs;uperiorem figuram, nemo dicat <lb/>celeritatem vniformiter incre&longs;centem po&longs;&longs;e meliùs <lb/>repræ&longs;entari, quàm diductione crurum anguli, linea<lb/>rumve AB, AC, quatenus complectuntur &longs;pa<lb/>tium, quod à puncto A magis continenter, vni<lb/>formiterque cre&longs;cere non po&longs;&longs;it: ac aliunde angu<lb/>lus BAC apertior, aut conductior (prout finge<lb/>tur maior, aut minor velocitas) valet v&longs;urpari. <lb/></s>

<s>Vt autem rem magis ob oculos ponam; duco ec<lb/>ce lineam VX, per ip&longs;um apicem A, quæ cum li-<pb pagenum="11"/>neis AB, AC, angulos con&longs;tituat vtrimque æqua<lb/><figure id="fig4"></figure><lb/>leis, & &longs;eruatâ eorum<lb/>dem angulorum men<lb/>&longs;urâ, ita fluere conci<lb/>piatur, vt totum &longs;pa<lb/>tium BAC peruadat. <lb/></s>

<s>Tunc enim manife<lb/>&longs;tum e&longs;t portiones <lb/>huius lineæ continuò <lb/>veluti re&longs;ectas, inter<lb/>cepta&longs;que à lineis AB, <lb/>AC, cre&longs;cere &longs;emper, <lb/>&longs;eu maiores, maiore&longs;<lb/>que vniformiter e&longs;&longs;e; ac non portiones &longs;emel inter<lb/>ceptas perire, &longs;ed ip&longs;is permanentibus nouas, nouaf<lb/>que heinc inde continenter &longs;uper-acquiri. </s>

<s>Cùm <lb/>verò etiam gradus velocitatis con&longs;imiliter cre&longs;cant, <lb/>&longs;iue maiores, maiore&longs;que vniformiter euadant, ac <lb/>&longs;emel acqui&longs;iti non pereant, &longs;ed ip&longs;is &longs;uper&longs;titibus, <lb/>per&longs;euerantibu&longs;que noua, atque noua momenta, &longs;iue <lb/>incrementa velocitatis &longs;uper-addantur; &longs;upere&longs;t, vt <lb/>quemadmodum linearum illarum incrementa fiunt, <lb/>&longs;ic fiant quoque velocitatum. </s>

<s>Notum e&longs;t autem. </s>

<s>vt <lb/>acceptis partibus æqualibus lineæ AC, verbi cau&longs;sâ, <lb/>incrementa earum portionum, &longs;iue linearum paralle<lb/>larum interceptarum, acquirantur &longs;emper æqualia <lb/>&longs;ub æqualibus illis partibus. </s>

<s>Nam, vt &longs;ub AE ac<lb/>qui&longs;ita e&longs;t linea DE, ita &longs;ub EG, acquiritur æqua<lb/>lis alia; cùm ip&longs;a FG &longs;it dupla ip&longs;ius DE; & &longs;ub <lb/>GI iterum alia; cùm ip&longs;a HI &longs;it eiu&longs;dem tripla; & <pb pagenum="12"/>&longs;ub IL rursùs alia, cùm ip&longs;a KL &longs;it eiu&longs;dem qua<lb/>drupla; atque ita porrò, &longs;eu vlteriùs pergas, &longs;eu <lb/>alia puncta intra ea&longs;dem parteis lineæ AC, alia&longs;<lb/>que parallelas commemoratis interceptas, &longs;ingula&longs;<lb/>que &longs;uis punctis re&longs;pondenteis, accipias. </s>

<s>Quare & <lb/>a&longs;&longs;umptis partibus æqualibus temporis per parteis <lb/>æqualeis lineæ AC repræ&longs;entatis, <expan abbr="not&utilde;">notum</expan> e&longs;t momenta, <lb/>&longs;eu incrementa velocitatis per parallelas repræ&longs;entatæ, <lb/>æqualia acquiri &longs;ub huiu&longs;modi partibus; adeò vt <lb/>qualis gradus velocitatis acqui&longs;itus e&longs;t in fine primi <lb/>temporis vnus, talis alius, hoc e&longs;t æqualis, &longs;it ip&longs;i &longs;uper<lb/>acqui&longs;itus in fine &longs;ecundi, ac &longs;int iam duo; & iterum <lb/>æqualis alius in fine tertij, ac &longs;in: iam tres; & rursùs <lb/>alius in fine quarti, ac &longs;int iam quatuor; atque ita de <lb/>cæteris, &longs;iue con&longs;equentibus, &longs;iue inter&longs;umptis. </s>

<s>Sic itaque mihi videtur Motus æquabili<lb/>ter, hoc e&longs;t continenter, vniformiterque acceleratus <lb/>perquàm appo&longs;itè definiri is, <emph type="italics"/>Qui à quiete recedens <lb/>temporibus æqualibus æqualia celeritatis momenta<emph.end type="italics"/> (aug<lb/>mentave) <emph type="italics"/>acquirat;<emph.end type="italics"/> cùm præ&longs;ertim non videam <lb/>po&longs;&longs;e ip&longs;um alia ratione concipi, aut de&longs;cribi talem. <lb/></s>

<s>Nam quod &longs;pectat quidem ad illam à te laudatam <lb/>definitionem, qua motus æquabiliter acceleratus de&longs;<lb/>cribitur is, <emph type="italics"/>Qui æqualibus spatiis æqualia celeritatis aug<lb/>menta acquirit:<emph.end type="italics"/> dic amabò quanam ratione concipere <lb/>exinde licear acceleratum æquabiliter motum? </s>

<s>E&longs;to <lb/>enim &longs;patium percurrendum v. </s>

<s>linea AB in par<lb/>teis æqualeis diui&longs;a ad puncta C, D, E, F, G, I, K. <lb/></s>

<s>Decidat mobile ex A; & in C fine primæ partis ac<lb/>qui&longs;ierit primum velocitatis gradum; in D autem <pb pagenum="13"/>&longs;ecundum, quo ad priorem per&longs;euerantem iunctp <lb/><figure id="fig5"></figure><lb/>duo iam &longs;int: in E tertium, quo <lb/>iuncto ad duos &longs;uperiores, per<lb/>&longs;euerantei&longs;que &longs;int tres; in F <lb/>quartum, & ita porrò, quo<lb/>v&longs;que in B acqui&longs;ierit nonum, <lb/>quo iuncto cum octo antece<lb/>dentibus &longs;int nouem. </s>

<s>Iam cùm <lb/>quilibet horum graduum la<lb/>titudinem quandam habeat; <lb/>neque enim e&longs;t magis indiui&longs;i<lb/>bilis, aut ex indiui&longs;ibilibus <lb/>con&longs;tans, quàm pars AC, CD, <lb/>DE, quælibet-ve alia: ac idcir<lb/>cò ip&longs;e quoque incre&longs;cat æqua<lb/>biliter, vnoque tenore: repræ&longs;entetur primus gradus <lb/>per triangulum ALC, vt pote à puncto, &longs;eu angulo <lb/>A ad ba&longs;in LC æquabiliter, vnóque tenore cre&longs;cen<lb/>tem. </s>

<s>Aptentur deinde ad CD duo triangula æqua<lb/>lia tum inter &longs;e, tum cum ip&longs;o ALC, <expan abbr="quor&utilde;">quorum</expan> CMD <lb/>repræ&longs;entet illum, qui &longs;ecundò acquiritur, LCM au<lb/>tem primò aqui&longs;itum, ac per&longs;euerantem. </s>

<s>Nihil e&longs;t <lb/>opus, vt de&longs;ude<gap/> ad o&longs;tendendum non increui&longs;&longs;e <lb/>velocitatem æquabiliter, eodemve tenore ex C in D, <lb/>quo inc&oelig;perat, perrexeratque v&longs;que in D; vt feci&longs;&longs;et <lb/>enim, oporteret de&longs;criptum e&longs;&longs;e non quadrangulum <lb/>LD con&longs;tans ex duobus triangulis; &longs;ed trapezion CN <lb/>con&longs;titutum ex tribus. </s>

<s>Eadem autem ratione mani<lb/>fe&longs;tum e&longs;t, &longs;i ad DE aptentur tria triangula, defutura <lb/>duo; &longs;i ad EF quatuor, defutura tria, & ita deinceps, <pb pagenum="14"/>quov&longs;que, &longs;i ad KB aptentur nouem, &longs;int defutura <lb/>octo; vt proinde intelligamus totidem dce&longs;&longs;e ad acce<lb/>lerationis æquabilitatem velocitatis gradus, quot nu<lb/>merare licet triangulos ad læuam è regione cuiu&longs;que <lb/>partis, complendo &longs;ummam triangulorum APB. <lb/></s>

<s>Con&longs;tare ergo videtur Motum æquabiliter accelera<lb/>tum definiti non po&longs;&longs;e illum, <emph type="italics"/>Qui æquabilibus &longs;patiis <lb/>æqualia celeritatis augmenta acquirat;<emph.end type="italics"/> &longs;ed potiùs illum, <lb/><emph type="italics"/>Qui acquirat æqualia æqualibus temporibus:<emph.end type="italics"/> atque idcircò <lb/>definitionem à Galileo traditam e&longs;&longs;e meritò præfe<lb/>rendam. </s>

<s><emph type="center"/><emph type="italics"/>De Paralogi&longs;mo, qui Galileo Definitionem &longs;puriam <lb/>impugnanti obiicitur.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Ac tu id quidem non fers; fed ais, <emph type="italics"/>Mirari to <lb/>&longs;atis non po&longs;&longs;e, quomodo<emph.end type="italics"/> G<emph type="italics"/>alileus vir alioquin perspicacis <lb/>ingenij receptam communi con&longs;en&longs;u motus accelerati defini<lb/>tionem non modò fal&longs;am, atque impoßibilem exi&longs;timauerit; <lb/>&longs;ed patenti quoque, ip&longs;i&longs;que tyronibus obuio paralogi&longs;mo <lb/>eiu&longs;dem fal&longs;itatem palam, atque euidenter demon&longs;tra&longs;&longs;e adeò <lb/>prafidenter a&longs;&longs;eruerit; & quod ampliùs e&longs;t, etiam viru non <lb/>ineruditis per&longs;ua&longs;erit.<emph.end type="italics"/></s><s> Tum autem pergis, <emph type="italics"/>Audi igitur; <lb/>mi<emph.end type="italics"/> G<emph type="italics"/>a&longs;&longs;ende, & mecum mirare tanti viri demon&longs;trationem. <lb/></s>

<s>Si acceleratio motus,<emph.end type="italics"/> inquit, <emph type="italics"/>in de&longs;cen&longs;u grauium æquali<lb/>bus &longs;patiis æqualia &longs;umeret velocitatu ineremema, e&longs;&longs;ent <lb/>&longs;ine dubio velocitates inter &longs;e, vt emen&longs;a spatia: At quoite&longs;. <lb/></s>

<s>cúmque velocitates inter &longs;e &longs;unt vt emen&longs;a &longs;patia, debent <lb/>nece&longs;&longs;ariò ea spatia aut eodem, aut æquali tempore percur<lb/>ri. </s>

<s>Si igitur velocitas acqui&longs;ita per totam AC eam <lb/>rationem habeat ad velocitatem acqui&longs;itam per AB, quam<emph.end type="italics"/><pb pagenum="15"/><emph type="italics"/>spatium AC ad spatium AB, nece&longs;&longs;e e&longs;t, vt spatium<emph.end type="italics"/><lb/><figure id="fig6"></figure><lb/><emph type="italics"/>totum AC eodem, aut æquali tempore decurratur, <lb/>quo spatium AB ab&longs;oluitur. </s>

<s>Jmpoßibile est au<lb/>tem, vt corpus graue de&longs;cendens per AC eodem, <lb/>aut æquali tempore percurrat totam AC, quo per<lb/>currit partem eius AB, ni&longs;i motus fiat in instanti. <lb/></s>

<s>Tam impoßibile e&longs;t igitur, vt velocitates in de&longs;cen&longs;u <lb/>grauium inter &longs;e &longs;int, vt emen&longs;a &longs;patia (ac proinde, <lb/>vt etiam æqualibus &longs;patiis cre&longs;cant æqualiter) quàm <lb/>impoßibile e&longs;t motum illum fieri in instanti.<emph.end type="italics"/></s><s> Pergis &longs;ub<lb/>inde, <emph type="italics"/>Proh tuam, mi<emph.end type="italics"/> G<emph type="italics"/>a&longs;&longs;ende, Philo&longs;ophorumque omnium, <lb/>ac Mathematicorum fidem! istud<gap/>ne demon&longs;trare e&longs;t? </s>

<s>Et <lb/>tamen mirum quantum Galileus de hac, vt putat, &longs;ubtili, <lb/>clara, euidenti, ac Mathematica demon&longs;tratione &longs;ibi applau<lb/><gap/>at, quam integra pagina mirificis laudibus exaggerat. </s>

<s>Sed <lb/>illud multò adhûc mirabiùus, quod Lynceus Philo&longs;ophus, ac <lb/>Mathematicus, Lynceorumque princeps in tam aperta <lb/>luce cæcutiat, & vir eius nominis tam facilè deludatur.<emph.end type="italics"/></s>

<s>Ego verò, ô optime, ac religio&longs;&longs;ime Vir, quo <lb/>me cen&longs;u putem iri habitum, qui non &longs;im ex viris <lb/>non ineruditis, & eandem tamen cum Galileo opi<lb/>nionem per&longs;ua&longs;us &longs;im, ac perinde cæcutiam, perinde <lb/>deludar? </s>

<s>Etenim cùm meam quæ&longs;is fidem, fatcor <lb/>ingenüè me non videre quem in eo notas Paralogi&longs;<lb/>mum; ac videri mihi nece&longs;&longs;ariò deduci, fore, vt &longs;i ve<lb/>locitas per totam AC acquiratur dupla illius, quæ <lb/>acquiritur per totam AB, ip&longs;a AC eodem, aut æqua<lb/>li tempore, quo AB percurratur. </s>

<s>Rem certe in <lb/>hunc modum concipio. </s>

<s>Intelligatur AC diui&longs;a in <lb/>duodecim parteis æqualcis, ac proinde eius dimidium <pb pagenum="16"/>AB, &longs;eu ip&longs;i æqualrs DE in &longs;ex: &longs;intque primùm <lb/>duo mobilia, quorum vnum di&longs;cedat ex A <lb/><figure id="fig7"></figure><lb/>ver&longs;us C, eodem momento, quo aliud ex D <lb/>ver&longs;us E. </s>

<s>Notum e&longs;t, &longs;i vtrumque quidem <lb/>ferretur non accelerato, &longs;ed æquabili motu, <lb/>euenturum e&longs;&longs;e, vt velocitate illius ex&longs;i&longs;tente <lb/>dupla ad velocitatem i&longs;tius, illud perueniret <lb/>in C eodem momento, quo i&longs;tud in E; quo<lb/>niam &longs;patium ab illo &longs;uperatum foret vbi<lb/>que ad &longs;patium ab i&longs;to &longs;uperatum duplum, hoc e&longs;t, <lb/>forent ab illo &longs;uperatæ duæ partes, cùm ab i&longs;to vna; <lb/>ab illo quatuor, cùm ab hoc duæ, &c. </s>

<s>quatenus &longs;pa<lb/>tia &longs;e haberent vbique vt velocitates, hoc e&longs;t veloci<lb/>tas per totam AC e&longs;&longs;et vbique dupla velocitatis per <lb/>totam DE. </s>

<s>At verò, quoniam heic agitur de motu <lb/>non æquabili, &longs;ed continenter accelerato; ita de&longs;cen<lb/>dant rur&longs;us mobilia eodem tempore, vnum ab A, <lb/>aliud à D, vt &longs;uccrefcentibus continuò velocitatis gra<lb/>dibus, illud perueniendo in C acqui&longs;ierit duodecim, <lb/>hoc perueniendo in E &longs;ex: Quæ&longs;o quid impediat, <lb/>quo minùs illud perueniat in C eodem tempore, quo <lb/>i&longs;tud in E? </s>

<s>Nam di&longs;crimen e&longs;t quidem inter mo<lb/>tum acceleratum, & æquabilem, quòd in æquabili <lb/>partes &longs;patiorum æquales percurrantur æqualibus <lb/>temporibus, vt &longs;ingulæ partes lineæ DE &longs;ingulis mi<lb/>nutis, & geminæ partes lineæ AC minutis item &longs;in<lb/>gulis; in accelerato non item: At in eo tamen motus <lb/>conueniunt, quòd vbique velocitas per totam AC <lb/>dupla &longs;it velocitatis per totam DE; & qua ratione <lb/>plures, plure&longs;que ex &longs;ingulis partibus lineæ DE <pb pagenum="17"/>percurruntur æqualibus temporibus, percurruntur <lb/>quoque plures, plure&longs;que ex geminatis lineæ AC. <lb/></s>

<s>Ex hoc autem &longs;it, vt quemadmodum in æquabili mo<lb/>tu, DE percurreb<gap/>tur &longs;ex minutis, & AC &longs;imiliter <lb/>&longs;ex, ob geminas parteis i&longs;tius corre&longs;pondenteis &longs;ingu<lb/>lis illius, ita in accelerato, &longs;i DE percurratur tribus <lb/>minutis, AC percurratur &longs;imiliter tribus; quòd dum <lb/>primo minuto percurritur pars illius vna, percurran<lb/>tur i&longs;tius duæ, ob ge minam velocitatem; & ob ean<lb/>dem cau&longs;&longs;am, dum &longs;ecundo minuto percurruntur <lb/>illius duæ, percurrantur i&longs;tius quatuor, dum tertio <lb/>demùm illius tres, percurrantur i&longs;tius &longs;ex. </s>

<s>Nim rùm <lb/>non alia ratione dici po&longs;&longs;ent habere &longs;e velocitates vt <lb/>&longs;patia: neque velocitas per totam AC dupla e&longs;&longs;et ve<lb/>locitatis per totam DE E&longs;to deinde vnicum mobile, <lb/>quod decedens ab A, tendat ver&longs;us C, & &longs;it rursùs <lb/>velocitas per totam AC dupla velocitatis per totam <lb/>AB, patet idem prorsùs dicendum de AC, re&longs;pectu <lb/>AB, quod dictum fuit de eadem re&longs;pectu DE. </s>

<s>Nam <lb/>in æquabili quidem motu oporteret mobile percur<lb/>rere &longs;imul, &longs;eu primo minuto primam, & &longs;ecundam <lb/>parteis; &longs;ecundo &longs;ecundam, & quartam; ac ita porrò <lb/>quov&longs;que &longs;exto, percurreret, &longs;eu attingeret &longs;imul <lb/>&longs;extam, atque duo &longs;ecimam. </s>

<s>In accelerato verò <lb/>e&longs;t nece&longs;&longs;e, vt percurrat &longs;imul vnam, & duas in pri<lb/>mo; duas, & quatuor in &longs;ecundo; treis, & &longs;ex in tertio; <lb/>atque adeò totam AB, & totam AC tempore eo<lb/>dem. </s>

<s>Atque ego quidem rem itaconcipio. </s>

<s>XI Verum tu &longs;i m&longs;tas, <emph type="italics"/>Vt prima illius Paralo<lb/>gi&longs;mi a&longs;&longs;umptio in motu vniformi, ac perpetuò &longs;ibi æquali<emph.end type="italics"/><pb pagenum="18"/><emph type="italics"/>vera, & nece&longs;&longs;aria &longs;it; in motu tamen accelerato min<gap/>me <lb/>nece&longs;&longs;aria e&longs;t, & non vno modo tantum, &longs;ed pluribus in<lb/>telligi potest, quo modo velocitates &longs;int inter &longs;e, vt emen&longs;a <lb/>&longs;patia: licet eadem &longs;patia neque eodem, neque æquali tem<lb/>pore percurrantur.<emph.end type="italics"/></s><s> Pergis autem, <emph type="italics"/>Vt, &longs;i graue de&longs;cen-<emph.end type="italics"/><lb/><emph type="italics"/>dens per AB tempus quodcumque in&longs;umat, putà qua<lb/><figure id="fig8"></figure><lb/>drantem; ac deinde BC ip&longs;i AB æquale, dimidio <lb/>quadrante percurrat; quis neget in<emph.end type="italics"/> C <emph type="italics"/>duplam ha<lb/>beri velocitatem eius, quæ fuit in B? & tamen <lb/>idem graue totam AC, & dimidium eius AB <lb/>non percurreret.<emph.end type="italics"/></s><s> Et hæc e&longs;t quidem tota tua ad <lb/>conuincendum paralogi&longs;mi Galileum proba<lb/>tio, ob quam continenter hæc verba &longs;ubiun<lb/>gis: <emph type="italics"/>A&longs;&longs;umptio igitur Galilei fal&longs;a e&longs;t, & tota eius <lb/>ratiocinatio merus Paralogi&longs;mus id óque nullo modo, vt ip&longs;e <lb/>gloriatur communem, &longs;anioremque aliorum &longs;en&longs;um erroris <lb/>reuincit, qui in naturali grauium de&longs;cen&longs;u volunt æqualibus <lb/>spatijs æqualia velocitatis momenta acquiri.<emph.end type="italics"/></s><s> An verò pa<lb/>tietur tua bonitas, &longs;i dicam po&longs;&longs;e cuipiam videri, e&longs;&longs;e <lb/>te potiùs, qui hoc loco incidas in paralogi&longs;mum? </s>

<s>Ni<lb/>mirum videris &longs;ic argumentari, vt id, quod contro<lb/>uertitur, a&longs;&longs;umas pro principio, dum nihil aliud, quàm <lb/>&longs;upponis &longs;patium AB, percurri duplo temporis, quo <lb/>&longs;patium BC; & velocitatem in C, e&longs;&longs;e duplam eius, <lb/>quæ fuit in B; quæ ip&longs;a tamen e&longs;t controuer&longs;ia. </s>

<s>Et <lb/>cùm &longs;oluenda e&longs;&longs;et ratio, qua conficitur fore, vt AC <lb/>percurratur eodem, aut æquali tempore, quo &longs;patium <lb/>AB, nihil aliud, quam conclu&longs;ionem negas, fore di<lb/>cendo, vt idem graue totam AC, & dimidium eius <lb/>AB eodem tempore non percurreret. </s>

<s>Teneri certè <pb pagenum="19"/>videbaris ad vberiorem paralogi&longs;mi detectionem, <lb/>&longs;olutionemque, cùm &longs;i i&longs;ta quidem methodus &longs;uffi<lb/>ciat, nihil e&longs;&longs;e videatur facilius, quàm paralogi&longs;mi ar<lb/>guere vniuer&longs;um Euclidem. </s>

<s>Et agno&longs;co quidem te <lb/>&longs;upponere tanquam rem nimis euidentem, totum <lb/>&longs;patium AC prolixiore tempore, quàm eius partem <lb/>AB percurri: &longs;ed cùm Galileus non neget e&longs;&longs;e illud <lb/>tempus prolixius, imò tale e&longs;&longs;e reuerâ &longs;upponat; ab <lb/>incommodo tamen arguit, probando prolixius non <lb/>fore, &longs;i velocitas acqui&longs;ita per totam AC dupla defen<lb/>datur illius, quæ acquiritur per totam AB: vnde & <lb/>videtur omnmò obiecta ratio fui&longs;&longs;e &longs;oluenda. </s>

<s>Agno&longs;co <lb/>etiam te heinc moueri, quòd non &longs;atis appareat ratio, <lb/>cur &longs;i ex A in B acquiratur vnus velocitatis gradus, <lb/>acquiri alius ex B in C, per&longs;euerante primo, non <lb/>valeat. </s>

<s>Sed cau&longs;&longs;a nimirùm intelligitur non modò <lb/>ex dictis in vulgarem definitionem; verùm etiam <lb/>maximè ex incommodo, in quod aliunde incidis, <lb/>dum con&longs;equenter loquens, vis &longs;patium BC percurri <lb/>dimidio temporis, quo AB; vt putà, quod AB vnico <lb/>gradu velocitatis BC, gemino percurratur. </s>

<s>XII. Nam, vt illud paucis deducam, &longs;equitur <lb/>exinde, vt tempore dato, quo decur&longs;a &longs;emel fuerit <lb/>pars AB, tempus aliud ip&longs;i æquale attingi nulla ra<lb/>tione valeat, ni&longs;i &longs;uperato &longs;patio infinito. </s>

<s>Intelliga<lb/>tur enim linea AC infinitè producta, diui&longs;aque in <lb/>parteis CD, DF, EF, &c. </s>

<s>ip&longs;is AB & BC <lb/>æqualeis. </s>

<s>Qua ratione tu vis tempus, quo percurri<lb/>tur AB, e&longs;&longs;e duplum temporis, quo percurritur BC <lb/>velis oportet tempus id, quo percurritur BC e&longs;&longs;e <pb pagenum="20"/>duplum temporis, quo percurritur CD, & hoc <lb/><figure id="fig9"></figure><lb/>duplum eius, quo DE, & i&longs;tud illius, quo EF, <lb/>& &longs;ic deinceps; neque enim maior vnius, <lb/>quàm alterius e&longs;t ratio; ac in accelerato poti&longs;<lb/>&longs;imù n æquabiliter motu, de quo præ&longs;ertim <lb/>quæ&longs;tio heic e&longs;t. </s>

<s>Quare & velis etiam opor<lb/>tet, vt cùm tempus, quo percurritur BC, &longs;it <lb/>dimidium temporis, quo percurritur AB; illud, <lb/>quo percurritur CD, &longs;it quadrans eiu&longs;dem <lb/>primi temporis; illud, quo DE, octans; quo <lb/>EF, pars decima &longs;exta; quo FG, trige&longs;ima &longs;e<lb/>cunda; quo GH &longs;exage&longs;ima quarta, &c. </s>

<s>Por<lb/>rò hæc omnia tempora &longs;imul iuncta nunquam <lb/>æquabuntur primo tempori, quo decur&longs;um <lb/>fuerit AB (quandò procedentes hoc modo <lb/>fractiones relinquunt &longs;emper ex integro, to<lb/>tove quidpiam inexhau&longs;tum) ni&longs;i lineam, &longs;eu <lb/>&longs;patium infinitum admi&longs;eris, & parteis æqua<lb/>leis in eo infinitas, quæ infinitis analogis (&longs;eu <lb/>dimidiorum dimidiis in tempore ip&longs;o, aut <lb/>æquali, quo AB percurritur) contineri intel<lb/>lectis, re&longs;pondeant. </s>

<s>Adderem heic etiam <lb/>incommodum aliud de &longs;patijs incre&longs;centibus, <lb/>& in fine cuiu&longs;libet æqualis temporis numerandis <lb/>&longs;ecundum rationem non modò duplam, verùm etiam <lb/>triplam, & ampliùs: &longs;ed res erit po&longs;teà vberiùs dicen<lb/>da. </s>

<s>Adderem rursùs alia quoque, vt Quòd &longs;equere<lb/>tur lineam proiectorum, & illam &longs;peciatim, quæ de&longs;<lb/>cribitur à lapide &longs;ur&longs;um, & &longs;ecundum mali altitudi<lb/>nem, dum nauis mouetur, proiecto, non e&longs;&longs;e Parabo-<pb pagenum="21"/>licam, neque tantum temporis, ex&longs;cendendo, quan<lb/>tum a&longs;cendendo con&longs;umi; ac proinde lapidem illum <lb/>neque peruenturum ad mali carche&longs;ium, neque reca<lb/>&longs;urum in pedem eiu&longs;dem: verùm i&longs;ta aut colliguntur <lb/>ex ijs, quæ &longs;unt dicta in Epi&longs;tolis, aut in promptu <lb/>&longs;unt, facileque occurrunt. </s>

<s>Et de Definitione huc<lb/>v&longs;que. </s>

<s><emph type="center"/><emph type="italics"/>De Po&longs;tulato Galilei circa Motum &longs;uper æquè altis, non <lb/>æquè inclinatis planis.<emph.end type="italics"/><emph.end type="center"/></s>

<s>In&longs;ectaris &longs;ecundo loco, tanquam aliam <lb/>erroris cau&longs;&longs;am, Quod Galileus &longs;ibi dari, & gratis <lb/>concedi, inquis, po&longs;tulat, <emph type="italics"/>Gradus velocitatis eiu&longs;dem <lb/>mobilis &longs;uper diuer&longs;as planorum inclinationes acqui&longs;itos tunc <lb/>e&longs;&longs;e æqualeis, cùm eorumdem planorum eleuationes ponuntur<emph.end type="italics"/><lb/><emph type="italics"/>æquales;<emph.end type="italics"/> hoc e&longs;t gradus velo<lb/><figure id="fig10"></figure><lb/>citatis ab eodem globo (exem<lb/>pli gratia) per plana CA, & <lb/>CD de&longs;cendente, in punctis <lb/>A, & D acqui&longs;itos, e&longs;&longs;e inter &longs;e <lb/>æqualeis, quòd æqualem, vel potiùs eandem eleua<lb/>tionem habeant, videlicet BC. <emph type="italics"/>Hoc enim po&longs;tula<lb/>tum,<emph.end type="italics"/> inquis, <emph type="italics"/>cùm neque ex terminis notum &longs;it, neque vlla <lb/>&longs;ufficiente experientia confirmatum; imò cùm rationes etiam <lb/>non de&longs;int, quibus oppo&longs;itum probabilius reddatur (nempe <lb/>gradus velocitatis per longius planum acqui&longs;itos gradi<gap/>us <lb/>per breuius planum acqui&longs;itis e&longs;&longs;e minores) id à Galileo non <lb/>peti, &longs;ed debuerat demon&longs;trari cùm præ&longs;ertim maxima pars <lb/>&longs;ub&longs;equentium theorematum hoc vnico postu ato nitantur. <lb/></s>

<s>Quid enim certi ex incertis concludi pote&longs;t. </s>

<s>aut ex principie,<emph.end type="italics"/><pb pagenum="22"/><emph type="italics"/>vt ip&longs;emet<emph.end type="italics"/> G<emph type="italics"/>alileus agno&longs;cit, veri&longs;imili tantum, ac probabili <lb/>demonstrari?<emph.end type="italics"/> Po&longs;tmodùm autem, vbi hæc præmi&longs;i&longs;ti, <lb/><emph type="italics"/>In &longs;cientiarum, ac demon&longs;trationum principiis euidentiam <lb/>exigimus, &longs;u&longs;piciones, ac veri&longs;imilitudines nulla ratione ad<lb/>mittimus,<emph.end type="italics"/> &longs;ubdis, <emph type="italics"/>Porrò quæ ex his con&longs;equuntur, aut <lb/>inferuntur theoremata, &longs;uis illis principiis certiora, aut eui<lb/>dentiora e&longs;&longs;e non po&longs;&longs;unt, & nominatim &longs;olemne illud, & <lb/>quod totius &longs;cientiæ à Galileo excogitatæ firmamentum est, <lb/>spatia &longs;cilicet æqualibus temporibus emen&longs;a eam inter &longs;e <lb/>rationem ob&longs;eruare, quæ est inter numeros omneis impareis <lb/>continua &longs;erie ab vnitate procedenteis (quamvis aliunde <lb/>fal&longs;um demon&longs;trari non po&longs;&longs;et) neque ex præ&longs;uppo&longs;itis illis <lb/>principiis euidenter, neque aliunde &longs;ufficienter conclude<lb/>retur.<emph.end type="italics"/></s>

<s>Hoc autem loco non video primùm, quì <lb/>reprchendendus Galileus &longs;it, &longs;i quam propo&longs;itionem <lb/>non demon&longs;tratam, &longs;ed veri&longs;imilem &longs;olùm habuit, <lb/>non vt demon&longs;tratam, &longs;ed vt veri&longs;imilem duntaxat <lb/>exhibuit. </s>

<s>Candidè nimirùm videtur egi&longs;&longs;e, neque <lb/>exegi&longs;&longs;e à Lectoribus, vt maiorem, quàm ip&longs;e Po&longs;tu<lb/>lato fidem haberent; &longs;ed illos potius qua&longs;i monui&longs;&longs;e, <lb/>ne ip&longs;um concederent, ni&longs;i deinceps agno&longs;cerent <lb/>con&longs;tabilitum variis ex eo deductis conclu&longs;ionibus, <lb/>quæ cum experientia planè con&longs;entirent. </s>

<s>Deinde <lb/>cùm in &longs;cientijs, ac demon&longs;trationibus attinent bus <lb/>ad Mathe&longs;in puram, mera euidentia, non &longs;ola &longs;u&longs;pi<lb/>cio, aut veri&longs;imilitudo admittenda &longs;it: in &longs;cientijs ta<lb/>men Phy&longs;icis, ac mi&longs;ta Mathe&longs;i, quacumque &longs;e&longs;e Phy<lb/>&longs;ica, hoc e&longs;t caligo humanæ mentis in rebus natura<lb/>libus inue&longs;tigandis, ingerit; f&oelig;lices &longs;imus, &longs;i non <pb pagenum="23"/>euidentiam, &longs;ed veri&longs;imilitudinem a&longs;&longs;equamur. </s>

<s>Vnde <lb/>& videtur po&longs;&longs;e Po&longs;tulatum, &longs;i veri&longs;imile modò &longs;it, ac <lb/>neque ratione, neque experientia vlla oppugnetur, ad<lb/>mitti ad &longs;cientiam, quæ vtcúmque perfecta ab&longs;olutè <lb/>non &longs;it, eiu&longs;modi tamen &longs;it, cuius &longs;it humana imbe<lb/>cillitas capax. </s>

<s>Ad hæc, addam-ne fui&longs;&longs;e rem mihi <lb/>quodammodò &longs;tupendam, acce&longs;&longs;i&longs;&longs;e ca&longs;u ad me i&longs;ta <lb/>con&longs;cribentem, nobili&longs;&longs;imum Senatorem Petrum <lb/>Calcauium virum omninò promouendis bonis arti<lb/>bus comparatum, puræque cum-primis Mathe&longs;eos <lb/>&longs;tudio&longs;i&longs;&longs;imum; ac vi&longs;a mihi præ manibus tua Di&longs;&longs;er<lb/>tatione, argumentóque cognito, innui&longs;&longs;e tran&longs;mi&longs;<lb/>&longs;um in hanc vrbem exemplum editi nuperrimè Libri <lb/>ab Euangeli&longs;ta Torricellio, qui Galilei &longs;ucce&longs;&longs;or exi<lb/>mius demon&longs;trauerit in eo i&longs;tud Po&longs;tulatum? </s>

<s>Præ<lb/>tereo autem, vt copiâ illius videndi &longs;tatim impetratâ, <lb/>deprehenderim rem confectam quinque propo&longs;itio<lb/>nibus, ac Præmi&longs;&longs;o illo, <emph type="italics"/>Non po&longs;&longs;e duo<emph.end type="italics"/> G<emph type="italics"/>rauia &longs;imul <lb/>iuncta ex &longs;e moueri, ni&longs;i centrum commune grauitatis ip&longs;o<lb/>rum de&longs;cendat.<emph.end type="italics"/></s><s> Videlicet prima Propo&longs;itio e&longs;t, <lb/>G<emph type="italics"/>rauia in planis inæqualiter inclinatis, ac eandem tamen <lb/>eleuationem habentibus, con&longs;tituta: &longs;i eandem inter &longs;e ratio<lb/>nem homologè habeant, quam habent planorum longitudi<lb/>nes, habere æqualia momenta.<emph.end type="italics"/></s><s> Secunda, <emph type="italics"/>Eadem grauia &longs;i <lb/>æqualia fuerint, habere momenta in ratione reciproca longi<lb/>tud num eorumdem planorum.<emph.end type="italics"/></s><s> Tertia, <emph type="italics"/>Illa <expan abbr="æquali&utilde;">æqualium</expan> grauium <lb/>momenta e&longs;&longs;e in ratione homologa cum perpendiculis par<lb/>tium æqualium eorumdem planorum.<emph.end type="italics"/></s><s> Quarta, <emph type="italics"/>Tempora <lb/>la<gap/>i<gap/>um ex quiete e&longs;&longs;e homologè vt longitudines eorum<lb/>dem planorum.<emph.end type="italics"/></s><s> Quinta autem e&longs;t ip&longs;um Po&longs;tulatum <pb pagenum="24"/>ex &longs;uperioribus deductum, G<emph type="italics"/>radus velocitatis eiu&longs;dem <lb/>mobilis &longs;uper diuer&longs;as planorum inclinationes acqui&longs;itos tunc <lb/>e&longs;&longs;e æqualeis, cùm eorumdem planorum eleuationes &ecedil;quales <lb/>&longs;unt.<emph.end type="italics"/></s>

<s>XV. Verùm, ne ad alia excurram, quàm quæ <lb/>ip&longs;emet ex Galileo commemoras, improbas ec<gap/>e ex<lb/>perimentum, quo ille e&longs;t conatus h<gap/>em Po&longs;tulato <lb/>a&longs;&longs;erere, quodque ad&longs;cripta figura &longs;ic refers E <emph type="italics"/>clauo A<emph.end type="italics"/><lb/><figure id="fig11"></figure><lb/><emph type="italics"/>parieti infixo, globus plumbeus, aut alius quilibet tenui filo, <lb/>tribus, aut quatuor digitis à pariete remoto &longs;u&longs;pendatur, &longs;it<lb/>que AB, De&longs;criptaque in pariete recta CD horizonti <lb/>parallela, globus B à perpendiculari eductus v&longs;que ad alti<lb/>tudinem rectæ CD manu altollatur, nempe ad C; indeque <lb/>liberè dimittatur. </s>

<s>Tum globus idem in uit<emph.end type="italics"/> G<emph type="italics"/>alileus, non <lb/>&longs;olùm de&longs;cendet ad punctum B, &longs;ed eodem impetu vlteriùs <lb/>v&longs;que ad D, aut proximè ad illud, a&longs;cendet.<emph.end type="italics"/> S<emph type="italics"/>imiliter, &longs;i <lb/>globus idem è puncto E &longs;uspendatur, & item ad altitudinem<emph.end type="italics"/><pb pagenum="25"/><emph type="italics"/>eiu&longs;dem rectæ<emph.end type="italics"/> C<emph type="italics"/>D attollatur ad<emph.end type="italics"/> G, <emph type="italics"/>inde liberè dimi&longs;&longs;us, <lb/>pari modo ad eandem rectam CD, aut proximè ad eam <lb/>con&longs;cendet ver&longs;us H. Jmò, &longs;i ex F &longs;u&longs;pen&longs;us attollatur ad <lb/>I, inde feretur, v&longs;que ad K. </s>

<s>Per diuer&longs;os igitur illos arcus <lb/>decidens globus, &longs;emper ad æqualem altitudinem con&longs;cendit. <lb/></s>

<s>Ergo è quolibet de&longs;cen&longs;u æqualem acquirit impetum; ni&longs;i <lb/>enim e&longs;&longs;et impetus æqualis, globum ad æqualem altitudinem <lb/>non attolleret. </s>

<s>Quid ni igitur idem quoque faciat globus, <lb/>&longs;i per plana CB, GB, IB de&longs;cendat?<emph.end type="italics"/> C<emph type="italics"/>redibile igitur <lb/>etiam e&longs;t globum per illa, aut &longs;imilia plana decidentem, æqua<lb/>lem tali de&longs;cen&longs;u impetum, ac proinde æqualem quoque ve<lb/>locitatis gradum acquirere.<emph.end type="italics"/></s><s> Subinde autem, vt o&longs;ten<lb/>das quàm hæc &longs;int incerta, incohæcentia, &c. <emph type="italics"/>Impri<lb/>mis quidem ne&longs;cio,<emph.end type="italics"/> inquis, <emph type="italics"/>an globi ea, qua vult<emph.end type="italics"/> G<emph type="italics"/>alileus <lb/>ratione &longs;u&longs;pen&longs;i, ac librati alitùs in Etruria, quàm in Gal<lb/>lia a&longs;&longs;urgant; at heic neque tam propè ad horizontalem li<lb/>neam, neque per diuer&longs;os arcus ad eam æqualiter accedunt. <lb/></s>

<s>Nempe filo pedum quatuor cum dimidio &longs;u&longs;pen&longs;us globus ad <lb/>lineam horizontalem tribus infra centum pedibus <expan abbr="de&longs;criptã">de&longs;criptam</expan>, <lb/>propiùs quàm duobus digitis nunquam acceßit. </s>

<s>At centro <lb/>nouem tantum digitis &longs;upra lineam horizontalem accepto, <lb/>filóque duorum pedum con&longs;tituto, iam globus ad lineam ho<lb/>rizontalem vno digito, quàm anteà propiùs acceßit. </s>

<s>Vbi <lb/>verò centrum &longs;eptem infra lineam horizontalem digitis a&longs;<lb/>&longs;umptum est, vix ad quatuor à linea horizontali digitos <lb/>globus a&longs;cendit.<emph.end type="italics"/></s><s> Concludis idcircò his verbis, <emph type="italics"/>Qua <lb/>igitur fide<emph.end type="italics"/> G<emph type="italics"/>alileus tam a&longs;&longs;eueranter ait globum ita &longs;u&longs;pen<lb/>&longs;um, ac per quo&longs;cumque arcus librarum, ad æqualem &longs;em<lb/>per altitudinem a&longs;&longs;urgere? </s>

<s>aut quomodo ex re adeò euiden<lb/>ter fal&longs;a petere au&longs;us e&longs;t testim<gap/>nium veritatis?<emph.end type="italics"/></s><pb pagenum="26"/>

<s>Imprimis porrò non retices ip&longs;e dictum <lb/>e&longs;&longs;e à Galileo demi&longs;&longs;um ex C globum a&longs;cen&longs;urum <lb/><emph type="italics"/>v&longs;que ad D, aut proxime:<emph.end type="italics"/> vt proinde non videatur di<lb/>ctum ab illo a&longs;&longs;eueranter a&longs;&longs;urrecturum globum <lb/>ad eandem altitudinem, aut veritatis te&longs;timonium <lb/>ex re fal&longs;a ab ip&longs;o peti; qua&longs;i intellexerit globum a&longs;<lb/>&longs;equi altitudinem exqui&longs;itè, &longs;eu præcisè eandem. </s>

<s>Et <lb/>certè non modò dixit ip&longs;e <emph type="italics"/>qua&longs;i,<emph.end type="italics"/> &longs;eu <emph type="italics"/>ferè,<emph.end type="italics"/> ac <emph type="italics"/>&longs;uperfu<lb/>turum interuallum quoddam perexiguum;<emph.end type="italics"/> &longs;ed etiam cau&longs;<lb/>&longs;am attigit, ob quam ita fiat; referens eam putà ad <lb/>impedimentum partim aëris, partim fili; de quo vtro<lb/>que heic dicerem, ni&longs;i iam dictum &longs;atis copiosè in <lb/>Epi&longs;tolis memoratis foret. </s>

<s>Deinde, quód globus ad <lb/>horizontalem lineam propiùs ad H, remotiùs ad <lb/>Ka&longs;cendat, quàm ad ip&longs;um D; videri pote&longs;t cau&longs;&longs;a <lb/>per&longs;picua, neque infringere vim experimenti. </s>

<s>Nam <lb/>quod &longs;pectat quidem ad H, res ideò contin git, quòd <lb/>quoties clauus defigitur inter A, & horizontalem <lb/>lineam, breuitas tum fili, tum &longs;pati<gap/> aërei, per quod <lb/>arcus de&longs;cribitur, minùs præ&longs;tet impedimenti: vnde <lb/>& abfui&longs;&longs;et globus adhûc propiùs, &longs;i fui&longs;&longs;et clauus <lb/>infra E defixus, vti & longiùs, &longs;i &longs;upra ip&longs;um Quod <lb/>verò ad K, res minùs e&longs;t mira; quòd quoties clauus <lb/>defigitur infra horizontalem lineam, dimi&longs;&longs;us ex I <lb/>globus non per totum arcum IB decidat, &longs;ed per <lb/>inferiorem &longs;olùm eius partem, in quam perpendicu<lb/>lariter cadit; vnde & minùs adhûc, minu&longs;que re&longs;i<lb/>lii&longs;&longs;et, &longs;i defixi&longs;&longs;es clauum inferiùs, quou&longs;que globus <lb/>non potui&longs;&longs;et ad lineam attolli; veluti & magis, ma<lb/>gi&longs;que, &longs;i &longs;uperiùs, quou&longs;que clauo defixo in linea, <pb pagenum="27"/>ip&longs;um re&longs;iliendo proximè attigi&longs;&longs;et. </s>

<s>Ex quo effici<lb/>tur, vt cùm res propriè attendenda non &longs;it, vbi cla<lb/>uus infra lineam defigitur, quòd tunc libratio &longs;implex <lb/>non &longs;it, &longs;ed mi&longs;tio duorum motuum, quorum im<lb/>petus &longs;e mutuò retundunt; &longs;it verò propriè atten<lb/>tenda, cùm clauo &longs;upra lineam defixo, vibrationis <lb/>motus &longs;implex e&longs;t; ideò non &longs;it exi&longs;timandum illam <lb/>qualemcumque interuallorum inæqualitatem in<lb/>terturbare negotium; ac poti&longs;&longs;imùm quidem, cùm <lb/>ip&longs;a ordinata &longs;int, ac eandem inter &longs;e, quàm fili, & <lb/>arcus prolixitates proportionem &longs;eruent. </s>

<s>Ad hæc, <lb/>id videtur præ&longs;ertim e&longs;&longs;e ob&longs;eruatione dignum in <lb/>his pendu orum vibrationibus, quòd, Si quatuor di<lb/>&longs;tinctos g obos quatuor di&longs;tinctis filis &longs;ic appendas, <lb/>vt primi longitudo &longs;it vnius, v. </s>

<s>pedis, &longs;ecundi qua<lb/>tuor, tertij nouem, quarti &longs;exdecim; experturus &longs;is, <lb/>vbi omnes dimi&longs;&longs;i &longs;imul fuerint, quartum perfectu<lb/>rum vnam vibrationem eodem tempore, quo ter<lb/>tius interim perfecerit duas, &longs;ecundus treis, & primus <lb/>quatuor. </s>

<s>Scilicet exinde intelligitur, tum pendulo<lb/>rum vibrationes tantò &longs;egnius fieri, quantò earum <lb/>arcus planiores, &longs;iue inclinatiores &longs;unt; tum inclina<lb/>tiones arcuum men&longs;uratas &longs;ecundum varias perpen<lb/>diculi, &longs;eu fili longitudines, habere &longs;e perinde vt qua<lb/>drata temporum, ac vibrationes habere &longs;e recipro<gap/><lb/>vt ip&longs;as radices; &longs;icque rem eximiè quadrare ad &longs;u<lb/>periùs expo&longs;itam motus æquabilis rationem; tum <lb/>globum quartum non acquirere impetum ad eleua<lb/>tionem nece&longs;&longs;arium, ni&longs;i tempore duplo tertij, tri<lb/>plo &longs;ecundi, quadruplo primi; ac e&longs;&longs;e quidem im-<pb pagenum="28"/>petus omnium globorum inter &longs;e æqualeis; &longs;ed <expan abbr="quõ">quom</expan> <lb/>tempore impetus exprimitur à quarto &longs;emel, exprimi <lb/>à tert<gap/>o bis, à &longs;ecundo ter, à primo quater, &c. </s>

<s>Quod attinet autem ad comparationem <lb/>arcuum CB, GB, IB, cum ip&longs;is planis punctim <lb/>notatis inter extrema eadem; tu &longs;ic in&longs;tas, vt licet <lb/>totum id e&longs;&longs;e verum concederetur, quod dicitur de <lb/>impetu globi per diuer&longs;os arcus librati, vrgeas <emph type="italics"/>aliam <lb/>e&longs;&longs;e rationem, aut meritò &longs;altem videri po&longs;&longs;e aliam,<emph.end type="italics"/> de&longs;<lb/>cendentis globi per diuer&longs;a plana. </s>

<s>G<emph type="italics"/>lobus enim,<emph.end type="italics"/> in<lb/>quis, <emph type="italics"/>per aërem &longs;emper toto &longs;uo pondere deorsùm nititur, <lb/>& eatenus &longs;olum eius de&longs;cen&longs;us interturbatur, quatenus à <lb/>recto, & perpendiculari cur&longs;u ad circularem cogitur, at<lb/>que adducitur: at præter impedimentum ex varia plano<lb/>rum inclinatione, adhûc maius, dum globus etiam magis <lb/>à perpendiculari de&longs;cen&longs;u di&longs;trahitur; tantò minoribus in<lb/>&longs;uper momentis globus per planum de&longs;cendit, quan ò mi<lb/>nùs accliue fuerit, vt facilè omnibus notum e&longs;t.<emph.end type="italics"/></s><s> Verùm <lb/>non video quî id concludas; quatenùs non a&longs;&longs;umis <lb/>planum, quantò minùs decliue e&longs;t, tantò e&longs;&longs;e quo<lb/>que prolixius. </s>

<s>Etenim notum quidem e&longs;t acquiri <lb/>minores velocitatis gradus in minus decliui, quod <lb/>&longs;it decliuiori æquale, at, &longs;i vt minùs decliue, ita etiam <lb/>prolixius &longs;it, notum quoque e&longs;t velocitatem in fine <lb/>illius quæ&longs;itam e&longs;&longs;e po&longs;&longs;e æqualem velocitati in fine <lb/>decliuioris acqui&longs;itæ, prolixitate nempe de&longs;cen&longs;us par<lb/>uitatem incrementorum velocitatis compen&longs;ante. <lb/></s>

<s>Interim autem æqualitas impetus in B acqui&longs;iti, &longs;iue <lb/>per arcum, &longs;iue per planum contingat globi delap&longs;io, <lb/>ex eo videtur con&longs;equi, quòd &longs;ilum &longs;upernè globum <pb pagenum="29"/>cohibens aliud nihil præ&longs;tare videatur, quam præ&longs;ta<lb/>ret infernè, & &longs;ine filo arcus marmoreus, aut <gap/>igneus <lb/>perfectè po<gap/>itus, qui e&longs;&longs;et CB, &longs;i &longs;upra ip&longs;um dela<lb/>beretur. </s>

<s>Atque id quidem tantò magis, quantò idem <lb/>Galileus o&longs;tendit arcum CB, & planum CB eodem, <lb/>&longs;eu æquali tempore percurri; ac pari modo arcum, <lb/>& planum GB, & porrò arcum quemlibet non ma<lb/>iorem quadrante cum plano vnà terminato. </s>

<s>Quin<lb/>etiam cùm o&longs;tenderit percurrere globum eodem, &longs;eu <lb/>æquali tempore quoduis planum inter quodlib<gap/>t cir<lb/>cumferentiæ circuli punctum, & infimum punctum, <lb/>quale e&longs;t heic B, con&longs;titutum, vt putà &longs;emper exæ<lb/>quato illi tempori, quo percurritur diameter circuli <lb/>eiu&longs;dem perpendicularis; elicitur quoque exinde, vbi <lb/>ea omnia plana fuerint in eandem reducta altitudi<lb/>nem, diuer&longs;a quidem tempora fore, &longs;ed impetum <lb/>nihilominùs parem. </s>

<s>Atque eadem quidem o&longs;tendit <lb/>præ larus vir Ioannes Bapti&longs;ta Balianus Genuen&longs;is, <lb/>edito hac dere libello, qui eodem ip&longs;o anno, quo Ga<lb/>lilei Liber prodijt, argumento &longs;umpto ab ip&longs;is pen<lb/>dulorum vibrationibus: &longs;ed, vt præmonui, nihil e&longs;t <lb/>nece&longs;&longs;e maiorem Galilei Po&longs;tulato a&longs;&longs;erere fidem, <lb/>quàm ip&longs;e a&longs;&longs;ertam voluerit; dum eatenùs &longs;olùm <lb/>adhibendam petijt, quatenus deductæ ex eo conclu<lb/>&longs;iones cum experientia con&longs;entirent. </s>

<s>XVIII. </s>

<s>Id prætereo, quod &longs;ub<gap/>icis, ex a&longs;cen&longs;u <lb/>globi ad eandem altitudinem, non &longs;atis rectè colli<lb/>gi impetus æqualitatem; quoniam id aduer&longs;<gap/>tur <lb/>recitandæ tuæ rationi, atque experientiæ: vti & dum <lb/>cau&longs;&longs;am petis ex eo, <emph type="italics"/>quòd, quò circulus minor e&longs;t, <gap/><emph.end type="italics"/><pb pagenum="30"/><emph type="italics"/>de&longs;cen&longs;us procliuior, faciliorque, & a&longs;cen&longs;us difficilior vi<lb/>deatur:<emph.end type="italics"/> id repugnaret tum compen&longs;ationi, aduer&longs;us <lb/>quam nihil obiicis, inter breuitatem, & decliu<gap/>ta<lb/>tem &longs;patij; tum familiari experientiæ de rebus deor<lb/>sùm impactis, quæ impetu pari deicctæ tantò emer<lb/>gunt altiùs, quantò incidentia e&longs;t magis perpendi<lb/>cularis. </s>

<s>Attingo ergo potiùs id, quod &longs;upere&longs;t, <lb/>dum id &longs;ugillas, quod Galileus &longs;e e&longs;&longs;e &longs;æpiùs exper<lb/>tum ait, <emph type="italics"/>tum globum ferreum per aërem cadentem, tum <lb/>globum æneum per excauatum in longiore tigillo alueolum, <lb/>in quacumque tigilli &longs;upra horizontem eleuatione de&longs;cenden<lb/>tem, perpetuò tantum præcisè temporis in de&longs;cen&longs;u per pri<lb/>mum totius percurrendi spatij quadrantem, quantum in <lb/>trium reliquorum decur&longs;u in&longs;ump&longs;i&longs;&longs;e: ex quo &longs;ine dubio con<lb/>&longs;equens e&longs;&longs;et, &longs;patia æqualibus temporibus decur&longs;a in ea <lb/>e&longs;&longs;e ratione, quæ reperitur inter numeros impareis ab vnita<lb/>te procedenteis.<emph.end type="italics"/></s><s> Nimirùm, vt o&longs;tendas ea, quæ ex i&longs;tis <lb/>qua&longs;i principiis con&longs;equuntur, aut inferuntur, e&longs;&longs;e ip<lb/>&longs;is certiora, aut cuidentiora non po&longs;&longs;e: <emph type="italics"/>Id,<emph.end type="italics"/> inquis, <emph type="italics"/>tot <lb/>erroribus obnoxium e&longs;t, & exploratu adcò difficile, vt nihil <lb/>inde certi concludi po&longs;&longs;e videatur.<emph.end type="italics"/></s><s> Enimverò, vtcum<lb/>que experiundi modus difficilis &longs;it, obnoxiu&longs;que er<lb/>roribus; non idcircò tamen experimentum conuin<lb/>citur fal&longs;um. </s>

<s>Tuum certè illud de Libra, cui totus <lb/>po&longs;teà inniteris, quot quæ&longs;o, vel te deducente, er<lb/>roribus obnoxium e&longs;t? </s>

<s>quàm exploratu difficile? </s>

<s>& <lb/>ip&longs;um tamen fal&longs;um non habes? </s>

<s>Cùm profectò illo <lb/>te&longs;tetur &longs;e &longs;altem centies rem explora&longs;&longs;e, & experi<lb/>mentum &longs;emper ita &longs;ucce&longs;&longs;i&longs;&longs;e, vt vix vlla vnquam <lb/>differentiola interce&longs;&longs;erit; videri pote&longs;t non e&longs;&longs;e tua <pb pagenum="31"/>&longs;atis idonea refutatio, ni&longs;i te&longs;teris te e&longs;&longs;e rem, aliquo<lb/>ties &longs;altem, accurati&longs;&longs;imè expertum, ac ip&longs;am fal&longs;am <lb/>deprehendi&longs;&longs;e: aut rationem certè congruam afferas, <lb/>qua impo&longs;libilem demon&longs;tres. </s>

<s>Et tamen, neque te <lb/>vel &longs;emel ip&longs;am explora&longs;&longs;e, fal&longs;amque comperi&longs;&longs;e di<lb/>cis, neque vllam rationem profers: &longs;ed cau&longs;aris &longs;olum<lb/>modo explorandi difficultatem; quam & repetis, <lb/>dum po&longs;tquam retuli&longs;ti tempora ab illo notata, no<lb/>tatis nempe, expen&longs;i&longs;que ponderibus aquæ, quæ è <lb/>clep&longs;ydra interim fluxi&longs;&longs;et: <emph type="italics"/>Quippe nemo,<emph.end type="italics"/> inquis, <emph type="italics"/>non <lb/>videt, quàm hic ob&longs;eruandi modus incertus &longs;it, & quàm <lb/>difficile, ne dicam impoßibile, tempus vtriu&longs;que illius de&longs;<lb/>cen&longs;us ad exactam men&longs;uram exigere, vel eo maximè no<lb/>mine, quòd in tanta celeritate initia, & fines horum mo<lb/>tuum &longs;atis præcisè aduerti, notarique po&longs;&longs;e non videantur.<emph.end type="italics"/><lb/>Sed nihil e&longs;t opus in&longs;i&longs;tam ad arguendum id non <lb/>&longs;ufficere; ni&longs;i aliunde aut resfactu impo&longs;&longs;ibilis de<lb/>mon&longs;tretur; aut ob&longs;eruator probetur fui&longs;&longs;e malæ fidei, <lb/>ac indiligens, & difficultates præcauere ne&longs;cius. </s>

<s>Ad<lb/>derem quemadmodum ip&longs;e rem explorare fuerim <lb/>conatus, tum dimi&longs;&longs;o per aërem globo, tum dela<lb/>bente globulo per tubulos vitreos etiam orgyiis dua<lb/>bus longiores, facto&longs;que nunc magis, nunc minùs de<lb/>cliueis, & adnotatis partibus æquis tum ad parietem, <lb/>&longs;ecundum quem globus decideret, tum ad vtram<lb/>que oram alueoli in tigno excauati, & tubulum quem<lb/>que continentis; ac &longs;imul adhibitis &longs;ociis, qui adno<lb/>tarent &longs;inguli parteis &longs;ingulas, quæ interim pertran<lb/>&longs;irentur, dum ip&longs;e temporis momenta nunc pul&longs;atio<lb/>nibus arteriæ, nunc itibus, reditibu&longs;que penduli di-<pb pagenum="32"/>&longs;tincta, vocibus mono&longs;yllabis cuique illorum &longs;igilla<lb/>tim a&longs;&longs;ignatis &longs;igni&longs;icarem: verùm memini rem ad te <lb/>per&longs;criptam; & circa hæc nimius iam &longs;um. </s>

<s><emph type="center"/><emph type="italics"/>De Experimentis circa ictum, impetumue grauium caden<lb/>tium, ad explorandum impetus-ne vt &longs;patium incre&longs;cat.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Venio igitur ad Po&longs;terius caput, &longs;ecun<lb/>damue partem tuæ Di&longs;&longs;ertationis; in qua &longs;cilicet re<lb/>cepi&longs;ti te veram, ac certam de Motu accelerato &longs;cien<lb/>tiam fal&longs;æ, ac incertæ Galileanæ &longs;ub&longs;tituturum; & in <lb/>qua profe&longs;&longs;us te iterùm omnia, quæ ab illo con&longs;cri<lb/>pta &longs;unt, fal&longs;a, ac inania e&longs;&longs;e demon&longs;traturum; prouo<lb/>cas me primum ad <emph type="italics"/>clara, facilia, indubitata experimenta:<emph.end type="italics"/><lb/>tamet&longs;i ego tenuitatis con&longs;cius per&longs;onam Arbitri, lu<lb/>dici&longs;que, quam mihi humani&longs;&longs;imè iteratò defers, re<lb/>cu&longs;o; iteratò profe&longs;&longs;us nihil aliud à me, quàm rationes <lb/>qua&longs;dam dubitandi ex&longs;pectari po&longs;&longs;e. </s>

<s>Et <emph type="italics"/>prima qui<lb/>dem experientia petitur,<emph.end type="italics"/> inquis, <emph type="italics"/>ex impetu, quo globus, <lb/>aut graue aliud corpus quodcumque per aërem sponte natu<lb/>ræ deorsùm cadit, ac percutit. </s>

<s>Indubitatum enim e&longs;t,<emph.end type="italics"/><lb/>pergis, <emph type="italics"/>quod ip&longs;emet<emph.end type="italics"/> G<emph type="italics"/>alileus paßim agno&longs;cit, tantam præ<lb/>ci&longs;e percutientis corporis e&longs;&longs;e velocitatem, quantus impetus, <lb/>quantaque ip&longs;a percußio fuerit. </s>

<s>Impetus enim omnis, & <lb/>percußio ex velocitate est; imò impetus ip&longs;e velocitas est, <lb/>nulloque hæc abinuicem di&longs;crimine dirimuntur, vt meritò, pro<lb/>inde, qua ratione accre&longs;cit velocitas, eadem impetus, & per<lb/>cußio augeantur.<emph.end type="italics"/></s><s> Hactenus nihil e&longs;t, quod non probem. <lb/></s>

<s>Pro&longs;equeris autem: <emph type="italics"/>At facilè experientiâ con&longs;tat corpus <lb/>graue quodcumque ex qualibet altitudine per aërem cadens, <lb/>& percutiens, vt libet, perpetuò ex altitudine dupla duplo<emph.end type="italics"/><pb pagenum="33"/><emph type="italics"/>præcisè ampliùs, & ex tripla, quadrupláue di&longs;tantia, triplo, <lb/>quadruplóue fortiùs percutere: velocitas igitur quoque ex <lb/>altitudine dupla, duplò maior e&longs;t, & tripla, aut quadrupla, <lb/>&longs;i tripla, quadrupláue altitudo &longs;uerit: ac proinde velocitas, <lb/>spatiis æqualibus, non autem æqualibus temporibus, æqualia <lb/>momenta acquirit.<emph.end type="italics"/></s><s> Quæ&longs;o verò heic patere, religio&longs;i&longs;<lb/>&longs;imè Vir, me meam te&longs;tari h<gap/> betudmem; neque enim <lb/>quod tu a&longs;&longs;umis, <emph type="italics"/>facilè experientiâ con&longs;tare,<emph.end type="italics"/> mihi vllà <lb/>prorsùs experientiâ con&longs;tat; neque tu vllam &longs;pecia<lb/>lem affers, ex qua res, vt tibi, ita mihi con&longs;tet. </s>

<s>Ac <lb/>deducis quidem deinceps, qua&longs;i &longs;ecundam experien<lb/>tiam, id, quod in Libra expertus es: &longs;ed interim circa <lb/>hanc primam, cæcutio planè, neque agno&longs;co, qui <lb/>rem facilè exploraris. </s>

<s>Et explora&longs;&longs;e tamen quis hæ<lb/>reat, quandò i&longs;thæc &longs;ubi<gap/>cis? <emph type="italics"/>Experientiam hanc Ga<lb/>lileus, nullo (vt credibile e&longs;t) facto ip&longs;ius periculo, tanquam <lb/>fal&longs;am, atque impoßibilem, eodem paralogi&longs;mo re-<emph.end type="italics"/><lb/><figure id="fig12"></figure><lb/><emph type="italics"/>iecit, quo definitionem motus accelerati vulgò re<lb/>ceptam, & ex eadem experientia &longs;ine dubio dedu<lb/>ctam, conatus e&longs;t reuellere. </s>

<s>Si ex altitudine dupla, <lb/>inquit, duplò maior percußio e&longs;t, vt puta ex A du<lb/>pla eius, quæ ex B, erit & velocitas dupla. </s>

<s>At <lb/>velocitas dupla e&longs;&longs;e non pote&longs;t, ni&longs;i graue, æquali, <lb/>imò eodem tempore, totum spatium AC, & di <lb/>midium eius AB percurrat, quod tamen e&longs;t impoßibile. <lb/></s>

<s>Nec percußio igitur, nec velocitas dupla e&longs;t, ex altitudine <lb/>dupla Do<gap/>eo equidem virum non ignobilem, in re tam <lb/>obuta, & facili adeò turpiter delu&longs;um e&longs;&longs;e; mirorque item <lb/>vehementer tales, támque apertos eius errores, non modò à <lb/>nenune hactenus e&longs;&longs;e reprehen&longs;os, &longs;ed tanquam prima<emph.end type="italics"/><pb pagenum="34"/><emph type="italics"/>&longs;cientiæ principia, à viris etiam eruditis e&longs;&longs;e receptos.<emph.end type="italics"/><lb/>Quandò, inquam, hæc &longs;ubiicis, nemo profectò fa<lb/>cilè hæreat, qum ip&longs;e, expertus, illa videris, quæ <lb/>neque Galileus, neque alij viderunt. </s>

<s>Quod meattinet; cùm lapidem video ex vna, <lb/>ex duabus, ex tribus, ex quatuor orgyiis cadentem in <lb/>terram; agno&longs;co quidem e&longs;&longs;e ictum, atque idcircò <lb/><expan abbr="impet&utilde;">impetum</expan>, velocitatem que maiorem ex duabus orgyiis, <lb/>quàm ex vna, ex tribus, quàm ex duabus, ex quatuor <lb/>quàm ex tribus; verùm e&longs;&longs;e duplò præcisè maiorem <lb/>ex duabus, quàm ex vna, triplò ex tribus, quadruplò <lb/>ex quatuor, nulla penitùs ratione agno&longs;co. </s>

<s>Neque <lb/>enim po&longs;&longs;um id di&longs;picere ex cauitate in terram facta, <lb/>aut penetratione in ip&longs;am; quoniam neque lapis du<lb/>plò profundiùs cauat, penetratque ex dupla altitudine, <lb/>aut triplò ex tripla; neque cognitus e&longs;t aut gradus <lb/>re&longs;i&longs;tentiæ, quo talis terra obnititur; aut progre&longs;&longs;us, <lb/>quo cre&longs;cit re&longs;i&longs;tentia, dum quò inferiùs tenditur, <lb/>eò partes terræ minùs &longs;eu deor&longs;um, &longs;eu in latera ce<lb/>dere, compelli, ac &longs;ubire po&longs;&longs;unt: vt habita proinde <lb/>ratione huius re&longs;i&longs;tentiæ, colligere valeam id, quod <lb/>ad duplam penetrationem ex altitudine dupla dce&longs;t, <lb/>non aliunde e&longs;&longs;e, quàm ex huiu&longs;modi re&longs;i&longs;tentia. </s>

<s>Sic <lb/>cùm video fi&longs;tucam in palum delap&longs;am ex &longs;implici, <lb/>dupla, aut tripla altitudine: quandoquidem neque <lb/>video palum defigi profundiùs in terram, duplo qui<lb/>dem ex dupla, aut triplò ex tripla altitudine; neque <lb/>per&longs;pectum habeo quo gradu, in qualibet profundi<lb/>tatis parte ip&longs;i vrgenti re&longs;i&longs;tatur; aduerto quidem <lb/>maiorem ictum, maioremque impetum, ac veloci-<pb pagenum="35"/>tatem e&longs;&longs;e ex altitudine dupla, quàm ex &longs;implici; item<lb/>que ex tripla, quàm ex dupla, &c. </s>

<s>At e&longs;&longs;e illam du<lb/>plo præcisè maiorem ex dupla, triplò ex tripla, &c. <lb/></s>

<s>nulla penitùs ratione per&longs;picio. </s>

<s>Sic, dum graue <lb/>quoduis ex dupla, triplaue altitudine decidens rem <lb/>&longs;ubiectam commouet, contundit, confringit: Sic, dum <lb/>cadens in cuneum &longs;cindendo ligno accommodatum, <lb/>ip&longs;um compellit, adigit, figit: Sic, dum cadens in ip<lb/>&longs;am manum, aliámue partem corporis, ip&longs;am vrget, <lb/>deprimit, lædit: Sic, dum alia huiu&longs;modi diuer&longs;imo<lb/>dè peraguntur; maiorem quidem &longs;emper ictum, &longs;ine <lb/>impetum, ac velocitatem ex altiore ca&longs;u fieri nullus <lb/>hæreo; at ex ca&longs;u duplò altiore duplò maiorem fieri, <lb/>triplò ex triplo, &c. </s>

<s>qui di&longs;cernam prorsùs non habeo. <lb/></s>

<s>Quocirca bea&longs;&longs;es me valdè, &longs;i experientiam, aut &longs;al<lb/>tem modum experiundi &longs;ubindica&longs;&longs;es; cùm dicas & <lb/>rem experientiâ in graui quocumque facilè con&longs;tare; <lb/>& Galileum, cætero&longs;que eruditos viros coniicis &longs;ic <lb/>fui&longs;&longs;e &longs;ocordeis, vt nullum ip&longs;ius periculum fecerint; <lb/>feci&longs;&longs;e autem eos, qui vulgarem definitionem accele<lb/>rati motus tradiderunt primi. </s>

<s>Addo videri po&longs;&longs;e me non ab&longs;que ratio<lb/>ne hacce de re ambigere; & coniicere ictum, percu&longs;<lb/>&longs;ionemque, atque idcircò impetum, velocitatemque <lb/>maiorem duplò non haberi, ni&longs;i ex altitudine qua<lb/>drupla; triplum, ni&longs;i ex nonupla; quadruplum, ni&longs;i <lb/>ex &longs;exdecupla, atque ita porrò iuxta numerorum qua<lb/>dratorum &longs;eriem. </s>

<s>Nam Primò, &longs;it vas cylindricum <lb/>erectum, & continens aquam ad certam altitudi<lb/>nem, exempli cau&longs;sâ vnius pedis: Certum e&longs;t aquam <pb pagenum="36"/>in fundo &longs;ub&longs;tantem vrgeri, ac premi à &longs;uper ex&longs;tan<lb/>te (& ab ip&longs;a quidem &longs;uperficie) vt per&longs;picuum fit vel <lb/>ex vehementia, qua ex&longs;ilire deprehenditur, forami<lb/>ne ad ba&longs;in aperto. </s>

<s>Aperiatur ergo foramen, & &longs;u<lb/>perfusâ leniter aquâ, ita vt contineatur &longs;emper ad <lb/>eandem altitudinem, excipiatur aqua, quæ interim <lb/>effluet, dato tempore, v. </s>

<s>&longs;extantis minuti, ac &longs;it <lb/>illius men&longs;ura certa, exempli gratiâ, congius. </s>

<s>Vt <lb/>deinde tempore eodem, & per idem foramen ex&longs;i<lb/>liant duo congij, & aqua proinde &longs;it duplò compre&longs;<lb/>&longs;ior, ad quam nam v&longs;que altitudinem adaugendus <lb/>erit, complendu&longs;ve cylindrus? </s>

<s>Ad duplam-ne &longs;olum? <lb/></s>

<s>Non &longs;anè, &longs;ed omninò ad <expan abbr="quadruplã">quadruplam</expan>. </s>

<s>Et vt ex&longs;iliant <lb/>tres, ad triplam-ne? </s>

<s>Haud-quaquam profectò, &longs;ed <lb/>ad nonuplam. </s>

<s>Et vt ex&longs;iliant quatuor, ad quadru<lb/>plam ne? </s>

<s>Minimè gentium, &longs;ed ad &longs;exdecuplam. </s>

<s>Quin <lb/>poterit etiam aliunde res facillimo negotio notari, &longs;i <lb/>repleto &longs;iue ad labium, &longs;iue ad certam v&longs;que altitudi<lb/>nem cylindro, & aperto foramine, totáque aqua vno <lb/>tenore, nullamque refundendo effluente, notentur in <lb/>va&longs;e aquæ decrementa æqualibus temporibus facta. <lb/></s>

<s>Quippe &longs;i interuallum vltimi decrementi fuerit vnius <lb/>v. </s>

<s>pedis, erit interuallum penultimi trium, ante<lb/>penultimi quinque, antecedentis &longs;eptem, ac ita &longs;em<lb/>per procedendo per &longs;uccedenteis impareis: vnde & &longs;i <lb/>primi temporis initio fuerit altitudo pedum &longs;exde<lb/>cim, erit initio &longs;ecundi nouem, tertij quatuor, quar<lb/>ti vnius. </s>

<s>Cùm ex&longs;ilitio verò aquæ continenter fiat <lb/>ex continente impetu, quo à &longs;uper&longs;tante vigetur, & <lb/>impetus i&longs;te nihil differat à continente velocitate, <pb pagenum="37"/>qua aqua &longs;uper&longs;tans continenter incumbit, ac premit; <lb/>An-non planum e&longs;t intelligere impetum, ac velocita<lb/>tem duplò maiorem fieri non ex altitudine dupla, <lb/>&longs;ed penitùs ex quadrupla; triplo non ex tripla, &longs;ed ex <lb/>nonupla, & ita deinceps? </s>

<s>Secundò, &longs;i alligatus vno <lb/>&longs;ui extremo ad parietem funis prælongus, altero ex<lb/>tremo dependeat ex fulcro, ac appen&longs;o pondere certo, <lb/>v. </s>

<s>vnius libræ, ten&longs;ione &longs;it leni inter ip&longs;a extrema: <lb/>verò digitis verò, ita abducatur, vt vltro citróque horizon<lb/>taliter vibretur, &longs;eu eat, ac redeat certo tempore (erunt <lb/>autem itus, reditu&longs;que omnes æqui-temporanei, &longs;eu <lb/>tam primi, quam vltimi, tam longi, quàm breues <lb/>eiu&longs;dem prorsù, durationis) &longs;itque tempus tantum, <lb/>quantum inter&longs;titium ab vna artenæ pul&longs;atione ad <lb/>aliam Vt fiat funis duplò inten&longs;ior, & itus, reditu&longs;<lb/>que ip&longs;ius euadant duplò velociores, hoc e&longs;t æquali <lb/>tempore duo; quantum, putas, erit ponderis adden<lb/>dum? </s>

<s>An duplum? </s>

<s>Non; &longs;ed quadruplum. </s>

<s>Et vt <lb/>fiat triplo, &longs;intque adeo itus reditu&longs;que eodem tem<lb/>pore triplò velociores, &longs;eu plures: an triplum dum<lb/>taxat' Nequaquam, verum nonuplum. </s>

<s>Et vt qua<lb/>druplò, an quadruplum? </s>

<s>Haud certè, &longs;ed &longs;exdecu<lb/>plum. </s>

<s>Cùm pondera porro æqualia primo &longs;uperad<lb/>dita &longs;e perinde habeant ad creandum hanc velocita<lb/>tem, ac partes æquales altitudinis, per quas pondus <lb/>demittitur: An non intelligi rursùs licet, quemadmo<lb/>dum velocitas non acquiritur duplò maior ex dupli<lb/>cato pondere, &longs;ed planè ex quadruplicato; ita duplam <lb/>quoque non ex duplicata altitudine, &longs;ed ex quadru<lb/>plicata acquiri? </s><pb pagenum="38"/>

<s>E&longs;t etiam Tertiò heic repetendum, quod <lb/>iam antè dixi de globis ad fila appen&longs;is, & liberè ire, <lb/>redireque permi&longs;&longs;is. </s>

<s>Videlicet globus appen&longs;us ex <lb/>vno v. </s>

<s>pede, dup ò quidem plureis vibrationes per<lb/>agit, quam appen&longs;us ad quatuor, triplo, quàm ap<lb/>pen&longs;us ad nouem, quadruplo, quàm appen&longs;us ad &longs;ex<lb/>decim; &longs;ed interim tamen &longs;ecundus &longs;patium conficit <lb/>dup ò maius, quàm primus, tertius triplò, quartus <lb/>quadruplò eodem tempore; ac velocitas interim ac<lb/>qui&longs;ita, impetu&longs;que ad perpendiculum expre&longs;&longs;us, non <lb/>vt &longs;patium pertran&longs;itum, &longs;ed vt tempus elap&longs;um &longs;e <lb/><figure id="fig13"></figure><lb/>habet. </s>

<s>Ego certè rem &longs;ic intelligo. </s>

<s>Sit linea per<lb/>pendicularis AB in pariete ducta, diui&longs;aque in &longs;ex<lb/>decim pedes; ac &longs;int appen&longs;i quatuor globi, vnus <lb/>ad primum, alius ad quartum, tertius ad nonum, <lb/>po&longs;tremus ad decimum&longs;extum. </s>

<s>Siquidem tamet&longs;i <pb pagenum="39"/>inter experiundum applicari diuer&longs;is &longs;eor&longs;im lineis <lb/>debeant, ne inter mouendum &longs;e&longs;e interturbent: om<lb/>neis tamen &longs;chemate vno repræ&longs;entari nihil prohibet. <lb/></s>

<s>Ducantur heinc inde duæ lineæ angulum &longs;tatuentes <lb/>in A, qui à perpendiculo bi&longs;ecctur, &longs;intque v. </s>

<s>IA, <lb/>KA; & centro A; agantur inter illas arcus CD ad <expan abbr="pri-m&utilde;">pri<lb/>mum</expan> pedem, EF ad quartum, GH ad nonum IK ad <lb/>&longs;extum-decimum; qui &longs;imiles proinde erunt, pares <lb/>videlicet portiones &longs;uotum cuiu&longs;que circulorum eo<lb/>dem angulo men&longs;uratæ. </s>

<s>Ducantur & &longs;ubten&longs;æ ar<lb/>cuum; & adnotentur qua&longs;i &longs;agittæ, &longs;eu appellati &longs;inus <lb/>ver&longs;i, lineæ nimirùm LM, NO, PQ, RB; cùm <lb/>&longs;int altitudines, quibus globi delabuntur ex linea AI <lb/>(vbi ad illam abducti, ex ea dimittuntur) in ip&longs;um <lb/>perpendiculum; primus putà ex C in M, &longs;ecundus <lb/>ex E in O, tertius ex G in Q, quartus ex I in B. <lb/></s>

<s>Abducantur proinde globi ad memoratam lineam <lb/>AI, vt &longs;uas, exinde dimi&longs;&longs;i, vibrationes peragant, ad <lb/>lineam AK, aut quam-proximè terminandas. </s>

<s>Nam & <lb/>quamuis quilibet globus, &longs;eu longiùs, &longs;eu breuiùs di<lb/>mi&longs;&longs;us, & &longs;eu moueri incipiat, &longs;eu de&longs;inat, vibrationes <lb/>omneis æqui-temporaneas &longs;ortiatur, temporibu&longs;ve <lb/>paribus perficiat; proportio tamen &longs;emper e&longs;t, quoties <lb/>&longs;ub æquali, eodemue angulo accipiuntur. </s>

<s>Dimittan<lb/>tur & globi &longs;imul, ac peruenire concipiantur ad v&longs;<lb/>que perpendiculum. </s>

<s>Quoniam tunc vt filum AO <lb/>quadruplum e&longs;t fili AM, & filum AQ nonuplum, <lb/>filum AB &longs;exdecuplum; ita altitudo NO dupla e&longs;t <lb/>altitudinis LM, & altitudo PQ nonupla, altitudo <lb/>RB &longs;exdecupla; quo pacto interuallum quoque per-<pb pagenum="40"/>tran&longs;itum EO quadruplum e&longs;t &longs;patij CM, & &longs;pa<lb/>tium GQ nonuplum, &longs;patium IB &longs;exdecuplum: Id<lb/>circò, cùm aliunde ob&longs;eruemus tempus, quo globus <lb/>&longs;ecundus peruenit ad O, e&longs;&longs;e duplum temporis, quo <lb/>primus peruenit ad M, & tempus, quo tertius ad Q, <lb/>triplum; tempus, quo quartus ad B, quadruplum; Id<lb/>circò, inquam, intelligimus, impetum, &longs;eu velocita<lb/>tem, quæ acquiritur ex E, aut N in O, & ex G, aut <lb/>P in <expan abbr="q;">que</expan> & ex I, aut R in B, pari ratione &longs;e habere <lb/>ad velocitatem acqui&longs;itam ex C, aut L, in M, qua <lb/>&longs;e habet impetus, &longs;eu velocitas, quæ acquiritur ex A <lb/>in O, in Q, in B, ad velocitatem acqui&longs;itam ex A in <lb/>M; &longs;eu comparando oppo&longs;itè, vt illam ad illam, &longs;ic <lb/>i&longs;tam ad i&longs;tam. </s>

<s>Hoc autem habito, quoniam im<lb/><figure id="fig14"></figure><lb/>petus, &longs;eu velocitas acqui&longs;ita ex E in O non e&longs;t ac<lb/>qui&longs;itæ ex C in M quadrupla, &longs;ed dupla; & acqui&longs;ita <pb pagenum="41"/>ex G in Q, non nonupla eiu&longs;dem, &longs;ed tripla: & ac<lb/>qui&longs;ita ex I in B, non &longs;exdecupla, &longs;ed quadrupla e&longs;t: <lb/>quatenus quidem experiundo ob&longs;eruare licuit, con<lb/>&longs;titutam pilam &longs;upra planum libellatum, appo&longs;itum<lb/>que ad M, ad O, ad Q, ad B, dum percuteretur, pro<lb/>pellereturque à globis incurrentibus, a&longs;&longs;equi velocita<lb/>tem, excurrereque, non iuxta numeros quadratos, <lb/>quales &longs;unt &longs;patiorum CM, EO, GQ, IB; &longs;ed iuxta <lb/>radices ip&longs;orum, qualia &longs;unt & tempora, vnum, duo, <lb/>tria, quatuor. </s>

<s>Quamobrem & fuit iteratò procliue <lb/>intelligere percu&longs;&longs;ionem quoque à re &longs;ecundum per<lb/>pendiculum cadente factam, &longs;equi rationem non <lb/>quadratorum, &longs;eu &longs;patiorum, &longs;ed radicum, &longs;eu tem<lb/>porum; atque ita, quò cadens graue vehementiùs <lb/>feriat duplò, triplò, quadruplò, cadere debere ex al<lb/>titudine non duplò, triplò quadruplò; verùm, quadru<lb/>plò, nonuplò, atque &longs;exdecuplò maiore. </s>

<s><emph type="center"/><emph type="italics"/>De Experimento in Bilance facto ac aliud reuera probante, <lb/>quàm velocitates e&longs;&longs;e &longs;icut spatia.<emph.end type="italics"/><emph.end type="center"/></s>

<s>XXIII. Verumtamen, hi&longs;ce dimi&longs;&longs;is, acceden<lb/>dum e&longs;t ad &longs;ecundam, peculiaremve experientiam, <lb/>cui totam &longs;cientiam &longs;uper-ex&longs;truis, & de qua in hunc <lb/>modum præfaris. <emph type="italics"/>Atque, vt quam tibi promi&longs;i expe<lb/>rientiam, cum f&oelig;nore etiam exhibeam, adiungam & aliam, <lb/>à nullo mortalium hactenus ob&longs;eruatam, quæ & priorem <lb/>perfectißimè includat, & non rationem &longs;olùm, quâ celeritas <lb/>in naturali de&longs;cen&longs;u grauium augetur, &longs;ed eiu&longs;dem quoque <lb/>celeritatis pene incredibilem modum, ac men&longs;uram, exacti&longs;-<emph.end type="italics"/><pb pagenum="42"/><emph type="italics"/>&longs;imè determinet.<emph.end type="italics"/></s><s> Pergis declarando ecqua illa &longs;ie <lb/><emph type="italics"/>Aio igitur, ita e&longs;&longs;e à natura con&longs;titutum, vt globus quilibet, <lb/>tuiu&longs;cumque materiæ, ex vnius diametri altitudine cadens, <lb/>duplum &longs;ui ponderis, hoc e&longs;t, præter pondus quod &longs;ine im<lb/>petu in æquilibrio retineret, aliud &longs;ibi æquale attollat; & <lb/>ex altitudine duarum diametrorum, triplum; ex tribus dia<lb/>metris, quadruplum; & ita deinceps: adeo vt ex quauis <lb/>altitudine cadens, &longs;emper (vltra æquilibrium) toties pro<lb/>prium pondus multiplieatum attollat, quot in tota, vnde <lb/>cadit, altitudine diametri continentur.<emph.end type="italics"/></s><s> Subiicis, rem exag<lb/>gerando, <emph type="italics"/>Mirum &longs;anè quòd globus, cuius figuram, vt<lb/>pote &longs;implicißimam, capacißimàmque, natura &longs;ingulariter <lb/>amare videtur, men&longs;uram, ac modum, tam velocitatis <lb/>motus in de&longs;cen&longs;u grauium, quàm virtutis eius motricis, <lb/>quæ in eadem velocitate continetur, &longs;uâ nobis diametro exhi<lb/>beat: adeo vt ex decem, aut centum diametrorum altitudine <lb/>decidens, eum acquirat impetum, qui attollendis decem, aut <lb/>centum &longs;imilibus globis, in altera lance impo&longs;itis, &longs;ufficere <lb/>poßit, &longs;i materiæ conditio id patiatur.<emph.end type="italics"/></s><s> Addis & quid <lb/>ip&longs;e ob&longs;eruaueris. <emph type="italics"/>Expertus &longs;um ego,<emph.end type="italics"/> inquis, <emph type="italics"/>globum plum<lb/>beum vnius vnciæ, ex altitudine &longs;ex pedum, &longs;iue dia<lb/>metrorum centum quatuordecim cadentem, vncias toti<lb/>dem vltra æquilibrium, hoc est, libras &longs;eptem, & <lb/>vncias tres in altera lance impo&longs;itas, &longs;uo impetu eleua&longs;&longs;e, <lb/>non &longs;ine ingenti eorum qui præ&longs;entes aderant admiratione, <lb/>ac stupore.<emph.end type="italics"/></s><s> Tum & hæc habes. <emph type="italics"/>Porrò &longs;i id in paucis <lb/>diametris experiri placuerit, non admodùm magna opus <lb/>erit diligentia: at &longs;i è maiore altitudine idem tentare pla<lb/>cuerit, tum in hac, vt in cæteris Phy&longs;icis experientiis,<emph.end type="italics"/><pb pagenum="43"/><emph type="italics"/>accurata, ac &longs;olerti diligentia, atque industria, variis incom<lb/>modis occurrendum erit; vt ne fortè ex conditione materiæ <lb/>effectus impediatur, nó&longs;que ex errore, aut ex ignorantia, id <lb/>impoßibile arbitremur, quod &longs;olius materiæ vitio, ac defectu, <lb/>in certis circum&longs;tantiis minùs ex animi &longs;ententia &longs;uccedit.<emph.end type="italics"/><lb/><figure id="fig15"></figure><lb/>Paginas de<lb/>inceps ali<lb/>quot in&longs;umis, <lb/>vt ea incom<lb/>moda de&longs;cri<lb/>bas, & mo<lb/>dum, quo il<lb/>lis occurra<lb/>tur, tradas; <lb/>depicta &longs;cili<lb/>cet Bilanco, <lb/>quæ ip&longs;i&longs;&longs;i<lb/>ma heic ap<lb/>pingitur, agi<lb/>na putà im<lb/>mobili, & al<lb/>tera lancium <lb/>&longs;u&longs;pen&longs;a in <lb/>aëre, altera <lb/>&longs;upra men<lb/>&longs;am CD qui<lb/>e&longs;cente, cum <lb/>impo&longs;ito pondere, ac &longs;peculatore ad&longs;tante, qui ad <lb/>quamque vel minimam eius elationem attendat (id<lb/>que dum globus manu H dimi&longs;&longs;us incidit in alterius <pb pagenum="44"/>medium, directione circuli G, cui ob æquilibrium <lb/>re&longs;pondet con&longs;imilis F) ac in&longs;uper vtraque lance ca<lb/>tenulis ferreis à &longs;capo AB per intermedios circulos, <lb/>triangulo&longs;-ve, dependente. </s>

<s>Denique autem &longs;ubiun<lb/>gis, <emph type="italics"/>Tam apertam e&longs;&longs;e eius rei demon&longs;trationem, vt nul<lb/>lus,<emph.end type="italics"/> inquis, <emph type="italics"/>intellectus refragari po&longs;&longs;e videatur; dum &longs;emel <lb/>con&longs;tet (quod quilibet &longs;ine tanto apparatu, tantáque diligen<lb/>tia facillimè experiri potest) globum quemcumque, ex vnius <lb/>diametri altitudine, po&longs;&longs;e (vltra æquilibrium) pondus &longs;ibi <lb/>æquale, & ex duabus diametris duplum pondus attollere.<emph.end type="italics"/><lb/>Prætereo autem demon&longs;trationem non alio nixam <lb/>fundamento, quàm ipsâ experientiâ à te &longs;uppo&longs;itâ; <lb/>prætereoque item, quod iterùm &longs;ubdis, <emph type="italics"/>Illud quoque <lb/>pari certitudine constare, quod antè dictum e&longs;t, nihil ad pro<lb/>po&longs;itionis veritatem, atque euidentiam opus e&longs;&longs;e, vt ex al<lb/>tiore di&longs;tantia, tantóque apparatu experientia inquiratur, <lb/>quæ ex aliquot diametrorum altitudine plu&longs;quam abundè; <lb/>ac facillimè habeatur.<emph.end type="italics"/></s>

<s>Et tale e&longs;t quidem tuum experimentum. <lb/></s>

<s>Ego autem, humani&longs;&longs;ime Vir, grati&longs;&longs;imo primùm <lb/>animo complector liberali&longs;&longs;imum erga me affectum; <lb/>ac deinde etiam tibi gratulor, quod primus morta<lb/>lium excogitâris quemadmodum negotium vi&longs;um <lb/>difficile reuocari ad trutinam po&longs;&longs;et. </s>

<s>Nempe quan<lb/>tumvis res non videatur pro tua &longs;tare &longs;ententia; fuit <lb/>tamen tua &longs;olertia dignum, id in mentem inducere, <lb/>vnde examen improbum, quacumque ex parte huiu&longs;<lb/>modi foret, po&longs;&longs;et ca&longs;tigari. </s>

<s>Ac &longs;i res quidem &longs;ic &longs;e <lb/>haberet, vt enarrati abs te videtur, reputari po&longs;&longs;et <lb/>penitus confecta; nullumque e&longs;&longs;et dubium, quin <pb pagenum="45"/>Galilei &longs;cientiam fal&longs;itatis conuinceres, tuam tan<lb/>quam veram &longs;ub&longs;titueres iure: at res potius ita &longs;e ha<lb/>bet, meo quidem iudicio, vt Galileanam confirmare, <lb/>euertere tuam omninò videatur. </s>

<s>Ecquid-nam verò, <lb/>inquies, Tu igitur meus amicus mihi referenti non <lb/>credis; ac virum me habes malæ fidei, dum hæres, id<lb/>ne verum &longs;it, quod ip&longs;e me fui&longs;&longs;e expertum enarro? <lb/></s>

<s>Ab&longs;it hoc à me, optime virorum, qui habeo te po<lb/>tiùs plenum fidei, & &longs;ummo candore, finceri&longs;&longs;ima<lb/>que &longs;inceritate vi&longs;a narrantem. </s>

<s>Sed patietur &longs;anè <lb/>&longs;inceritas tua, vt, quod &longs;upere&longs;t, &longs;i quid erroneum <lb/>videbitur, culpam coniiciam aut in quidpiam non <lb/>&longs;atis fortè animaduer&longs;um, vt omnes &longs;umus homines; <lb/>aut, &longs;i malis, etiam in illos, quorum operâ v&longs;us fueris, <lb/>quibu&longs;ve referentibus cen&longs;ueris pro tua bonitate non <lb/>e&longs;&longs;e negandum a&longs;&longs;en&longs;um. </s>

<s>Itaque cùm tua verba <lb/>relegens, deprehendam te nihil aliud tibi, tanquam <lb/>ob&longs;eruatum à te vindicare; quàm illud, quod iam re<lb/>tuli, <emph type="italics"/>Expertus &longs;um ego globum plumbeum vnius vnciæ ex <lb/>altitudine &longs;ex pedum, &longs;iue diametrorum centum quatuorde<lb/>cim cadentem, vncias totidem vltra æquilibrium, hoc e&longs;t li<lb/>bras &longs;eptem, & vncias treis in altera lance impo&longs;itas &longs;uo <lb/>impetu eleua&longs;&longs;e.<emph.end type="italics"/></s><s> Itemque illud, quod po&longs;teà impedi<lb/>menta memorans, <emph type="italics"/>Propria,<emph.end type="italics"/> inquis, <emph type="italics"/>experientia ip&longs;e <lb/>edoctus &longs;um, qui adhibita omni indu&longs;tria globum vnius vn<lb/>ciæ ex altitudine &longs;ex pedum in lancem &longs;ubiectam, viginti <lb/>quinque, aut triginta vicibus dimittens, ter &longs;olùm centrum <lb/>attingere, & pondus perfectè attollere potui.<emph.end type="italics"/> Cùm, in<lb/>quam, ita deprehendam, non cau&longs;or tuam fidem, <lb/>quam cum per&longs;ua&longs;ione aliqua non vera (re familiari <pb pagenum="46"/>hominibus, etiam optimis) &longs;tare nihil vetat. </s>

<s>Cùm ad<lb/>dis autem prætereà generale e&longs;&longs;e, vt pro numero dia<lb/>metrorum, quibus idem globus dimi&longs;&longs;us abfuerit à <lb/>lance, pondera cleuet &longs;uo paria; qua&longs;i cùm id præ<lb/>&longs;titerit in certo quodam numero, non valeat citra <lb/>illum plureis, vltrà pauciores eleuare; hoc e&longs;t, quod <lb/>peto mihi condones, vt dicere liceat, in veritatis gra<lb/>tiam, te aut &longs;atis non attendi&longs;&longs;e, aut alijs etiam ni<lb/>miùm credidi&longs;&longs;e. </s>

<s>Vt &longs;altem liceat quid-nam mihi contige<lb/>rit, commemorare; Tu &longs;æpe adeò repetii&longs;ti non e&longs;&longs;e <lb/>magno apparatu, magnaque diligentia opus ad <lb/>peragendum experimentum, vt ni&longs;i argumentis &longs;u<lb/>perioribus fui&longs;&longs;em oppo&longs;itum per&longs;ua&longs;us, vix induxi&longs;<lb/>&longs;em in animum (nihil &longs;cilicet hæ&longs;itans, imò hæ&longs;itan<lb/>di pudore &longs;uffu&longs;us) periculum facere vllum. </s>

<s>Feci <lb/>tamen, & ip&longs;a præ&longs;ertim à te inculcata facilitate in<lb/>uitatus; vnde & obuiam primò Bilancen, qua numu<lb/>larius &longs;olebat nuper monetæ argenteæ &longs;ummam ali<lb/>quot librarum Marcarum non-numeratam appen<lb/>dere, probaréque, a&longs;&longs;umendam duxi. </s>

<s>Quoniam ve<lb/>rò tu a&longs;&longs;erebas <emph type="italics"/>ita à natura e&longs;&longs;e con&longs;titutum, vt globus <lb/>quilibet cuiu&longs;cumque materiæ ex vnius diametri altitudine <lb/>cadens, pondus attollat &longs;ibi æquale, præter illud, quod in &ecedil;qui<lb/>librio &longs;ine impetu retineret,<emph.end type="italics"/> &c. </s>

<s>ideo &longs;ufficere putaui, &longs;i <lb/>globum marmoreum, quem habebam præ manibus, <lb/>duorum cum &longs;extante digitorum pedis Pari&longs;ini dia<lb/>metro, ac vnciarum proximè decem, Libræ itidem <lb/>Pari&longs;inæ pondere, ad experiundum v&longs;urparem. </s>

<s>Ap<lb/>paratis ergo ponderibus variis, quæ ex æquo cum <pb pagenum="47"/>ip&longs;o feci, appo&longs;ui ad lancem in æquilibrio &longs;u&longs;tenta<lb/>tam (à &longs;uppo&longs;ita nempe tabula) duplum eiu&longs;ce pon<lb/>deris, hoc e&longs;t vncias prope viginti; ac &longs;ubinde elatum <lb/>globum vna &longs;ui diametro &longs;upra fundum alterius lan<lb/>cis con&longs;tantis in aëre, placidè in ip&longs;am dimi&longs;i. </s>

<s>Tum <lb/>autem verum quidem fuit attolli ex ip&longs;ius ca&longs;u op<lb/>po&longs;itam lancem cum ponderis duplo; at quia vidi <lb/>interim ip&longs;am &longs;upra expectatam attolli altitudinem, <lb/>idcircò &longs;tatim duo intellexi, alterum po&longs;&longs;e idem pon<lb/>dus ex altitudine minore, alterum po&longs;&longs;e ex ip&longs;a ea<lb/>dem, pondus adhûc maius attolli. </s>

<s>Et aduocatis cer<lb/>tè amicis, qui ad lancis elationem, emotionemve à <lb/>tabula, me globum dimittente, attenderent, aut me <lb/>attendente globum ip&longs;i dimitterent, res ita &longs;ucce&longs;&longs;it, <lb/>vt lanx &longs;u&longs;tentata cum duplo eodem pondere elata <lb/>fuerit dimi&longs;&longs;o globo non modo ex diametro vna, <lb/>verùm ex dimidio etiam diametri, etiam ex triente, <lb/>quadrante, &longs;extante, octante, dextante; ac vice ver&longs;a, <lb/>vt dimi&longs;&longs;o globo ex eadem vnius diametri altitudi<lb/>ne, elata lanx fuerit cum impo&longs;ito pondere, non <lb/>modo duplo, &longs;ed etiam triplo, quadruplo, quin<lb/>tuplo, & ampliùs. </s>

<s>Experiri etiam con&longs;equenter lu<lb/>buit, an &longs;altem globus decidens ex duplo altitudinis <lb/>(diametrorum &longs;cilicte duarum) eleuaret duplum eius <lb/>ponderis, quod &longs;ummum mox extulerat; &longs;ed longè <lb/>&longs;anè abfuit; ac magis adhûc, vt ex triplo triplum, ex <lb/>quadruplo quadruplum. </s>

<s>Quandoquidem verò ip&longs;e globum plum<lb/>beum vnius vnciæ v&longs;urpâras; ideò talem quoque <lb/>v&longs;urpandum cen&longs;ui, plumbeum &longs;cilicet, ac vnius <pb pagenum="48"/>vnciæ Pari&longs;ini ponderis, diametro eius deprehen&longs;a <lb/>continere digiti be&longs;&longs;em, ac idcircò partem Pari&longs;ini <lb/>pedis decimam-octauam. </s>

<s>Cæterùm idem mihi eue<lb/>nit, quod circa globum marmorum; impo&longs;itis enim <lb/>in lance &longs;uffulta duabus vncijs, extulit eas globus <lb/>&longs;en&longs;ibiliter non ex altitudine modo diametri vnius, <lb/>&longs;ed ex dimidio etiam eiu&longs;dem, etiam ex triente, qua<lb/>drante, &longs;extante, octante, dextante, imò, & ex vncia, <lb/>duodecimáve diametri parte. </s>

<s>Ac rur&longs;us ex eadem <lb/>diametri vnius altitudine, non duas modò extulit <lb/>vncias, verùm etiam treis, etiam quatuor, quinque, <lb/>&longs;ex, &longs;eptem, dua&longs;que drachmas in&longs;uper, quadrantem<lb/>ve vnius vnciæ. </s>

<s>Et cùm experiri iterum placuerit, <lb/>an duplum huius ponderis eleuaretur ex ca&longs;u globi <lb/>à duplo altitudinis, triplumque ex ca&longs;u à triplo, &c. <lb/></s>

<s>deprehendi dimi&longs;&longs;o globo ex diametris duabus alti<lb/>tudinis, attolli non duplum, hoc e&longs;t, vncias quatuor<lb/>decim cum &longs;emi&longs;&longs;e; &longs;ed vncias &longs;olummodò nouem, <lb/>cum be&longs;&longs;e, aut dodrante duntaxat. </s>

<s>Quo pacto de<lb/>inceps ex diametro tertia extulit non triplum, hoc <lb/>e&longs;t viginti vnam vncias cum dodrante; &longs;ed vncias <lb/>&longs;olummodò duodecim, ac ferè dimidium; & ex dia<lb/>metro quarta extulit, non quadruplum, hoc e&longs;t vn<lb/>cias viginti nouem; &longs;ed duplum &longs;olùm, hoc e&longs;t vn<lb/>cias quatuordecim, atque &longs;emi&longs;&longs;em. </s>

<s>Prætereo au<lb/>tem, quemadmodum, vt extulit dumtaxat duplum ex <lb/>diametris quatuor, &longs;ic etiam deinceps extulerit &longs;olum<lb/>modò triplum ex diametris nouem, & quadruplum, <lb/>ex &longs;exdecim. </s>

<s>Adnoto iam &longs;olùm, licui&longs;&longs;e ex i&longs;tis in<lb/>telligere, po&longs;&longs;e tuam hanc experientiam meritò vocari <pb pagenum="49"/>in dubium; nec po&longs;&longs;e te a&longs;&longs;erere quemlibet globum <lb/>ita e&longs;&longs;e à natura comparatum, vt illius diameter &longs;it <lb/>men&longs;ura præci&longs;a velocitatis, &longs;eu impetus, quem inter <lb/>cadendum acquirit; ea &longs;cilicet lege, vt cadens ex dia<lb/>metro vna in liberam lancem, attollat &longs;uffultam, & <lb/>præter æquilibrium, ponderis tantumdem, non iti<lb/>dem amplius (veluti etiam neque minus, &longs;i minor <lb/>fuerit altitudo) ac deinceps &longs;ic progredi, vt ex dua<lb/>bus diametris attollat præcisè duplum, ex tribus tri<lb/>plum, ex quatuor quadruplum, ex decem decuplum, <lb/>ex centum centuplum, atque ita porrò. </s>

<s>XXVII. </s>

<s>At quor&longs;um ergo contigit, inquies, vt <lb/>dimi&longs;&longs;us vncialis globus ex altitudine diametrorum <lb/>centum, & quatuordecim, vncias totidem eleuârit? <lb/></s>

<s>Ego profectò id præcisè diuinare non valeo; quan<lb/>doquidem tu nullam &longs;eriem ob&longs;eruationum appo<lb/>&longs;ui&longs;ti, neque expre&longs;&longs;i&longs;ti quid contigerit, &longs;i quid for<lb/>ta&longs;&longs;is expertus es citra, vltrave numerum illum. </s>

<s>Nam, <lb/>&longs;i &longs;altem commemora&longs;&longs;es ecquid tibi euenerit dimit<lb/>tenti globum ex altitudine diametrorum aut centum; <lb/>aut octoginta, aut quinquaginta, &c. </s>

<s>liceret forta&longs;<lb/>&longs;is rem coniicere; at tale nihil recita&longs;ti, neque expli<lb/>cui&longs;ti quali pondere, pedeve v&longs;us fueris; cùm &longs;i Pa<lb/>ri&longs;ino quidem, videri po&longs;&longs;is hallucinatus quinta, aut <lb/>&longs;exta ponderis parte; quatenus globi diameter fuit <lb/>tibi duntaxat decima-nona pedis pars, quam ego de<lb/>prehendi decimam-octauam. </s>

<s>Vtcumque fuerit; ex ijs, <lb/>quæ &longs;unt à me ob&longs;eruata, deducitur, quò diametri <lb/>&longs;iunt multiplicatiores, eò &longs;ingulas &longs;uper-additas at<lb/>tollere minus &longs;uper-additi ponderis; quandò ex <pb pagenum="50"/>&longs;ecunda non attollitur duplum, ex tertia triplum, &c. <lb/></s>

<s>&longs;ed res &longs;emper ita decre&longs;cit, vt ex tribus &longs;olùm pri<lb/>mam con&longs;equentibus eleuetur tantumdem, ex quin<lb/>que aliis rursùs tantumdem, ex &longs;eptem aliis &longs;imili<lb/>ter, ac rut&longs;us ex nouem, & ita deinceps. </s>

<s>Deducitur <lb/>prætereà ex incre&longs;cente numero diametrorum, & de<lb/>cre&longs;cente numero additorum ponderum, perueniri <lb/>demùm ad æqualitatem; ita &longs;cilicet, vt &longs;it diametro<lb/>rum, ponderumque numerus par, quo &longs;uperato &longs;it <lb/>deinceps minor ponderum, maior diametrorum. </s>

<s>Et <lb/>quia talis numerus incipiendo v. </s>

<s>à duodecima v&longs;<lb/>que parte diametri, è qua fuere duæ vnciæ eleuatæ, <lb/>reperitur e&longs;&longs;e proximè quinquaginta; & incipiendo à <lb/>diametro integra, è qua eleuari vi&longs;æ &longs;unt vnciæ &longs;ep<lb/>tem cum quadrante, reperitur e&longs;&longs;e itidem quinqua<lb/>ginta: idcircò videmur po&longs;&longs;e dicere, &longs;i dimittatur <lb/>globus vnam pendens vnciam, ex altitudine diame<lb/>trorum &longs;uarum quinquaginta, fore vt parem nume<lb/>rum vnciarum attollat; tamet&longs;i citra hunc numerum, <lb/>&longs;it diametrorum numerus minor, vltrà maior nu<lb/>mero vnciarum. </s>

<s>Vides igitur contingere po&longs;&longs;e, vt <lb/>aliquo ca&longs;u diametrorum numerus ponderum nume<lb/>ro exæquetur; neque licere tamen inferre e&longs;&longs;e vbi<lb/>que diametrorum numerum numero ponderum <lb/>æqualem. </s>

<s>Ac &longs;i res quidem tibi contigi&longs;&longs;et circiter <lb/>quinquage&longs;imam, aut &longs;exage&longs;imam diametrum, foret <lb/>mihi, vt vides, re&longs;pon&longs;io in promptu; quandò verò <lb/>numerus i&longs;tum &longs;uperat duplò circiter; ac is e&longs;t aliunde, <lb/>è quo eleuari non debuerint, ni&longs;i vnciæ &longs;eptuaginta <lb/>quatuor; vnde exce&longs;&longs;us e&longs;t circiter trientis: idcircò par <pb pagenum="51"/>e&longs;t, vt quid id &longs;it rei, tibi di&longs;cutiendum relinquam, <lb/>vi&longs;uro, an, &longs;i quid impo&longs;uit circa vnam, paucula&longs;ve <lb/>diametros, non aliquid etiam potuerit imponere cir<lb/>ca tam multas. </s>

<s>Mihi certè hactenùs non licuit pe<lb/>riculum facere, qui Bilancem neque maiorem, neque <lb/>exqui&longs;itiorem ea, de qua iam dixi, v&longs;urpaui. </s>

<s>Vnde <lb/>neque velim numeros à me de&longs;criptos ita habeas, <lb/>qua&longs;i &longs;crupulosè, præci&longs;eve definiti fuerint; cùm &longs;atis <lb/>e&longs;&longs;e duxerim, &longs;i præter-propter veri forent, po&longs;&longs;em<lb/>que intelligere &longs;equi illos haud-dubiè aliam, quàm à <lb/>te præ&longs;criptam rationem. </s>

<s>XXVIII. </s>

<s>Nihil verò nece&longs;&longs;e e&longs;t dicam circa id, <lb/>quod ais, <emph type="italics"/>Et&longs;i natura illud in globo peculiare, ac pro<lb/>prium e&longs;&longs;e voluit, vt eius diameter præci&longs;a e&longs;&longs;et men&longs;ura <lb/>illius altitudinis, ex qua &longs;uo nutu cadens, æquale &longs;ibi pon<lb/>dus attolleret; ac proinde, &c. </s>

<s>in cæteris tamen etiam <lb/>corporibus idem quoque &longs;eruata proportione accidere; vt &longs;i ex <lb/>quacumque di&longs;tantia æquale &longs;ibi pondus attollant, ex eadem <lb/>di&longs;tantia duplicata duplicatum, & ex triplicata <expan abbr="triplicat&utilde;">triplicatum</expan> <lb/>attollant, atque ita con&longs;equenter, ob eandem rationem; cui <lb/>rationi ip&longs;a quoque experientia &longs;uffragetur, &c. </s>

<s>hac ta<lb/>men differentia, quòd in globis, diameter altitudines præ<lb/>cisè definiat, vnde pondus ip&longs;orum multiplicetur, in cæteris <lb/>figuris non item; &longs;ed in illis altitudines diametris ip&longs;arum <lb/>&longs;int minores; ratio verò po&longs;tulet vt vniuer&longs;im in figuris om<lb/>nibus tales altitudines diametro &longs;phæræ eiu&longs;dem molis, ac <lb/>ponderis inueniantur æquales.<emph.end type="italics"/></s><s> Nihil, inquam, e&longs;t opus <lb/>vt ad i&longs;tud dicam; cùm neque &longs;uffragari experien<lb/>tiam videam, neque ip&longs;e globus, quicum corpora <lb/>aliarum figurarum confers, habeat pro men&longs;ura præ-<pb pagenum="52"/>ci&longs;a illius altitudinis, ex qua &longs;uo nutu cadens, æquale <lb/>&longs;ibi pondus attollat, &longs;uam diametrum; &longs;ed potiùs duo<lb/>decimam circiter &longs;uæ diametri partem; neque aliun<lb/>de eadem diameter præcisè definiat altitudines, vnde <lb/>pondus, &longs;eu impetus multiplicetur, euadatque tri<lb/>plus ex tripla, quadruplus ex quadrupla, &c. </s>

<s>&longs;ed id <lb/>potiù faciat progre&longs;&longs;io numerorum imparium, qua<lb/>dratorumve, ad quos terminantur. </s>

<s>Addo autem <lb/>videri mihi rem e&longs;&longs;e dignam con&longs;ideratu, quæ acci<lb/>deret circa globos, &longs;i velocitatis, &longs;iue impetus acqui<lb/>&longs;iti gradus men&longs;urandi e&longs;&longs;ent penes &longs;ingulas diame<lb/>tros, quæ men&longs;urarent &longs;ingulorum ca&longs;us. </s>

<s>Sunto <lb/>enim globi, v.c. </s>

<s>duo ex eadem materia, quorum <lb/>vnus &longs;it diametro decies maiore, quàm alius, & di<lb/>mittatur vterque ex eadem altitudine. </s>

<s>Tunc, quia mi<lb/>nor decidet per diametros decuplò plureis, quàm ma<lb/>ior, fiet, vt attollat pondera &longs;ibi æqualia decuplò <lb/>multipliciora, quàm attollat, maior ex &longs;ibi æqualibus; <lb/>Quare & &longs;equetur, vt per idem &longs;patium feratur de<lb/>cuplò citiùs, temporeve decies breuiore perueniat <lb/>ad lancem, quàm maior. </s>

<s>Hoc autem con&longs;tat, quàm <lb/>fal&longs;um &longs;it; cùm &longs;i globorum alteruter deberet velo<lb/>ciùs moueri, & peruenire citiùs, is non &longs;ine quadam <lb/>veri&longs;imilitudine deberet potiùs e&longs;&longs;e maior (quandò <lb/>& Ari&longs;toteles per&longs;ua&longs;us id fuit, & toti penè mundo <lb/>hactenus per&longs;ua&longs;it) ac doceat tamen experientia duo <lb/>pondera eiu&longs;dem materiæ, inæquabili&longs;&longs;ima licet, ve<lb/>luti vnum vnius vnciæ, alterum verò librarum cen<lb/>tum, ex eadem cadentia altitudine, cadere eadem <lb/>velocitate, ac momento eodem peruenire in terram. <pb pagenum="53"/>Atque ex hoc quidem ratio obiter petitur, cur in <lb/>exemplo repetito de pen&longs;ilibus, nihil referat, quod<lb/>cumque pondus filo appendas, vt celeritate eadem <lb/>vibrationes fiant; ideò enim pen&longs;ile centum libra<lb/>rum non vibratur velociùs, quàm pen&longs;ile vnius vn<lb/>ciæ, quoniam altitudo, ex qua vtrumque cadit, ea<lb/>dem e&longs;t, men&longs;urata nempe, eadem portione perpen<lb/>di uli, quemadmodum e&longs;t ante declaratum: cùm <lb/>celeritas aliunde &longs;tatim augeatur vel minuatur, ac fi<lb/>lum breuius fit, vel prolixius. </s>

<s>Et hactenus quidem <lb/>de tua Experientia. </s>

<s><emph type="center"/><emph type="italics"/>De Tempore, quo R. P. colligit parteis spatij &longs;imgulas <lb/>decur&longs;um non iri.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Sequitur iam Secundum membrum Po<lb/>&longs;terioris capitis, quod tibi fuit præcipus &longs;copus. <lb/></s>

<s>Videlicet ita concludis. <emph type="italics"/>Atque ex his iam manife&longs;tè, at<lb/>que euidenter con&longs;tat, celeritatem motus in naturali grauium <lb/>de&longs;cen&longs;u per aërem, &longs;eclu&longs;is externis impedimentis, vniformi <lb/>&longs;emper incremento augeri, & in spatijs æqualibus cre&longs;cere <lb/>æqualiter: ita &longs;cilicet, vt ex dupla di&longs;tantia, celeritas dupla, <lb/>& ex tripla di&longs;tantia, celeritas tripla, atque ita deinceps, <lb/>eadem ratione, maior &longs;emper celeritas habeatur: ni&longs;i fortè <lb/>eò v&longs;que iam progre&longs;&longs;a e&longs;&longs;et celeritas, vt nec celeriùs <expan abbr="a&etilde;r">aerr</expan> di<lb/>uidi, nec citiùs rarefieri, & accurrere ad replendum va<lb/>cuum naturaliter po&longs;&longs;et.<emph.end type="italics"/></s><s> Et po&longs;teà: <emph type="italics"/>Ex quo vlteriùs il<lb/>lud etiam con&longs;tat, quàm non rectè<emph.end type="italics"/> G<emph type="italics"/>alileus, vulgò receptam <lb/>motus æquabiliter accelerati definitionem eam reiecerit, qua <lb/>motus eiu&longs;modi is dicitur; qui spatijs æqualibus, æqualia cele<lb/>ritatis augmenta acquirit; & quàm o&longs;citanter idem halluci-<emph.end type="italics"/><pb pagenum="54"/><emph type="italics"/>natus &longs;it, cùm etiam in&longs;uper, clara, euidentíque demon&longs;tra<lb/>tione, eiu&longs;dem &longs;e fal&longs;itatem, impoßibilitatémque o&longs;tendi&longs;&longs;e, <lb/>tam facilè &longs;ibi, atque incon&longs;uliè per&longs;ua&longs;it: cùm aperta iam, <lb/>indubitatáque experientiâ con&longs;tet, in naturali grauium de&longs;<lb/>cen&longs;u, æqualibus spatijs, æqualia celeritatis augmenta perpe<lb/>tuò acquiri, &longs;emperque velocitates, emen&longs;aque ab initio mo<lb/>tus spatia, in eadem ratione reperiri.<emph.end type="italics"/></s><s> Ad i&longs;ta verò vides <lb/>profectò quid &longs;it iam promptum re&longs;pondere; cùm <lb/>tantum abe&longs;t, vt aperta indubitatáque experientia de<lb/>finitionem illam vulgarem, aut incrementa velocitatis <lb/>pro ip&longs;a &longs;patiorum ratione &longs;tabiliat, quin illam potiùs <lb/>planè euertat, & Galileanum ita confirmet, vt mani<lb/>fe&longs;tò exinde con&longs;tet incrementa velocitatis acquiri <lb/>duntaxat æqualia æqualibus temporibus; acqui&longs;ita <lb/>verò, &longs;eu &longs;uperata &longs;patia e&longs;&longs;e vt ip&longs;orum temporum <lb/>quadrata. </s>

<s>Ex quo fit, vt allatis illis antè argumen<lb/>tis, quibus permouebar, vt coniicerem percu&longs;&longs;ionem, <lb/>atque idcircò impetum, velocitatémque rei deciden<lb/>tis maiorem duplò non haberi, ni&longs;i ex altitudine qua<lb/>drupla, triplum, ni&longs;i ex nonupla, quadruplum, ni&longs;i ex <lb/>&longs;exdecupla, i&longs;tud iam nouum acce&longs;&longs;erit. </s>

<s>quatenus ob<lb/>&longs;eruatum e&longs;t duplum ponderis ex vnius diametri alti<lb/>tudine elati non efferri ex dupla, &longs;ed ex quadrupla; <lb/>triplum non ex tripla, &longs;ed ex nonupla; quadruplum <lb/>non ex quadrupla, &longs;ed ex &longs;exdecupla duntaxat. </s>

<s>Sunt <lb/>autem tibi habendæ gratiæ, qui pro tua &longs;olertia eò <lb/>re&longs;pexeris, vnde argumentum adeò cuidens ducere<lb/>tur; ip&longs;eque debes ex eo lætari, quòd tamet&longs;i expe<lb/>rimentum præconceptæ à te opinioni non faueat; <lb/>conferat nihilominùs ad veritatis illu&longs;trationem. </s><pb pagenum="55"/>

<s>Pro&longs;equeris deinde &longs;ic. <emph type="italics"/>Porrò cùm celeritas <lb/>motus in naturali de&longs;cen&longs;u grauium, non modò ad locum, &longs;ed <lb/>ad tempus quoque re&longs;pectum includat, iamque de altero <expan abbr="dictã">dictam</expan> <lb/>&longs;it, qua videlicet ratione, celeritas &longs;patijs æqualibus augea<lb/>tur; vt ne quid ad perfectam motus accelerati notitiam de<lb/>&longs;it, nece&longs;&longs;arium e&longs;t, vt de &longs;patiis quoque, quæ temporibus <lb/>æqualibus percurruntur, quam inter &longs;e rationem ob&longs;eruent, <lb/>reliqua di&longs;putatione inquiramus, & ex ii&longs;dem quoque expe<lb/>rientiis definiamus.<emph.end type="italics"/></s><s> Hoc iam loco, optimè Vir, agno&longs;<lb/>cere potes originem mali. </s>

<s>Nempe labes tota vide<lb/>tur ex definitione vulgari contracta, quatenus ratio<lb/>nem incre&longs;centis celeritatis ita cum &longs;patio comparat, <lb/>vt nullam interim in&longs;tituat comparationem cum tem<lb/>pore, &longs;ine quo tamen neque celeritas, neque acce<lb/>leratio intelligi pote&longs;t. </s>

<s>Non modò certè Ari&longs;toteles, <lb/>verùm etiam communis &longs;en&longs;us id Velox definit, <lb/><emph type="italics"/>quod &longs;patium multum tempore pauco:<emph.end type="italics"/> & Tardum, <emph type="italics"/>quod <lb/>paucum multò conficit;<emph.end type="italics"/> con&longs;tatque aliunde, &longs;i velocitas <lb/>attendatur &longs;olùm penes &longs;patia, debere &longs;emper id <lb/>mobile, quod decem percurrerit &longs;tadia, dici moueri <lb/>celeriter, & &longs;emper id, quod vnicum percurrerit, tar<lb/>dè; cùm contingere tamen po&longs;&longs;it, vt quod percurrit <lb/>vnicum, moueatur decuplo velocius, quàm illud, <lb/>quod percurrit decem. </s>

<s>Ex quo fit, vt cùm celeri<lb/>tas nihil &longs;it aliud, quàm pa&longs;&longs;io motus; intelligatur <lb/>quidem motus ab&longs;olutè &longs;umptus ex relatione ad &longs;pa<lb/>tium, cùm & definiatur progre&longs;&longs;io è loco in locum <lb/>(nulla mentione temporis) & duo loca &longs;ine &longs;patio <lb/>interiecto non accipiantur; at celeritas non intelli<lb/>gatur &longs;ine relatione ad tempus, & illud quidem breue <pb pagenum="56"/>comparatum ad id, quo ex vno loco perueniri ad <lb/>alium pote&longs;t. </s>

<s>Fit etiam proinde, vt idem dicendum <lb/>de acceleratione &longs;it; quippe acceleratio duo &longs;altem <lb/>tempora de&longs;ignat, in quorum vno celeriter, in alio <lb/>celeriùs mobile feratur; ac intelligimus aliunde tem<lb/>poribus illis æqualibus &longs;umptis, pauciores &longs;patij par<lb/>teis priore, plureis po&longs;teriore percurri. </s>

<s>Et adnitere <lb/>facere per&longs;pectum, quidnam acceleratio &longs;it, nulla men<lb/>tione temporis; ac perno&longs;ces rem impo&longs;&longs;ibilem factu <lb/>e&longs;&longs;e. </s>

<s>Vtcumque enim plureis, plurei&longs;que &longs;patij par<lb/>teis memores<gap/> ni&longs;i tamen adiicias voces <emph type="italics"/>deinceps, con&longs;e<lb/>quenter, &longs;ucceßiuè,<emph.end type="italics"/> aut &longs;imileis alias, quæ ad tempus at<lb/>tineant, non magis accelerationem, quàm &longs;implicem <lb/>celeritatem, aut potiu&longs;-quam motum &longs;impliciter &longs;pe<lb/>ctatum de&longs;cribes. </s>

<s>Quanquam nihil e&longs;t opus id vr<lb/>geam, cùm tu pro confe&longs;&longs;o iam habeas; profe&longs;&longs;us <lb/>nempe <emph type="italics"/>celeritatem in naturali de&longs;cen&longs;u grauium non modò <lb/>ad locum, &longs;ed ad tempus quoque re&longs;pectum includere:<emph.end type="italics"/> ac <lb/>mirari &longs;olùm quis po&longs;&longs;it, agno&longs;cere te in celeritate <lb/>duplicem re&longs;pectum, & velle tamen alterum, ip&longs;um<lb/>que præcipuum in tradenda definitione accelerati mo<lb/>tus exclu&longs;um; ac inuehi in Galileum, qui inclu&longs;um <lb/>voluerit. </s>

<s>Nam & licet, veluti tu re&longs;pectum ad tem<lb/>pus prætermi&longs;&longs;um fers, &longs;ic ille re&longs;pectum ad locum <lb/>prætermitti po&longs;&longs;e cen&longs;uerit: excu&longs;ari pote&longs;t, quòd qui <lb/>motum dicit, locum etiam dicat, quemadmodum <lb/>mox attigi; & cùm foret &longs;olùm de celeritate &longs;uperue<lb/>niento quæ&longs;tio, ideò nugationem deuitans, illam per <lb/>re&longs;pectum ad tempus, &longs;ine quo intelligi nequeat, pu<lb/><gap/>rit e&longs;&longs;e de&longs;iniendam. </s><pb pagenum="57"/>

<s>Subdis con&longs;equenter; <emph type="italics"/>Quod vt certiùs <lb/>fiat, primùm occurrendum est errori, qui facilè obrepere <lb/>potest, &longs;i quæ de cele itatis augmento in &longs;patiis æqualibus <lb/>antè demonstrata &longs;unt, minùs accuratè perpendantur. </s>

<s>Cùm <lb/>enim ex &longs;uperioribus iam euidenter con&longs;tet, in naturali gra<lb/>uium de&longs;cen&longs;u, &longs;emper ex dupla di&longs;tantia, celeritatem ha<lb/>beri duplam; & ex tripla distantia, triplam; atque ita <lb/>deinceps, eadem ratione celeritatem augeri: nihil procliuius <lb/>e&longs;&longs;e potest, quàm vt quis exi&longs;timet, accelerationem <gap/><lb/>fieri per &longs;ubdiui&longs;ionem primi cuiu&longs;libet temporis, in paricis <lb/>&longs;emper minores, pro multitudine, & ratione &longs;patiorum æqua<lb/>lium, quæ motu decurruntur; ita videlicet, vt pars &longs;ecunda <lb/>spatij, ab&longs;oluatur dimidia parte temporis, quo prima pars <lb/>decur&longs;a est; & tertia pars &longs;patij, tertia parte eiu&longs;dem primi <lb/>temporis percurratur, & ita de cæteris: maximè cùm in hac <lb/>etiam hypothe&longs;i, &longs;patia & velocitates in eadem e&longs;&longs;e ratione, <lb/>& quod con&longs;equens e&longs;t, ex impeta quoque decidentium corpo<lb/>rum hac ratione inuariato, iidem omnes, quos experientia <lb/>docet effectus haberi, primo a&longs;pectu videantur.<emph.end type="italics"/></s><s> Heic pro<lb/>fectò rur&longs;us mirari tuam &longs;agacitatem par e&longs;t, qua<lb/>tenus eam non fugit error qui ex po&longs;itione à te a&longs;<lb/>&longs;erta con&longs;equitur; tamet&longs;i ip&longs;e non con&longs;equi ex iis, <lb/>quæ &longs;ubiicis, contendas. </s>

<s>Me quod attinet, is e&longs;t <lb/>ip&longs;emet, quem deduxi aliàs aduer&longs;us Michaelem <lb/>Varronem, qui primus, quod &longs;ciam, eandem po&longs;itio<lb/>nem ante annos plus minùs &longs;exaginta defendit; de<lb/>clarando ex ea id incommodi inter cætera con&longs;equi, <lb/>vt, quemadmodum antè in&longs;inuaui, &longs;patia acqui&longs;ita <lb/>in &longs;ine æqualis cuiu&longs;libet temporis numeranda &longs;int, <lb/>vt difformiter, &longs;ic in plu&longs;quàm tripla ratione. </s>

<s>Vt <pb pagenum="58"/>autem iam rem te iudice experiar; ecce a&longs;&longs;umptâ, diui<lb/>&longs;aque linea, quam ip&longs;e v&longs;urpas, AB, & &longs;up<lb/><figure id="fig16"></figure><lb/>po&longs;ito tempore minutorum &longs;ex, quo &longs;uppo<lb/>nis AD primam partem percurri; Con&longs;tat <lb/>omninò, &longs;i &longs;ecunda æqualis pars DE per<lb/>curratur velocitate dupla ad illam, qua per<lb/>curritur AD, non in&longs;umi plus temporis in <lb/>percurrenda parte &longs;ecunda, quàm dimidium <lb/>eius, quod fuerit in&longs;umptum in prima (cùm <lb/>hac ratione tempora velocitatum &longs;ubmultipla <lb/>&longs;int) atque ita, &longs;i prima pars &longs;uperata fuerit mi<lb/>nutis &longs;ex, percurri &longs;ecundam dimidio, &longs;eu mi<lb/>nutis tribus. </s>

<s>Eadem autem ratione &longs;i tertia <lb/>æqualis EF percurratur tripla, nece&longs;&longs;e e&longs;t <lb/>percurratur temporis triente, &longs;eu minutis duo<lb/>bus; ac eodem modo quarta FG quadrante, <lb/>&longs;eu &longs;e&longs;quiminuto, & quinta GH quinta par<lb/>te temporis, &longs;eu minuto vno cum &longs;ecundis duodecim; <lb/>ac &longs;exta HB, &longs;extante, &longs;eu minuto vno, & ita deinceps. <lb/></s>

<s>Atque ego quidem hûc v&longs;que nullum video paralo<lb/>gi&longs;mum. </s>

<s>Quamobrem re&longs;tat, vt di&longs;quiratur, quot<lb/>nam æqualia &longs;patia, parte&longs;ve &longs;patii æquales tem<lb/>poribus primum con&longs;equentibus, ip&longs;ique æqualibus <lb/>percurrantur. </s>

<s>Porrò cùm ad id perno&longs;cendum, ni<lb/>hil oporteat aliud, quàm iungere &longs;imul varia hæc <lb/>fragmenta primi temporis, hoc e&longs;t dimidium, trien<lb/>tem, quadrantem, & porrò parteis quintam, &longs;extam, <lb/>&longs;eptimam, &c. </s>

<s>deprehendimus in ip&longs;o fine quarti <lb/>&longs;patij, ex iunctis &longs;imul dimidio, triente & quadrante, <lb/>confectum e&longs;&longs;e &longs;ecundum tempus, &longs;eu iteratò minuta <pb pagenum="59"/>&longs;ex, cum &longs;uperante duodecima parte. </s>

<s>Ac pari ratio<lb/>ne in fine vndecimi &longs;patij, ex &longs;uper-adiunctis parti<lb/>bus quinta, &longs;exta, &longs;eptima, octaua, nona, decima, <lb/>vndecima, confectum e&longs;&longs;e tertium tempus, &longs;eu ite<lb/>rum minuta &longs;ex, cum &longs;uperante vna &longs;exage&longs;ima par<lb/>te. </s>

<s>Et in fine &longs;patij trige&longs;imi primi, ex &longs;uperadiun<lb/>ctis duodecima, decimatertia, &c. </s>

<s>confectum quar<lb/>tum, &longs;eu &longs;ex minuta, cum &longs;uperante parte circiter <lb/>quadrage&longs;ima. </s>

<s>Et in fine octoge&longs;imi quarti, ex &longs;u<lb/>peradiunctis trige&longs;ima &longs;ecunda, trige&longs;ima tertia, &c. <lb/></s>

<s>confectum quintum, &longs;eu &longs;ex minuta, cum &longs;uperante <lb/>vna parte proximè nonage&longs;ima, atque ita deinceps. <lb/></s>

<s>Vnde licet aduertere, fore vt &longs;patia ea ratione incre&longs;<lb/>cant, quæ a&longs;&longs;umptis quibu&longs;libet æqualibus tempori<lb/>bus deprehendatur excedere, & difformiter quidem, <lb/>&longs;eu inæquabiliter, triplam; quippe procedendo per <lb/>hos numeros, vnum, quatuor, vndecim, triginta <expan abbr="vn&utilde;">vnum</expan>, <lb/>octoginta quatuor, &c. </s>

<s>&longs;icque lapide decidente pri<lb/>mo momento per vnam v. </s>

<s>orgyiam, fore vt &longs;ecun<lb/>do æquali momento decidendo per treis, in tertio <lb/>per &longs;eptem, in quarto per viginti, in quinto per quin<lb/>quaginta duas, deciderit in fine quinti, orgyiis octo<lb/>ginta quatuor, ac breui res &longs;it abitura in immen&longs;um, <lb/>&longs;ecu&longs;que quàm docet ip&longs;a experientia, iuxta quam <lb/>orgyiiæ in fine quinti momenti &longs;uperatæ, colliguntur <lb/>plures e&longs;&longs;e non debere, quàm viginti quinque. </s>

<s>XXXII. </s>

<s>Demon&longs;tras ip&longs;e alia ratione (&longs;ed nimi<lb/>rùm aduer&longs;um te) non fieri accelerationem pro &longs;ub<lb/>diui&longs;ione i&longs;ta temporis. <emph type="italics"/>Si igitur,<emph.end type="italics"/> inquis, <emph type="italics"/>accelera io <lb/>motus per eam primi temporis &longs;ubdiui&longs;ionem fieret, de qua<emph.end type="italics"/><pb pagenum="60"/><emph type="italics"/>heic &longs;ermo e&longs;t, pars &longs;ecunda DE tribus minutis percurri <lb/>deberet, hoc e&longs;t dimidia parte primi temporis; & pars ter<lb/>tia EF duobus minutis, nempe tertia parte eiu&longs;aem primi <lb/>temporis, & ita de cæteris.<emph.end type="italics"/></s><s> Quamobrem verò id non <lb/>fieret; cùm &longs;uppo&longs;ito tuo illo principio de velocita<lb/>tibus &longs;e&longs;e habentibus vt &longs;patijs, & nullus &longs;it paralo<lb/>gi&longs;mus, & res &longs;ponte &longs;ua &longs;e prodat, neque videatur <lb/>euerti po&longs;&longs;e, abs te, vt mox tentas euertere, ni&longs;i tua <lb/>ip&longs;ius euertas principia, & fal&longs;itatem prodens con&longs;e<lb/>quentis, quod tamen ex tuis principiis tam nece&longs;&longs;a<lb/>riò deducitur, videaris etiam prodere fal&longs;itatem ante<lb/>cedentis? </s>

<s>Pergis itaque, <emph type="italics"/>At rem non ita accidere facilè <lb/>intelligimus, diui&longs;a bifariam parte AD in S, & parte <lb/>item DE &longs;imiliter in X. </s>

<s>Tunc enim ob eandem ratio<lb/>nem nece&longs;&longs;e fuerit, vt pars SD percurratur in dimidio <lb/>eius temporis, quo pars AS decurritur; & DX in ter<lb/>tia parte, itemque XE in quarta parte eiu&longs;dem temporis, <lb/>vt manife&longs;tum e&longs;t.<emph.end type="italics"/></s><s> Quor&longs;um verò id nece&longs;&longs;e non fue<lb/>rit; cùm eadem &longs;it ratio dimidij ad dimidium, quæ <lb/>totius ad totum, & nulla &longs;it ob&longs;eruatio, aut ratio, ex <lb/>qua aliud inferatur potiùs de partibus AD, DE, EF, <lb/>&c. </s>

<s>quàm de partibus AS, SD, DX, &c. </s>

<s>aut de <lb/>quibu&longs;libet minoribus, dummodò &longs;int omnes inter <lb/>&longs;e æquales? </s>

<s>Pergis iterum, C<emph type="italics"/>ùm igitur &longs;upponamus <lb/>totam AD minutis &longs;ex pertran&longs;iri, nece&longs;&longs;e erit, vt decur<lb/>&longs;us per AS quatuor minuta, & de&longs;cen&longs;us per SD duo <lb/>tantum minuta in&longs;umat: vt &longs;cilicet ea ratione tempus de&longs;<lb/>cen&longs;us per SD &longs;it dimidia pars temporis in de&longs;cen&longs;u per AS <lb/>in&longs;umpti; ideoque etiam pars DX minuti.<emph.end type="italics"/> 1 <gap/> <emph type="italics"/>nempe tertia <lb/>parte temporis AS; & pars XE minuto vno, &longs;iue<emph.end type="italics"/><pb pagenum="61"/><emph type="italics"/>quarta parte eiu&longs;dem temporis percurreretur; &longs;icque de&longs;cen<lb/>&longs;us per totam DE minutis<emph.end type="italics"/> (2 <gap/>) <emph type="italics"/>ab&longs;olueretur.<emph.end type="italics"/></s><s> Quid ni <lb/>verò id quoque nece&longs;&longs;e non &longs;it, ex&longs;i&longs;tente &longs;emper <lb/>eadem ratione dimidiorum ad dimidia, quæ toto<lb/>rum ad tota? </s>

<s>At <emph type="italics"/>paullò antè,<emph.end type="italics"/> inquis, <emph type="italics"/>&longs;uppo&longs;uimus ean<lb/>dem partem non ni&longs;i tribus minutis decurri.<emph.end type="italics"/></s><s> Id verò &longs;anè <lb/>non &longs;uppo&longs;ui&longs;ti, vt aliquid gratis conce&longs;&longs;um; &longs;ed vt <lb/>aliquid nece&longs;&longs;ariò cum tuis principiis cohærens. <lb/></s>

<s>Quare & fit quidem, vt euincas rem e&longs;&longs;e impo&longs;&longs;ibi<lb/>lem, percurri partem DE dimidio eius temporis, quo <lb/>percurritur AD; &longs;ed euincas tamen aduer&longs;us teip&longs;um; <lb/>cùm ex hoc rursùs efficiatur, vt motu æquabiliter ac<lb/>celerato ex A in E, non fuerint in E acqui&longs;iti duo <lb/>celeritatis gradus, quemadmodum in D fuit acqui&longs;i<lb/>tus vnus, &longs;i mobile quidem per totam DE non &longs;it <lb/>motum duplò velocius, quàm per totam DA; atque <lb/>idcircò in dimidio temporis, durationeve minuto<lb/>rum trium. </s>

<s>Fit etiam, vt quando concludis, <emph type="italics"/>Per <lb/>hanc igitur primi temporis &longs;ubdiui&longs;ionem, accelerationem <lb/>motus in de&longs;cen&longs;u grauium &longs;atis exactè non explicari;<emph.end type="italics"/> adiici <lb/>po&longs;&longs;it, neque explicari per tuam illam po&longs;itionem, <lb/>cum qua hæc &longs;ubdiui&longs;io indiuiduè connexa e&longs;t, & <lb/>à qua illam auertere, ob contradictionem con&longs;equen<lb/>tem conatus, nihil aliud videris, quàm, quod vulgò <lb/>aiunt, incommodum per incommodum &longs;oluere. </s>

<s>XXXIII. </s>

<s>Prætextu &longs;ubinde quæ&longs;ito vlterioris <lb/><expan abbr="incõmodi">incommodi</expan>, &longs;ub&longs;ternis qua&longs;i fundamentum con&longs;tituen<lb/>dæ po&longs;teà à te progre&longs;&longs;ionis motus per parteis tem<lb/>poris æqualeis &longs;ecundum rationem continenter du<lb/>plam. </s>

<s>Nam, <emph type="italics"/>Accedit,<emph.end type="italics"/> inquis, <emph type="italics"/>quòd tota DE eodem<emph.end type="italics"/><pb pagenum="62"/><emph type="italics"/>præcisè tempore, quo pars<emph.end type="italics"/> S<emph type="italics"/>D tran&longs;curreretur<emph.end type="italics"/> (tempore <lb/>nimirùm non trium, non duorum cum triente, vt <lb/>priùs, &longs;ed minutorum præcisè duorum) id autem &longs;ic <lb/>probas. <emph type="italics"/>Cùm enim AD dupla ponatur ip&longs;ius A<emph.end type="italics"/>S, <emph type="italics"/>& <lb/>&longs;imiliter AE dupla &longs;it ip&longs;ius AD, nece&longs;&longs;e e&longs;t, vt velocitas <lb/>in D dupla &longs;it velocitatis in<emph.end type="italics"/> S; <emph type="italics"/>& velocitas in E eodem <lb/>modo dupla reperiatur velocitatis in D; imò, vt velocitas <lb/>etiam quæcumque in quovis puncto inter D, & E con&longs;titu<lb/>to de&longs;ignabilis perpetuò dupla &longs;it velocitatis alterius inter S, <lb/>& D etiam aßignabilis, vt facilè quilibet per &longs;e intelligere <lb/>pote&longs;t. </s>

<s>Sumpto enim puncto quocumque inter D, & E, <lb/>ex empli gratiâ T, diui&longs;oque bifariam interuallo AT, &longs;ectio <lb/>nece&longs;&longs;ario cadet inter D, &<emph.end type="italics"/> S, <emph type="italics"/>puta in V. </s>

<s>Et quia erit <lb/>AT dupla ip&longs;ius AV, erit etiam velocitas in T dupla ve<lb/>locitatis in V, & ita in cæteris punctis, quæ de&longs;ignari po&longs;&longs;unt <lb/>inter D, & E. </s>

<s>Quare per totum interuallum DE velocitas <lb/>erit dupla velocitatis per totum spatium<emph.end type="italics"/> SD, <emph type="italics"/>&longs;icut interual<lb/>lum DE duplum e&longs;t interualli<emph.end type="italics"/> SD. <emph type="italics"/>Ambo igitur hæc in<lb/>terualla nempe<emph.end type="italics"/> SD, <emph type="italics"/>& DE æquali tempore percurruntur.<emph.end type="italics"/><lb/>Quo loco admitto imprimis, vt nouum incommo<lb/>dum, eandem partem DE, quæ probata e&longs;t primùm <lb/>percurri debere ex tuo principio minutis tribus, ac <lb/>deinde minutis duobus cum triente, probari iam per<lb/>curri debere minutis duobus. </s>

<s>Quippe nihil e&longs;t, quod <lb/>magis prodat fal&longs;itatem principii, quàm tot repu<lb/>gnantium, atque ab&longs;urdorum capitum deductio. <lb/></s>

<s>Neque verò heic adhûc finis; quandò alia innumera <lb/>pari ratione con&longs;equentur. </s>

<s>Nam &longs;i, v.c. </s>

<s>AS bifa<lb/>riam &longs;ecetur in P, conficietur eodem tuo ratiocinio, <lb/>vt PS percurratur eodem tempore, quo SD, atque <pb pagenum="63"/>idcirco eodem, quo DE. </s>

<s>Et quia &longs;eruatâ analogià <lb/>PS percurri debet vno minuto cum triente, efficie<lb/>tur, vt non modò SD, verùm ip&longs;a quoque DE per<lb/>curratur rursùs non duobus minutis, &longs;ed vno&longs;olùm <lb/>cum triente; atque ita bifariam &longs;ecando, diminuendo<lb/>que in infinitum. </s>

<s>Adnoto deinde non tran&longs;ire te <lb/>vltrà comparationem partis DE cum parte SD, ne<lb/>que comparare ip&longs;am cum parte PS, vt mox factum <lb/>e&longs;t, & fieri po&longs;&longs;e nihil prohibet; cùm nulla &longs;it ratio, <lb/>ob <expan abbr="quã">quam</expan> in hac potiùs bi&longs;ectione, <expan abbr="quã">quam</expan> in vlteriore vlla <lb/>con&longs;i&longs;tatur; verùm a&longs;&longs;umere te &longs;olum, id <emph type="italics"/>tempus, quo <lb/>ab&longs;oluitur interuallum<emph.end type="italics"/> SD <emph type="italics"/>breuius e&longs;&longs;e tempore, quo pars <lb/>&longs;uperior<emph.end type="italics"/> AS <emph type="italics"/>tran&longs;curritur, alioquin de&longs;cen&longs;us &longs;ine accelera<lb/>tione vniformis e&longs;&longs;et;<emph.end type="italics"/> idque, vt inferas, <emph type="italics"/>partem primùm <lb/>de&longs;ignatam<emph.end type="italics"/> DE, <emph type="italics"/>cum eodem præcisè tempore percurratur, <lb/>quo interuallum<emph.end type="italics"/> SD, <emph type="italics"/>non in dimidio prioris temporis, &longs;ed <lb/>tempore breuiore ab&longs;olui.<emph.end type="italics"/></s><s> Adnoto, inquam, vt appareat, <lb/>cui fundamento &longs;uper-ex&longs;truas quicquid deinceps <lb/>ædificas, &longs;upponens nimirùm vt ratum principium <lb/>(quod obiter, & aliud agendo &longs;tabilieris) æqualita<lb/>tem temporis, quo pars SD, & ip&longs;ius dupla DE per<lb/>curruntur. </s>

<s><emph type="center"/><emph type="italics"/>DeTempore, quo R. P. colligit &longs;ingulas parteis decur &longs;umiri.<emph.end type="italics"/><emph.end type="center"/></s>

<s>XXXIV. </s>

<s>Etenim illicò &longs;ic habes; <emph type="italics"/>Sed ex his, <lb/>& eadem pror&longs;us ratione aliud demonstratur, quod ingentis, <lb/>atque admirabilis paradoxi loco non immeritò fortaßis habe<lb/>ri poßit, nempe &longs;i spatium, per quod corpus graue quod<lb/>cumque de&longs;cendit, in parteis quotlibet æqualeis diui&longs;um intel<lb/>ligatur, & primæ, ac &longs;upremæ partis etiam de&longs;ignetur<emph.end type="italics"/><pb pagenum="64"/><emph type="italics"/>dimidia pars, & tertia, & quarta, ac deinceps cæteræ, inci<lb/>piendo diui&longs;iones i&longs;tas omneis ab infimo eiu&longs;dem primæ par<lb/>tis puncto, donec totidem de&longs;ignatæ &longs;int, quo<gap/> in reliquo &longs;patio <lb/>partes æquales acceptæ fuerint: tum &longs;ingulæ partes buiu&longs;mo<lb/>di æquales tanto præcisè tempore à corpore graui<emph.end type="italics"/><lb/><figure id="fig17"></figure><lb/><emph type="italics"/>de&longs;cendente percurrantur, quanto partes ip&longs;is analo<lb/>gæ, ac respondentes in &longs;uprema parte<emph.end type="italics"/> (&longs;eu infe<lb/>riore eius dimidio) <emph type="italics"/>ab eodem corpore graui de<lb/>cur&longs;æ fuerint.<emph.end type="italics"/></s><s> Rem con&longs;equenter ita declaras; <lb/>S<emph type="italics"/>it &longs;patium<emph.end type="italics"/> AB (in &longs;chemate hoc) <emph type="italics"/>per quod <lb/>corpus graue de&longs;cendat, in parteis exempli gratiâ <lb/>&longs;ex æqualeis diui&longs;um in<emph.end type="italics"/> C, D, E, F, & G: <emph type="italics"/>primæ<lb/>que, ac &longs;upremæ partis<emph.end type="italics"/> AC, <emph type="italics"/>ex infimo eius pun<lb/>cto<emph.end type="italics"/> C <emph type="italics"/>de&longs;ignetur primùm media pars<emph.end type="italics"/> CH, <emph type="italics"/>dein<lb/>de tertia<emph.end type="italics"/> CI, <emph type="italics"/>& quarta<emph.end type="italics"/> CK, <emph type="italics"/>itemque quinta, & <lb/>&longs;exta<emph.end type="italics"/> CL, <emph type="italics"/>&<emph.end type="italics"/> CM. <emph type="italics"/>Dico corpus graue de&longs;cen<lb/>dens per<emph.end type="italics"/> AB <emph type="italics"/>tanto præcisè tempore pertran&longs;ire &longs;e<lb/>cundam partem<emph.end type="italics"/> CD, <emph type="italics"/>quanto dimidiam primæ par<lb/>tis<emph.end type="italics"/> HC, <emph type="italics"/>antè pertran&longs;iuit; & &longs;imiliter pari, atque <lb/>æquali tempore partem<emph.end type="italics"/> DE, <emph type="italics"/>quæ ordine tertia est, <lb/>& tertiam prim&ecedil; partis, nempe<emph.end type="italics"/> IC <emph type="italics"/>ab eodem cor<lb/>pore de&longs;cendente tran&longs;curri, & ita de c&ecedil;teris.<emph.end type="italics"/></s><s> Tunc <lb/>autem pergis. <emph type="italics"/>Et quidem de &longs;ecunda parte<emph.end type="italics"/> CD, <lb/><emph type="italics"/>eam non longiore tempore decurri, quàm quo prim&ecedil; <lb/>partis posterior dimidia pars tran&longs;ini&longs;&longs;a fuerit, iam <lb/>paulò antè o&longs;ten&longs;um est, nec maiore negotio idem <lb/>de c&ecedil;teris quoque partibus concludetur. </s>

<s>Sumpto <lb/>enim<emph.end type="italics"/> CN, <emph type="italics"/>&c.<emph.end type="italics"/></s>

<s>Verùm priu&longs;quàm gradus ad <lb/>cæteras fiat, con&longs;i&longs;tendum e&longs;t in hac prima; cùm <pb pagenum="65"/>non &longs;it nequicquam, quod de ip&longs;a admonui. </s>

<s>O&longs;ten<lb/>&longs;um e&longs;&longs;e ais tempus, quo percurritur CD, æquale e&longs;&longs;e <lb/>tempori, quo decur&longs;um fuerit HC: &longs;eu, ne confun<lb/>damus, & rem explicemus, qua&longs;i repetendam ex &longs;u<lb/>periore &longs;chemate, o&longs;ten&longs;um e&longs;&longs;e ais id tempus, quo <lb/>percurritur DE, æquale e&longs;&longs;e tempori, quo de<lb/><figure id="fig18"></figure><lb/>cur&longs;um fuerit SD. </s>

<s>At primò, in&longs;inuatum iam <lb/>e&longs;t id e&longs;&longs;e impo&longs;&longs;ibile; cùm quo iure ip&longs;e bi<lb/>&longs;ecui&longs;ti primam partem AD in S, liceat bi<lb/>&longs;ecare primum dimidium AS in P; & rursùs <lb/>primum horum dimidiorum in duo alia, & <lb/>primum i&longs;torum in duo, & ita porrò quoties <lb/>libuerit: Iuxta tuum verò ratiocinium, &longs;e qua<lb/>tur tempus, quo percurritur SD, e&longs;&longs;e æqua<lb/>le tempori, quo decur&longs;um fuerit PS, quate<lb/>nus, vt velocitas per totam DE e&longs;t dupla ve<lb/>locitatis per totam SD, quemadmodum in<lb/>teruallum duplum e&longs;t; ita velocitas per totam <lb/>SD dupla e&longs;t velocitatis per totam PS, &longs;icut <lb/>interuallum e&longs;t itidem duplum; Hoc autem <lb/>po&longs;ito, vlteriùs &longs;equatur tempus per SD, atque <lb/>idcircò per DE ip&longs;i æquale, e&longs;&longs;e non iam minuto<lb/>rum duorum, vt o&longs;tendi&longs;ti, &longs;ed minuti vnius cum <lb/>triente; vt pote coæquatum tempori per PS, quod <lb/>tam e&longs;&longs;e debet triens quatuor minutorum (quibus <lb/><gap/>is AS percurri) quàm tempus per SD &longs;tatuitur à <lb/>te triens minutorum &longs;ex (quibus percurritur AD) <lb/>cùm id tamen factuimpo&longs;&longs;ibile &longs;it, repugnantia putà <lb/>inuoluens, ac tantò magis, quantò ex vlterioribus <lb/>&longs;ubdiui&longs;ionibus probari pote&longs;t eandem DE percurri <pb pagenum="66"/>rursùs non vno minuto, ac triente, &longs;ed &longs;ecundis &longs;olùm <lb/>proximè quinquaginta tribus; & rursùs proximè <lb/>octodecim, & rursùs &longs;ex, &c. </s>

<s>Deinde, cùm ad id <lb/>o&longs;tendendum v&longs;us fueris ea ratione, quòd nece&longs;&longs;e &longs;it, <lb/><emph type="italics"/>velocitatem in D duplam e&longs;&longs;e velocitatis in<emph.end type="italics"/> S, <emph type="italics"/>& veloci<lb/>tatem in E duplam velocitatis in D, &longs;icuti<emph.end type="italics"/> AD <emph type="italics"/>ponitur du<lb/>pla ip&longs;ius<emph.end type="italics"/> AS, <emph type="italics"/>& &longs;imiliter<emph.end type="italics"/> AE <emph type="italics"/>dupla e&longs;t ip&longs;ius<emph.end type="italics"/> AD; &longs;e<lb/>quitur exinde, vt tam tota DE, quàm tota SD per<lb/>curratur non triente, &longs;ed dimidio temporis, quo tota <lb/>AD: cùm vbicumque e&longs;t velocitatis duplum, vbi &longs;it <lb/>dimidium temporis duntaxat, neque tu id infregeris, <lb/>&longs;ed incommodum &longs;olùm attuleris, quod cùm euertat <lb/>con&longs;equutionem de &longs;ubdiui&longs;ione primi temporis, &longs;up<lb/>po&longs;itionem quoque euertit de velocitate dupla in du<lb/>plo &longs;patii, tripla in triplo, &c. </s>

<s>vt aliquoties e&longs;t incul<lb/>catum. </s>

<s>Nam & quod po&longs;teà a&longs;&longs;umis tempus per <lb/>SD, atque adeò DE e&longs;&longs;e breuius, quàm dimidium <lb/>eius, quo tran&longs;curritur AD, id facis quidem rectè, <lb/>verumtamen iure non tuo; quippe id facis &longs;olùm me<lb/>tu eius incommodi, quod præ&longs;en&longs;iti po&longs;&longs;e vrgeri de <lb/>motus acceleratione vniformiter, continenterque in<lb/>cre&longs;cente: cùm id alioquin & repugnet tuæ &longs;uppo&longs;i<lb/>tioni de velocitate dupla in duplo &longs;patio, tripla in <lb/>triplo, &c. </s>

<s>& euertat demon&longs;trationem ip&longs;am, ad <lb/>quam iam recurris, cùm o&longs;ten&longs;um ais tempus, quo <lb/>percurritur &longs;ecunda pars, æquale e&longs;&longs;e tempori, quo <lb/>tran&longs;mittitur dimidium po&longs;terius, &longs;eu inferius primæ: <lb/>neque enim id fuit o&longs;ten&longs;um alio ratiocinio, quam <lb/>quod ip&longs;emet &longs;tatim pernega&longs;ti. </s>

<s>XXXVI. </s>

<s>Attamen &longs;upponatur etiam tua huiu&longs;-<pb pagenum="67"/>modi de mon&longs;tratio; Sequitur ecce rursùs, vt tempus, <lb/>quo percurritur DE &longs;e&longs;quialterum &longs;it, non verò æqua<lb/>le illi tempori, quo percurritur SD. </s>

<s>Cum velocita<lb/>tes enim &longs;int per te, vt &longs;patia; ac aliunde &longs;it manife<lb/>&longs;tum, vbi e&longs;t duplum velocitatis, ibi dimidium e&longs;&longs;e <lb/>temporis, vbi triplum trientem, atque ita&longs;emper in ra<lb/>tione &longs;ubmultipla; &longs;i &longs;it primò vt AE ad AD, ita <lb/>AD ad AS; erit igitur diuidendo vt AS ad SD, ita <lb/>AD, ad DE; ac deinde, &longs;i &longs;it AS tempus minuto<lb/>rum quatuor, & SD minutorum duorum; Erit igitur <lb/>tempus AD quidem minutorum &longs;ex, & DE minuto<lb/>rum trium, atque adeò &longs;e&longs;qui-alterum, non æquale <lb/>tempori SD. </s>

<s>Sequitur iterùm, vt non &longs;ecùs, quàm <lb/>Galileus ratiocineris, dum Paralogi&longs;mi illum arguis. <lb/></s>

<s>Siquidem ex tuo quoque ratiocinio euineitur, vt to<lb/>ta AE eodem tempore, quo ip&longs;a AD, quæ pars eius <lb/>e&longs;t, percurratur. </s>

<s>Nam &longs;i vt AE ad AD, ita DE ad <lb/>SD; ergo vt DE tempus ad SC tempus, ita AE tem<lb/>pus ad AD tempus: Atqui DE tempus per te e&longs;t <lb/>æquale tempori SD; igitur AE tempus æquale erit <lb/>AD tempori; hoc e&longs;t totum, & pars percurrentur <lb/>tempore æquali, aut eodem. </s>

<s>Sequitur prætereà, vt <lb/>quia quælibet magnitudo etiam ip&longs;a diameter Mundi <lb/>tam e&longs;t dupla &longs;ui dimidij, quàm AE e&longs;t ip&longs;ius AD, & <lb/>tam in fine dupli e&longs;t velocitas dupla, quam in fine <lb/>dimidij dimidia; ideò etiam diameter Mundi ita &longs;e <lb/>ad &longs;emidiametrum habeat, vt DE ad SD; quare & <lb/>quemadmodum DE percurritur eodem tempore, quo <lb/>SD, duobus videlicet minutis; ita etiam Mundi &longs;emi<lb/>diameter debeat eodem tempore, &longs;eu duobus minutis <pb pagenum="68"/>percurri. </s>

<s>Quippe & tamet&longs;i partes &longs;int incompara<lb/>biliter plures in &longs;emidiametro Mundi, quàm in &longs;pa<lb/>tiolo DE, &longs;unt tamen gradus velocitatis incompara<lb/>biliter etiam plures, ac proportione totidem; vt tem<lb/>pora &longs;ubmultipla illis &longs;uperandis &longs;ufficere valeant. </s>

<s>Vt <lb/>breue faciam, erroris origo ex eo profluxi&longs;&longs;e videtur, <lb/>quòd merè gratis con&longs;titeris in parte AD, eiu&longs;que <lb/>dimidio inferiore SD; & rem perinde habueris, ac &longs;i <lb/>dimidium &longs;uperius AS diuidi perinde non po&longs;&longs;et, ne<lb/>que haberet &longs;peciatim dimidium eadem ratione, qua <lb/>habet AD. </s>

<s>Proptereà enim accepi&longs;ti &longs;olùm omnia <lb/>de&longs;ignabilia punctaper totam DE, in quibus veloci<lb/>tas e&longs;&longs;et dupla velocitatis in totidem punctis per to<lb/>tam SD; neque reputa&longs;ti pergendum, vt haberes <lb/>eodem tenore puncta de&longs;ignabilia per totam SD, in <lb/>quibus velocitas e&longs;&longs;et dupla velocitatis in totidem <lb/>punctis de&longs;ignabilibus per totam PS, atque ita in in<lb/>finitum; vt prorsùs nece&longs;&longs;arium e&longs;t ex tua ip&longs;ius &longs;up<lb/>po&longs;itione. </s>

<s>Quanquam res vberiùs cogno&longs;cenda e&longs;t <lb/>circa cæteras, quas de&longs;cribis parteis. </s>

<s>XXXVII. </s>

<s>Vt enim probes (re&longs;umpto iam recen<lb/>tiore &longs;chemate) tempus per tertiam partem DE æqua<lb/>le e&longs;&longs;e tempori per trientem primæ partis IC, <emph type="italics"/>Sumpto,<emph.end type="italics"/><lb/>inquis, CN <emph type="italics"/>æquali ip&longs;i<emph.end type="italics"/> CE, <emph type="italics"/>erit tota<emph.end type="italics"/> AD <emph type="italics"/>diui&longs;a in <lb/>treis parteis æqualeis<emph.end type="italics"/> AI, IN, <emph type="italics"/>&<emph.end type="italics"/> ND; <emph type="italics"/>eritque veloci<lb/>tas in<emph.end type="italics"/> D <emph type="italics"/>ad velocitatem in<emph.end type="italics"/> I, <emph type="italics"/>vt tota<emph.end type="italics"/> AD <emph type="italics"/>ad ip&longs;am<emph.end type="italics"/> AI, <emph type="italics"/>hoc <lb/>e&longs;t tripla. </s>

<s>Cumque ob eandem cau&longs;&longs;am velocitas quoque in<emph.end type="italics"/> E <lb/><emph type="italics"/>tripla etiam &longs;it velocitatis in<emph.end type="italics"/> C, <emph type="italics"/>erit velocitas per totam<emph.end type="italics"/> DE <lb/><emph type="italics"/>tripla velocitatis per totam<emph.end type="italics"/> IC, <emph type="italics"/>&longs;icut tota<emph.end type="italics"/> DE <emph type="italics"/>tripla e&longs;t ip&longs;ius<emph.end type="italics"/><lb/>IC; <emph type="italics"/>ac proinde percurrentur<emph.end type="italics"/> IC, <emph type="italics"/>&<emph.end type="italics"/> DE <emph type="italics"/>æquali tempore.<emph.end type="italics"/><pb pagenum="69"/>Et con&longs;equenter, vt pergas probate tempus per <lb/><figure id="fig19"></figure><lb/>quartam partem EF æquale e&longs;&longs;e tempori per <lb/>KC quadrantem primæ, <emph type="italics"/>Similiter,<emph.end type="italics"/> inquis, <emph type="italics"/>di<lb/>ui&longs;a bifariàm<emph.end type="italics"/> CD <emph type="italics"/>in<emph.end type="italics"/> O, <emph type="italics"/>&longs;umptoque quadr inte<emph.end type="italics"/><lb/>DP <emph type="italics"/>æquali ip&longs;i<emph.end type="italics"/> KC, <emph type="italics"/>tota<emph.end type="italics"/> AE <emph type="italics"/>diui&longs;a erit in par<lb/>teis quatuor æqualeis<emph.end type="italics"/> AK KO, OP, PE; <emph type="italics"/>ideó <lb/>que velocitas in<emph.end type="italics"/> E <emph type="italics"/>erit quadrupla velocitatis in<emph.end type="italics"/> K, <emph type="italics"/>vt <lb/>tota<emph.end type="italics"/> AE <emph type="italics"/>quadrupla e&longs;t ip&longs;ius<emph.end type="italics"/> AK. <emph type="italics"/>At velocitas <lb/>quoque in<emph.end type="italics"/> F <emph type="italics"/>ob eandem rationem quadrupla etiam e&longs;t <lb/>velocitatis in<emph.end type="italics"/> C; <emph type="italics"/>velocitas igitur per totam<emph.end type="italics"/> EF <lb/><emph type="italics"/>quadrupla e&longs;t velocitatis per totam<emph.end type="italics"/> KC, <emph type="italics"/>&longs;icut tota<emph.end type="italics"/><lb/>EF <emph type="italics"/>quadrupla e&longs;t ip&longs;ius<emph.end type="italics"/> KC. <emph type="italics"/>Percurrentur igitur<emph.end type="italics"/><lb/>KC, <emph type="italics"/>&<emph.end type="italics"/> EF <emph type="italics"/>æquali tempore.<emph.end type="italics"/></s><s> Sequitur, <emph type="italics"/>Ea <lb/>dem autem etiam ratio e&longs;t cæterarum omnium par<lb/>tium, vt facilè quilibet ex i&longs;tis per &longs;e intelliget.<emph.end type="italics"/></s><s> Con<lb/>cludis, <emph type="italics"/>Si &longs;patium igitur, per quod corpus quodcum<lb/>que graue de&longs;cendit, ea, qua dictum e&longs;t, ratione diui<lb/>&longs;um intelligatur, &longs;ingulæ partes huiu&longs;modi æquales tanto <lb/>præcisè tempore à corpore graui de&longs;cendente percur<lb/>rentur, quantò partes ip&longs;is analogæ ac re&longs;pondentes <lb/>in &longs;uprema parte<emph.end type="italics"/> (aut inferiore eius dimidio) <emph type="italics"/>de&longs;i <lb/>gnatæ ab eodem corpore graui decur&longs;æ fuerint, vt est <lb/>propo&longs;itum.<emph.end type="italics"/></s><s> Prætereo autem, quod &longs;ubinde de<lb/>claras te ad&longs;crip&longs;i&longs;&longs;e fini cuiu&longs;que &longs;ex partium <lb/>numerum integrum, incipiendo ab vnitate, <lb/>ad de&longs;ignandum velocitatis gradus illeic acqui&longs;itos, & <lb/>ex æquo factos cum decur&longs;is partibus; ad&longs;crip&longs;i&longs;&longs;e au<lb/>tem mediis interuallis &longs;ecundæ, & &longs;equentium partium <lb/>fractos numeros, ad de&longs;ignandum tempora, &longs;iue fra<lb/>ctiones temporis primi, quibus vnumquodque &longs;pa-<pb pagenum="70"/>tiorum primum con&longs;equentium percurritur. </s>

<s>XXXVIII. </s>

<s>Videris itaque imprimis haud abs re <lb/>dixi&longs;&longs;e <emph type="italics"/>admirabile Paradoxum:<emph.end type="italics"/> cùm habui&longs;ti videlicet <lb/>po&longs;terius primæ partis dimidium, vt &longs;calam Prototy<lb/>picam, cuius gradibus coæquetur, exqui&longs;itéque men<lb/>&longs;uretur cæterarum omnium con&longs;equentium duratio; <lb/>tamet&longs;i illud e&longs;&longs;e po&longs;&longs;it parte digiti mille&longs;ima minus, <lb/>& i&longs;tarum aggeries, quanta e&longs;t tota &longs;emidiameter <lb/>mundi. </s>

<s>Non &longs;anè, quod negem dari lineas, alia&longs;que <lb/>magnitudines, in quibus arcana prorsùs admiranda, <lb/>& quæ nemo vnquam &longs;u&longs;picatus fui&longs;&longs;et, detegantur à <lb/>Geometris: &longs;ed quod videri iure po&longs;&longs;it penitus incre<lb/>dibile alliga&longs;&longs;e potius naturam ip&longs;a qua&longs;i fat&adot; cætera<lb/>rum partiumip&longs;i po&longs;teriori, quàm prioridimidio; imò <lb/>& non tam toti ip&longs;i dimidio, quàm infimo illius pun<lb/>cto, à quo triens, quadrans, cæteræ fractiones debeant <lb/>&longs;upputari. </s>

<s>Ecquod-nam e&longs;&longs;e enim pote&longs;t illius pri<lb/>uilegium; aut quid-nam admi&longs;&longs;um à priore dimidio <lb/>e&longs;t, vt eo excidi&longs;&longs;e, & pro nihilo reputari iure cen&longs;ea<lb/>tur? </s>

<s>Quid habere <expan abbr="cõmune">commune</expan> pote&longs;t cente&longs;ima, mille&longs;ima <lb/>decie&longs;que, & centies mille&longs;ima pars <expan abbr="c&utilde;">cum</expan> po&longs;teriore hoc <lb/>dimidio; non habere autem cum illo priore, à quo to<lb/>tus motus dependet; non cùm cæteris partibus perinde <lb/>&longs;uccedentibus; non &longs;altem cum vicinis, quibu&longs;cum <lb/>proximè cohæret? </s>

<s>Deinde, ne hac in re hæream, ea<lb/>dem prorsùs incommoda ex triente pro tertia parte, <lb/>ex quadrante pro quarta, atque ita de cæteris, quæ ex <lb/>ip&longs;o dimidio pro &longs;ecunda con&longs;equuntur. </s>

<s>Nam, vt <lb/>rem circa ip&longs;um trientem, partemque tertiam &longs;olùm <lb/>atringam, Sicuti primùm totam AC in treis diui&longs;i&longs;ti <pb pagenum="71"/>trienteis quorum po&longs;tremus &longs;it IC; &longs;ic tota AH diui<lb/>di pote&longs;t in trienteis treis, quorum po&longs;tremus &longs;it QH; <lb/>& vt facis tempus per IC minuti vnius cum triente; <lb/>cùm &longs;it nempe triens minutorum quatuor, &longs;iue duo<lb/>rum bes; ita facere licet tempus per QH quadragin<lb/>ta &longs;ecundorum, cùm &longs;it triens minutorum duorum, <lb/>&longs;iue bes vnius minuti. </s>

<s>Cùm autem hoc modo QH <lb/>&longs;e habeat ad IC, vt IC, ad ND; & CA non minùs &longs;it <lb/>tripla ip&longs;ius AQ, quàm DA ip&longs;ius AI, vtráque nem<lb/>pe pari modo, quo EA ip&longs;ius AC; adeò vt velocitati<lb/>bus ob rationem triplam exæquatis, &longs;ic ego po&longs;&longs;im <lb/>concludere QH &longs;e habere ad IC, vt tu concludis IC <lb/>&longs;e habere ad DE, &longs;equitur, vt, quia concludis tempora <lb/>per IC, & DE e&longs;&longs;e æqualia; tempora quoque per QH, <lb/>& IC æqualia &longs;int, ac proinde tempus per IC &longs;it iam <lb/>non vnius minuti cum be&longs;&longs;e, &longs;ed dimidium minuti <lb/>cum &longs;extante; & qua ratione hoc &longs;equitur, &longs;equetur vt <lb/>a&longs;&longs;umpto dimidio ip&longs;ius AH, ac ita &longs;umptis in infini<lb/>tum dimidiorum dimidiis, quæ per trienteis diuidan<lb/>tur, futurum, vt ip&longs;a IC minore &longs;emper, ac minore in <lb/>in&longs;initum tempore, quàm ip&longs;e admi&longs;eris, cen&longs;eatur per<lb/>curri. </s>

<s>Sic ex eo, quod vis velocitatem in E e&longs;&longs;e tri<lb/>plam velocitatis in C; & velocitatem in D triplam <lb/>velocitatis in I, pro ratione nempe &longs;patiorum, Sequi<lb/>tur vt tam tota DE, quàm tota IC percurrantur non <lb/>iam vno minuto cum triente, &longs;ed omninò duobus <lb/>minutis, trienteve minutorum &longs;ex, quibus percurritur <lb/>AC: cùm vbicumque e&longs;t velocitatis triplum, ibi ma<lb/>nife&longs;tò non &longs;it nec ampliùs nec minùs, quàm tempo<lb/>ris triens. </s>

<s>Sic incidis rursùs in eum, quem e&longs;&longs;e cau&longs;-<pb pagenum="72"/>&longs;atus es in Galileo Paralogi&longs;mum. </s>

<s>Nam &longs;i vt AE ad; <lb/>AC ita DE ad IC; ergo vt DE tempus ad IC tempus, <lb/>ita AE tempus ad AC tempus; atqui tempus DE per <lb/>te e&longs;t æquale tempori IC; ergo AE tempus tempori <lb/>AC æquale erit; hoc e&longs;t pars, & totum æquali tempo<lb/>re percurrentur. </s>

<s>Sic quia totum quodlibet ita &longs;e habet <lb/>ad &longs;ui trientem, & velocitas in fine totius ad velocita<lb/>tem in fine trientis, vt &longs;e habet magnitudo, & veloci<lb/>tas AE comparata ad AC: &longs;equitur, vt etiam pari mo<lb/>do &longs;e habeat, quo DE comparata ad IC; quare & <lb/>quemadmodum DE triens ip&longs;ius AE eodem tempo<lb/>re percurritur, quo IC: ita diametri mundi triens eo<lb/>dem tempore percurratur. </s>

<s>Neque enim dicas maio<lb/>rem e&longs;&longs;e connexionem ip&longs;ius DE, quàm trientis dia<lb/>metri mundi cum ip&longs;a IC; nam vis ratiocinij e&longs;t &longs;o<lb/>lùm in comparatione totius ad trientem; & aliunde <lb/>quot &longs;unt plures partes in triente diametri mundi, <lb/>quàm in triente &longs;patij DE: totidem &longs;unt etiam veloci<lb/>tates plures, quibus tempore eodem &longs;uperetur, atque <lb/>ita de cæteris. </s>

<s><emph type="center"/><emph type="italics"/>De Ratione continuò dupla, qua &longs;patia decurri temporibus <lb/>æqualibus R. P. concludit.<emph.end type="italics"/><emph.end type="center"/></s>

<s>XXXIX. </s>

<s>Supere&longs;t po&longs;tremum, &longs;iue tertium mem<lb/>brum, de Ratione continuò dupla, qua pertran&longs;iri <lb/>&longs;patia temporibus continuò æqualibus infers. </s>

<s>Primùm <lb/>autem, vbi adnota&longs;ti non po&longs;&longs;e quidem ex deductio<lb/>ne à te mox facta, <emph type="italics"/>ab&longs;olutè colligi quantum præcisè tem<lb/>poris graue ex aßignata altitudine de&longs;cendens in toto de&longs;<lb/>cen&longs;u in&longs;umat, ni&longs;i di&longs;tinctè etiam cogno&longs;eatur tempus de&longs;-<emph.end type="italics"/><pb pagenum="73"/><emph type="italics"/>cen&longs;us non tantum per totam primam partem<emph.end type="italics"/> AC (in nu<lb/>pero &longs;chemate) <emph type="italics"/>&longs;ed etiam &longs;eor&longs;um per<emph.end type="italics"/> AH, <emph type="italics"/>& per<emph.end type="italics"/> HC; <lb/><emph type="italics"/>quod multò difficilius e&longs;&longs;e arbitreris, quàm<emph.end type="italics"/> G<emph type="italics"/>alileo videatur; <lb/>at cognitis, aut præ&longs;uppo&longs;itis temporibus illis, facilè deinceps <lb/>totum tempus totius de&longs;cen&longs;us per quamcumque de&longs;ignatam <lb/>altitudinem determinari:<emph.end type="italics"/> id quod <emph type="italics"/>postmodum te osten&longs;u<lb/>rum recipis.<emph.end type="italics"/></s><s> Tum &longs;upponens me ex&longs;pectare <lb/><figure id="fig20"></figure><lb/>diutiùs, quid &longs;is dicturus de <emph type="italics"/>Ratione, qua &longs;e ha<lb/>bent &longs;patia æquali tempore emen&longs;a,<emph.end type="italics"/> &longs;ic infis, <emph type="italics"/>Aio <lb/>verò æqualibus temporibus &longs;patia decurri maiora <lb/>&longs;emper, ac maiora in Ratione dupla. </s>

<s>Diui&longs;o enim <lb/>spatio<emph.end type="italics"/> AB, <emph type="italics"/>per quod &longs;upponitur fieri de&longs;cen&longs;us, in <lb/>parteis quotcumque æqualeis in<emph.end type="italics"/> C, D, E, F, <emph type="italics"/>&c. </s>

<s>iam <lb/>osten&longs;um est partem &longs;ecundam<emph.end type="italics"/> CD, <emph type="italics"/>& primæ par<lb/>tis dimidiam partem inferiorem<emph.end type="italics"/> NC <emph type="italics"/>æquali tempore <lb/>percurri; & ob eam quidem cau&longs;&longs;am, quòd, vt pars<emph.end type="italics"/><lb/>CD <emph type="italics"/>dupla e&longs;t partis<emph.end type="italics"/> NC, <emph type="italics"/>ita velocitas quoque per <lb/>totam<emph.end type="italics"/> CD <emph type="italics"/>dupla &longs;it velocitatis per totam<emph.end type="italics"/> NC. <emph type="italics"/>At <lb/>&longs;imili ratione etiam efficitur, velocitatem per totam<emph.end type="italics"/><lb/>DF <emph type="italics"/>duplam e&longs;&longs;e velocitatis eius, quæ habetur per <lb/>totam<emph.end type="italics"/> CD; <emph type="italics"/>&longs;icut tota<emph.end type="italics"/> DF <emph type="italics"/>dupla e&longs;t ip&longs;ius<emph.end type="italics"/> CD. <lb/>Æ<emph type="italics"/>quali igitur tempore<emph.end type="italics"/> CD, <emph type="italics"/>&<emph.end type="italics"/> DF <emph type="italics"/>decurruntur; <lb/>eademque omninò ratio e&longs;t ip&longs;arum<emph.end type="italics"/> DF, <emph type="italics"/>&<emph.end type="italics"/> FK, <lb/><emph type="italics"/>cæterarumque omnium &longs;e pariter in ratione dupla &longs;u <lb/>perantium; vt &longs;atis manife&longs;tum e&longs;t.<emph.end type="italics"/> S<emph type="italics"/>patia igitur <lb/>æqualibus temporibus emen&longs;a, & velocitates ii&longs;dem <lb/>temporibus æqualibus acqui&longs;itæ &longs;emper augentur in <lb/>continua ratione dupla.<emph.end type="italics"/></s>

<s>XL. Cæterùm, cùm i&longs;te habeatur qua&longs;i <lb/>prouentus quidam eximius totius tuæ Di&longs;&longs;ertationis; <pb pagenum="74"/>Patietur tua bonitas adm rari imprimis me, quid e&longs;&longs;e <lb/>agendum cogitaueris de primo dimidio AN. </s>

<s>Vide<lb/>licet rationem duplam, progre&longs;&longs;ionemque à puncto <lb/>N ita inchoas, vt &longs;i motus inciperer, ac vniformiter <lb/>quidem, non à puncto A, &longs;ed à puncto N. </s>

<s>An dices <lb/>fortè po&longs;&longs;e AN ita bi&longs;ecari, vt motus, & ratio, pro<lb/>gre&longs;&longs;ioque illius incipiat à puncto inter A, & N me<lb/>dio? </s>

<s>Sed bi&longs;eca, vt voles, eadem erit ruina. </s>

<s>Bi&longs;eca <lb/>rursùs, iterumque, & porrò v&longs;que in infinitum; atta<lb/>men &longs;emper &longs;upererit pars, à cuius medio, non autem <lb/>ab A fieri inc&oelig;ptio cogitetur; adeò vt prorsùs perinde <lb/>&longs;it con&longs;i&longs;tere in dimidio AN. </s>

<s>Cùm autem dicturus <lb/>prætereà non &longs;is fieri &longs;olùm quoddam qua&longs;i tyroci<lb/>nium, &longs;eu præludium ex A in N, ac motum deinde, <lb/>& rationem, progre&longs;&longs;ionemque incipere &longs;eriò ab N; <lb/>cùm non &longs;is, in quam, id dicturus, vt pote, qui motum <lb/>admittas à primo v&longs;que &longs;ui momento accelerari vni<lb/>formiter; ac &longs;upponas etiam, vbi tempus per AC mi<lb/>nutorum &longs;ex fuerit, tempus per AN futurum minuto<lb/>rum quatuor; quæ&longs;o te, ecquis modus e&longs;t progre&longs;&longs;io<lb/>nis ex A in N? </s>

<s>Nam ab A quidem incipiens motus <lb/>acceleratur continuò, & progre&longs;&longs;u accelerationis in<lb/>alterato tran&longs;it per N, ac pergit vlterius, nec dicere <lb/>licet quid illi &longs;peciale contingat in N, quod in alio <lb/>quovis puncto non contingat. </s>

<s>An non ergo, &longs;i tem<lb/>poribus æqualibus &longs;patia decurruntur in ratione du<lb/>pla; debet omninò &longs;patium AN percurti tempore <lb/>æquali cum &longs;patio con&longs;equente duplo, vt putà ip&longs;o <lb/>NS? </s>

<s>Id autem cùm pror&longs;us ita e&longs;&longs;e debeat, qui fit, vt <lb/>per te etiam triplum percurratur &longs;patium, putà ND? <pb pagenum="75"/>Quippe, vt tempus per AN e&longs;t <expan abbr="minutor&utilde;">minutorum</expan> quatuor; ita <lb/>tempus per NC, & CD, vtrumque, ex te, minutorum <lb/>duorum, &longs;tatuitur coniunctim minutorum quatuor. <lb/></s>

<s>Ecquo ergo modo &longs;anari id putas? </s>

<s>Patere rursùs mi<lb/>rari me, quor&longs;um ablegandam cen&longs;ueris progre&longs;&longs;io<lb/>nem illam arithmeticam, qua velocitates &longs;e, vt &longs;patia <lb/>habent, & quam &longs;ternendam, vt fundamentum ædifi<lb/>cij totius cen&longs;ui&longs;ti? </s>

<s>Ecce enim, cùm velles gradus ce<lb/>leritatis ita di&longs;tribui, vt in D e&longs;&longs;ent duo gradus, quo<lb/>rum vnus e&longs;&longs;et acqui&longs;itus ab A in C, & alius ip&longs;i æqua<lb/>lis acqui&longs;itus à C in D; vis iam à C in D talem gra<lb/>dum acquiri, qualis acquiritur ab N in C; quando<lb/>quidem CD tanto tempore, quanto NC, cuius e&longs;t <lb/>dupla, percurritur. </s>

<s>Ex quo rur&longs;us con&longs;equitur, vt ve<lb/>locitates per AC, & NC acqui&longs;itæ &longs;int prorsùs æqua<lb/>les; ac proinde, vt AC, & NC hoc e&longs;t totum, & pars <lb/>eodem tempore percurrantur; ac &longs;patium CD non <lb/>percurratur modò eodem tempore, quo NC, &longs;ed <lb/>etiam eodem, quo AC; quæ iterùm ne&longs;cio &longs;anari quá <lb/>valeant. </s>

<s>Patere in&longs;uper, vt requiram, &longs;ub&longs;it-ne tibi <lb/>ratio, quamobrem diuisâ lineâ AB in parteis æqua<lb/>leis, deligere po&longs;&longs;is dimidium NC, &i pergendo pro<lb/>portione dupla dicere, vt NC ad CD, ita CD ad <lb/>DF, & DF ad FK, &c. </s>

<s>dicere autem perinde non <lb/>liceat, vt AC ad CE, ita CE ad EI, & EI ad &longs;ui du<lb/>plam? </s>

<s>Dicere certè accipiendum e&longs;&longs;e po&longs;terius pri<lb/>mæ partis dimidium, quòd contineatur in eo men<lb/>&longs;ura cæterarum partium con&longs;equentium, videtur e&longs;&longs;e <lb/>dicere gratis, ip&longs;amque petere quæ&longs;tionem; ac aliunde <pb pagenum="76"/>agitur &longs;olùm de progre&longs;&longs;ione Geometrica, quam ge<lb/>neralem cùm &longs;tatuas, incipere vndelibet licet, & nullo <lb/>quidem ex puncto magis &longs;ecundum naturam, quàm <lb/>ex puncto A. </s>

<s>Dic enim, amabò, &longs;i qui&longs;piam perno&longs;&longs;e <lb/>rationem exoptet, qua decidens graue progrediatur <lb/>ab A in B, & tu o&longs;ten&longs;urus ita exordiaris, Vt NC ad <lb/>CD, ita CD ad DF, &c. </s>

<s>putas te illi facturum <lb/>&longs;atis, ac tibi obiectum non iri quæ&longs;tionem e&longs;&longs;e, non <lb/>de progre&longs;&longs;u ab N &longs;olùm, &longs;ed de progre&longs;&longs;u ab v&longs;que <lb/>A, de quo &longs;i nolles dicere, nihil dicere foret præ&longs;tabi<lb/>lius? </s>

<s>Patere quin etiam, vt rogitem te, quî ea expedi<lb/>re, quæ à te deinceps &longs;ubiunguntur, valeas? </s>

<s>Compa<lb/>rans enim tempora, quibus partes omnes prim<gap/>m &longs;e<lb/>quentes percurruntur, cum temporibus, quibus vis <lb/>fragmenta po&longs;terioris illius dimidij &longs;igillatim &longs;umpta <lb/>percurri, i&longs;thæc habes verba, <emph type="italics"/>Sic tempus, quo primi in<lb/>terualli media pars inferior ab&longs;oluitur, & quo duæ &longs;equen<lb/>tes partes, nempe<emph.end type="italics"/> 3, <emph type="italics"/>&<emph.end type="italics"/> 4, <emph type="italics"/>&longs;igillatim tran&longs;currerentur; <lb/>itemque illud, quo quatuor &longs;equentes<emph.end type="italics"/> 5, 6, 7, <emph type="italics"/>&<emph.end type="italics"/> 8, <emph type="italics"/>vel <lb/>&longs;equentes octo<emph.end type="italics"/> 9, 10, 11, 12, 13, 14, 15, <emph type="italics"/>&<emph.end type="italics"/> 16, <emph type="italics"/>aut cæ<lb/>teræ con&longs;equenter, &longs;eor&longs;im tamen, & &longs;ucceßiuè ab&longs;olueren<lb/>tur.<emph.end type="italics"/></s><s> Quæ&longs;o te verò, quî id fieri, quod hac ratione <lb/>deducis valeat? </s>

<s>A&longs;&longs;ume enim integrum tempus, quod<lb/>cúmque volueris, vt ad illud referas qua&longs;cúmque heic <lb/>enumeras parteis, & peruidebis ratio-ne dupla id ip<lb/>&longs;um, quod moliris, ab&longs;oluat. </s>

<s>E&longs;to v. </s>

<s>tempus per <lb/>AC triginta &longs;ex, vt triens, &longs;eu tempus, quod tribuis <lb/>po&longs;teriori dimidio, quodque primum facis, &longs;it duode<lb/>cim; cùm &longs;ubinde &longs;patium æquale dimidio, cui d<gap/>bi<lb/>tum &longs;it tempus 6. ideò duplices, vt pro &longs;ecundo &longs;patio <pb pagenum="77"/>habeas iterum duodecim; compone deinde in vnum <lb/>duo tempora duorum &longs;equentium interuallorum, vi<lb/>delicet trientem 4, & quadrantem 3, ac habebis non <lb/>duodecim, hoc e&longs;t tempus æquale primo, &longs;ed &longs;eptem <lb/>illius duodecimas dumtaxat; aut &longs;i duplices, etiam duo<lb/>decimas quatuordecim. </s>

<s>Adde pari modo quatuor <lb/>tempora quatuor aliorum interuallorum, hoc e&longs;t par<lb/>teis 5, 6, 7, 8, & habebis iterùm non duodecim, &longs;ed <lb/>vix ampliùs quàm duodecimas &longs;eptem, cum &longs;emi&longs;&longs;e; <lb/>aut &longs;i duplices, etiam quidpiam amplius, quàm duode<lb/>cimas quin lecim. </s>

<s>Adde & quæ octo &longs;equuntur inter<lb/>uallorum con&longs;equentium; & habebis rursùs non duo<lb/>decim, &longs;ed duodecimas non omninò octo: aut &longs;i <lb/>duplices, etiam duodecimas ferè &longs;exdecim. </s>

<s>Imò & <lb/>adde &longs;exdecim, quæ interuallorum &longs;uccedentium &longs;unt, <lb/>& vix habebis ampliùs, quàm duodecimas octo: <lb/>aut &longs;i duplices, etiam aliquid amplius quàm duodeci<lb/>mas &longs;exdecim. </s>

<s>Adde & quæ &longs;unt triginta duorum <lb/>proximorum, & habebis &longs;olùm duodecimas non om<lb/>ninò octo cum triente: aut &longs;i duplices, etiam duodeci<lb/>mas &longs;exdecim cum proximè be&longs;&longs;e, atque ita de cæteris. <lb/></s>

<s>Ex quo profecto &longs;it, vt videas nulla ratione cohærere, <lb/>quam &longs;ube&longs;&longs;e exi&longs;tima&longs;ti, æqualitatem temporum cum <lb/>ratione dupla &longs;patiorum. </s>

<s>XLII. Denique, vt alia præteream, quæ tuo ex ra<lb/>tiocinio, dum rationem duplam &longs;tabilire conaris, con<lb/>&longs;equuntur incommoda; Sequitur ecce vt &longs;tabilias <lb/>non modò duplam, &longs;ed etiam triplam, quadruplam, <lb/>decuplam, & quamlibet aliam. </s>

<s>Nam vt de tripla &longs;o<lb/>lùm dicam (cùm in cæteris idem iuris &longs;it) ac non <pb pagenum="78"/>repetam, quod iam in&longs;inuaui, velle te AN, & ND, <lb/>quod &longs;patium e&longs;t triplum, æquali tempore percurri, ac <lb/>ita rationem incipere triplam, deberéque eodem pro<lb/>gredi tenore ex D in T ip&longs;ius ND triplam, & ita <lb/>deinceps; ne id, inquam, repetam: accipiatur non NC, <lb/>&longs;ed XC infimus triens primæ partis. </s>

<s>Vis tu tempora <lb/>XC, & DE e&longs;&longs;e æqualia, quoniam XC e&longs;t triens ip<lb/>&longs;ius DE, eo modo, quo vis tempora per NC, & CD, <lb/>e&longs;&longs;e æqualia; quoniam NC e&longs;t dimidium ip&longs;ius CD: <lb/>Quare, vt, a&longs;&longs;umendo partem analogam ip&longs;i NC, vt <lb/>putà CD, progrederis deinceps in ratione dupla CD, <lb/>DF, FK, &c. </s>

<s>ita a&longs;&longs;umendo partem analogam ip&longs;i <lb/>XC, progredi deinceps licebit in ratione tripla DE, <lb/>EH, HB, &c. </s>

<s>Sequitur quoque te recidi&longs;&longs;e in illud <lb/>ip&longs;um incommodum, quod deduxi antè aduer&longs;us <lb/>eandem rationem duplam: nempe, vt debeas admit<lb/>tere, peracto primo tempore in percurrendo aliquo <lb/>&longs;patio, percurri deinceps debere &longs;patia omninò infini<lb/>ta, priu&longs;quam finis temporis alterius æqualis adueniat. <lb/></s>

<s>Quippe, &longs;i vt tu bi&longs;ecui&longs;ti partem primam AC in N, <lb/>ita cæteræ bi&longs;centur in S, V, &c. </s>

<s>Quemadmodum <lb/>tempus NC fit per te dimidium temporis AN, ita <lb/>tempus CS erit dimidium temporis NC, & tempus <lb/>SD dimidium temporis CS, &c. </s>

<s>Et vtcumque con<lb/>tendas iam, incipiendum e&longs;&longs;e non à puncto A, &longs;ed à <lb/>puncto N: idem nihilominùs &longs;equetur. </s>

<s>Nam rema<lb/>nente eadem bi&longs;ectiore partium, ac habentibus, &longs;e <lb/>dimidiis eadem ratione, qua habent tota; cùm &longs;i ex <lb/>N in C certus velocitatis gradus acquiratur, is &longs;it dein<lb/>de in S duplus, ac pari ratione e&longs;&longs;e debeat in D qua-<pb pagenum="79"/>druplus, in V octuplus, &c. </s>

<s>quòd vt geminatur à pri<lb/>mo interuallo in &longs;ecundum, &longs;ic geminati debeat à &longs;e<lb/>cundo in tertium, à tertio in quartum, &c. </s>

<s>ideò tem<lb/>pora fient &longs;emper dimidiorum dimidia. </s>

<s>Vnde eueniet, <lb/>vt peracto tempore primo, procedatur &longs;olùm con&longs;e<lb/>quenter per eiu&longs;dem dimidium, quadrantem, octan<lb/>tem, & fractiones cæteras nunquam ip&longs;i toti, ni&longs;i <lb/>tran&longs;actis &longs;patiis infinitis, exæquandas. </s>

<s><emph type="center"/><emph type="italics"/>De Tempore, quo<emph.end type="italics"/> G<emph type="italics"/>lobum ferreum ca&longs;urum ex Luna in <lb/>Terram contendit.<emph.end type="italics"/><emph.end type="center"/></s>

<s>XLIII. </s>

<s>Cùm tibi &longs;ubinde in animo e&longs;&longs;et &longs;pecimen <lb/>quoddam in&longs;igne dare huiu&longs;ce tuæ rationis duplæ, <lb/>ca&longs;um delegi&longs;ti globi ferrei ex Luna v&longs;que in centrum <lb/>Terræ. </s>

<s>Ac primùm quidem adnotas &longs;equi ex tua illa <lb/>ratione, G<emph type="italics"/>rauia omnia longè celeriùs deor&longs;um moueri, <lb/>quàm à<emph.end type="italics"/> G<emph type="italics"/>alileo con&longs;tituatur; quoniam cùm ex eius principiis <lb/>corpus graue quodcumque &longs;ex temporibus, exempli gratiâ, <lb/>inter &longs;e æqualibus de&longs;cendens, non ni&longs;i triginta &longs;ex interualla <lb/>æqualia percurrat; po&longs;ita aliunde acceleratione motus <lb/>æqualibus temporibus in ratione dupla, demon&longs;tratum<emph.end type="italics"/> à te <lb/>dicis <emph type="italics"/>nece&longs;&longs;e omninò e&longs;&longs;e, vt idem corpus graue &longs;ex ii&longs;dem <lb/>temporibus de&longs;cendens in terualla non tantum triginta &longs;ex, <lb/>&longs;ed &longs;exaginta tria decurrat.<emph.end type="italics"/></s><s> Verùm hac in re non e&longs;t <lb/>immoiandum, neque exaggeranda e&longs;t exorbitatio, <lb/>qua facta progre&longs;&longs;io in ratione dupla, vtcumque initio <lb/>moderata &longs;it, & progre&longs;&longs;ionem &longs;ecundum &longs;eriem nu<lb/>merorum imparium proximè circum&longs;tat; <gap/> eò tamen <lb/>omneis metas probabilitatis prætergreditur, cùm res <lb/>&longs;tatim pateat in ip&longs;o de ca&longs;u ex Luna exemplo. </s>

<s>Ecce <pb pagenum="80"/>enim quia Galileus, &longs;upponendo e&longs;&longs;e à Luna in cen<lb/>trum terræ milliaria 196000. ratiocinatur globum <lb/>ferreum è Luna dimi&longs;&longs;um peruenturum ad centrum <lb/>Terræ intra horas 3. & minuta 22. cum &longs;ecundis 4. <lb/>quatenus ex ob&longs;eruatione ab eo peracta decidit ini<lb/>tio, intra &longs;ecunda quinque, centum cubitis; ac perre<lb/>cturus e&longs;t deinceps iuxta progre&longs;&longs;ionem ab eo a&longs;&longs;i<lb/>gnatam: idcircò tu illa milliaria diuidens in pedes <lb/>980000000 (quanquam Galileus non pedes v&longs;urpa<lb/>uit, &longs;ed cubitos, quorum numerus foret 588000000) <lb/>& numerum reducens in pedum centena 9800000, <lb/>a&longs;&longs;umis 100 pedes (a&longs;&longs;ump&longs;it ille ex ob&longs;eruatione 100 <lb/>cubitos, qui continent pedes (166 2/3)) pro &longs;patio, quod <lb/>percurritur quinque &longs;ecundis, &longs;eu tempore vno, qua<lb/>lia &longs;unt duodecim in vno minuto, & 24 in duobus mi<lb/>nutis: ac tum extendendo 24. hæc tempora, tribuis <lb/>primo 100, &longs;ecundo 200, tertio 400, quarto 800, at<lb/>que ita ingeminando, quov&longs;que vige&longs;imo quarto tri<lb/>buas 838860800: & colligis po&longs;tea omnium &longs;um<lb/>mam 1677721500, numerum videlicet pedum, qui <lb/>percurruntur intra duo minuta. </s>

<s>Et quia illi &longs;unt pedes <lb/>longè plures, quàm in prædicto &longs;patio à Luna ad cen<lb/>trum teriæ a&longs;&longs;ignentur, concludis fore, vt <emph type="italics"/>prædictus glo<lb/>bus in eo de&longs;cen&longs;u à Luna v&longs;que ad <expan abbr="centr&utilde;">centrum</expan> Terræ, duo prima <lb/>horæ minuta, &longs;iue trige&longs;imam vnius horæ partem non in&longs;u<lb/>meret:<emph.end type="italics"/> ac iubes me <emph type="italics"/>videre, quàm dispar celeritatis ratio in<lb/>ter vtrumque calculum inueniatur.<emph.end type="italics"/></s>

<s>XLIIII. </s>

<s>Ego autem & video &longs;anè, & quantum <lb/>a&longs;&longs;equor, debet globus ferreus cadere per te à Luna in <lb/>centrum aut vno minuto, & quinquaginta &longs;eptem <pb pagenum="81"/>&longs;ecundis, quatenus v&longs;urpas pedes; aut minuto vno, &longs;e<lb/>cudis quinquaginta quatuor, quatenus videris debui&longs;<lb/>&longs;e v&longs;urpare cubitos. </s>

<s>Verum neque video, neque a&longs;&longs;e<lb/>quor pernicitatem vllam tantam, qua decidens graue <lb/>tempore tam breui percurrat tam immane &longs;patium, <lb/>quale continere admittis ducenta milliarium, prope<lb/>modum millia. </s>

<s>Certè, cùm attendo globum tormen<lb/>tarium è machina quapiam maiore explo&longs;um vertica<lb/>liter, vno circiter pò&longs;t minuto repetitam terram attin<lb/>gere, & vix tamen, ex &longs;upputatis ob&longs;eruationibus variis, <lb/>pertigi&longs;&longs;e ad vnum milliare altitudinis, ex qua v&longs;que <lb/>recidens dimidium eius temporis, &longs;eu &longs;emi-minutum <lb/>in&longs;ump&longs;erit: (&longs;æpe enim &longs;æpiùs ob&longs;eruauimus e&longs;&longs;e re<lb/>rum grauium &longs;ur&longs;um proiectarum de&longs;cen&longs;um æqui<lb/>temporaneum a&longs;cen&longs;ui) cùm ad i&longs;tud, inquam, at<lb/>tendo, con&longs;ideróque &longs;imul globum per hoc milliare <lb/>decidere eadem illa velocitate, qua inciperet cadere à <lb/>Luna; a&longs;&longs;equor quidem euenturum, vt ex Luna deci<lb/>dens, & iuxta progre&longs;&longs;ionem Arithmeticam numero<lb/>rum ab vnitate imparium incedens, decideret altero <lb/>&longs;emi-minuto milliaribus tribus, tertio quinque, & <lb/>quarto &longs;eptem; adeò vt, &longs;ub finem &longs;ecundi minuti de<lb/>prehenderetur decidi&longs;&longs;e milliaribus &longs;exdecim, &longs;eu <lb/>iuxta Galileum, nouemdecim, cum vna quinta millia<lb/>ris parte: At quid-nam hoc e&longs;t ad milliarium ducenta <lb/>millia comparatum? </s>

<s>Quanquam & iuxta illam tuam, <lb/>Geometricamve rationem duplam, po&longs;&longs;et res prope <lb/>verum haberi, quod ad milliaria illa prima, ac minuta <lb/>duo prima attinet, &longs;i diceremus eundem globum de<lb/>cur&longs;urum primo &longs;emi-minuto milliare vnum, &longs;ecundo <pb pagenum="82"/>duo, tertio quatuor, quarto octo: ex quo futurum <lb/>vides, vt duobus minutis milliaria non decideret plu&longs;<lb/>quam quindecim; cùm a<gap/>as mirà incohærentiâ de<lb/>ducatur, vt primo &longs;emi-minuto decidere velis globum <lb/>milliaribus &longs;ex cum fere triente; &longs;ecundo milliaribus <lb/>quadringentis, ac tribus, & vna quinta milliaris parte, <lb/>tertio vicies quinquies mille octingentis quatuor, cum <lb/>dodrante; & quarto totis milliarium myriadibus cem<lb/>tum &longs;extaginta quinque; ac in&longs;uper mille quingentis <lb/>&longs;eptem, cum vna quinta; totidem enim ex tua &longs;erie, ac <lb/>&longs;umma pedum colliguntur. </s>

<s>Quæ admonere &longs;anè po<lb/>tui&longs;&longs;e videntur, quàm incredibilem admitteres rem, <lb/>dum concluderes, & ad marginem exprimeres <emph type="italics"/>fore, vt <lb/>globus ferreus à Lunæ concauo ad centrum de&longs;cendens, &longs;er<lb/>uata temporibus æqualibus acceleratione in ratione dupla, in <lb/>toto de&longs;cen&longs;u duo vnius horæ minuta prima integre non in<lb/>&longs;umeret.<emph.end type="italics"/></s>

<s><emph type="center"/><emph type="italics"/>De Tempore per primas parteis ob&longs;eruatione determinandos <lb/>pauca de cau&longs;&longs;a Phy&longs;ica, deque lap&longs;u circa eam admi&longs;&longs;o.<emph.end type="italics"/><emph.end type="center"/></s>

<s>Videris deinde fidem liberare circa id, <lb/>quod facturum te receperas de tempore determinan<lb/>do, quo duo illa primæ partis percurruntur dimidia; <lb/>vt quo habito di&longs;tinctè deinde præ i&longs;um tempus cog<lb/>no&longs;ceremus, quo decidens graue de&longs;ignatum &longs;patium <lb/>&longs;uo de&longs;cen&longs;u percurteret. </s>

<s>Dicis autem primò, G<emph type="italics"/>alileum <lb/>quidem id fidenter promittere, dum ait &longs;e iteratis &longs;æpiùs ac <lb/>diligenter experient is ob&longs;erua&longs;&longs;e globum ferreum ex altitud ne <lb/>cubitorum centum decidentem quinque &longs;ecundis horæ minutis <lb/>totum illud &longs;patium decurri&longs;&longs;e: verùm, cùm idem non minùs<emph.end type="italics"/><pb pagenum="83"/><emph type="italics"/>audacter etiam affirmet &longs;e item eadem methodo expertum <lb/>e&longs;&longs;e spatia &ecedil;qualibus temporibus emen&longs;a eam inter &longs;e ratio<lb/>nem ob&longs;eruare, quæ inter numeros omneis impareis ab vni<lb/>tate continua &longs;erie procedenteis inuenitur; & in hac tamen <lb/>po&longs;teriore ob&longs;eruatione vehementer errauerit, magnoperè <lb/>verendum e&longs;&longs;e, ne in priore quoque non minùs hallucinatus <lb/>&longs;it.<emph.end type="italics"/></s><s> Dicis deinde, <emph type="italics"/>Satis non e&longs;&longs;e, &longs;i tempus habeatur, quo <lb/>prima quælibet pars de&longs;ignati spatij tran&longs;mittitur, ni&longs;i tem<lb/>pus quoque cogno&longs;catur, quo pars &longs;equens priori æqualis, vel <lb/>duæ medietates prim&ecedil; &longs;eor&longs;im decurruntur; quod tamen <lb/>exactè determinare,<emph.end type="italics"/> inquis, <emph type="italics"/>per quam difficile arbitror, ob <lb/>cau&longs;&longs;as iam &longs;æpiùs adductas.<emph.end type="italics"/></s><s> Et quænam quidem fue<lb/>rint huiu&longs;modi cau&longs;&longs;æ non commemini; &longs;ed interim <lb/>tamen candorem commendo, quo dicis Tertiò, <emph type="italics"/>te qua<lb/>cúmque diligentia adhibita nihil habere potui&longs;&longs;e, in quo in<lb/>tellectus conquie&longs;ceret:<emph.end type="italics"/> ac author es; vt &longs;i aliquis &longs;e id <lb/>f&oelig;liciùs a&longs;&longs;equi po&longs;&longs;e confidat, <emph type="italics"/>turrim &longs;atis excel&longs;am <lb/>eligat, puta<emph.end type="italics"/> 200 <emph type="italics"/>pedum; ac deinde aliam altitudinem duplò <lb/>præcisè minorem, pedum videlicet centum; & ex vtraque <lb/>altitudine, tempus de&longs;cen&longs;us exactißimè inquirat; tum mino<lb/>re tempore, ex maiore &longs;ubducto, re&longs;iduum daturum tempus <lb/>de&longs;cen&longs;us per turris maioris centum pedes infimos: tempus <lb/>verò illud minus, quo idem corpus ex &longs;ola centum pedum al<lb/>titudine de&longs;cendet, &ecedil;quale tempori futurum, quo ex maiori <lb/>quoque altitudine, per centum pedes &longs;uperiores de&longs;cenderit.<emph.end type="italics"/></s>

<s>Ad primum porrò quod attinet; videtur <lb/>&longs;anè non &longs;atis idonea refutatio experimenti, quod <lb/>ille te&longs;tatur &longs;e &longs;æpiùs, ac diligenter peregi&longs;&longs;e, ni&longs;i te&longs;te<lb/>ris temetip&longs;um idem tenta&longs;&longs;e, peregi&longs;&longs;eque, ac fui&longs;&longs;e <lb/>rem &longs;ecùs à te ob&longs;eruatam, fal&longs;itati&longs;que adeò con-<pb pagenum="84"/>uictam. </s>

<s>Quod enim e&longs;&longs;e verendum ais, ne halluci<lb/>natus fuerit, hoc &longs;atis profectò non e&longs;t; & quòd argu<lb/>mento e&longs;t tibi error vehemens, quem admi&longs;i&longs;&longs;e illum <lb/>ais, circa progre&longs;&longs;ionem iuxta &longs;eriem numerorum im<lb/>parium; declaratum iam antè e&longs;t, vt ea quoque ip&longs;a in <lb/>re non fuerit erroris conuictus; imò & &longs;uffragium <lb/>etiam tulerit cùm ex aliis experimentis, tum etiam ex <lb/>tuo, hoc e&longs;t in Bilance peracto. </s>

<s>Ad &longs;ecundum quod <lb/>&longs;pectat, determinauit ille, quo præcisè tempore &longs;ecun<lb/>da &longs;patij pars, ac dimidium primæ, & quævis alia per<lb/>curreretur, ex a&longs;&longs;ignato tempore, quo pars prima de<lb/>curritur. </s>

<s>O&longs;tendit nimirum ex &longs;uis principijs, <emph type="italics"/>Si à <lb/>lationis principio duo quælibet spatia &longs;umantur, tempora <lb/>ip&longs;orum fore inter &longs;e, vt alterum eorum ad spatium medium <lb/>proportionale inter ip&longs;a.<emph.end type="italics"/></s><s> Adeò vt, &longs;i inter AB pri<lb/>mam partem, & AC aggregatum primæ cum <lb/><figure id="fig21"></figure><lb/>&longs;ecunda inuenias mediam proportionalem AD, <lb/>tempus ca&longs;us per AB, ad tempus ca&longs;us per AC, <lb/>futurum &longs;it vt AB, ad AD. </s>

<s>Nimirùm id <lb/>con&longs;equitur ex eo, quòd &longs;patia &longs;int inter &longs;e <lb/>in duplicata temporum ratione; &longs;eu vt quadra<lb/>ta temporum; quódque &longs;it per&longs;picuum ratio<lb/>nem &longs;patij AC ad &longs;patium AB e&longs;&longs;e duplam <lb/>rationis AC, ad AD, &longs;eu eandem, quam ha<lb/>bent quadrata AC, & AD. </s>

<s>Ex quo fiet, vt cùm AB <lb/>&longs;upponas e&longs;&longs;e &longs;ex minutorum, AC compobetur mi<lb/>nutorum octo, & 29. &longs;ecundorum proximè; ac proin<lb/>de tempus per BC &longs;it minutorum duorum, & viginti <lb/>nouem proximè &longs;ecundorum. </s>

<s>Eadem autem ratione <lb/>diui&longs;a bifariam prima parte in E, & accepta AF media <pb pagenum="85"/>proportionali inter AB, & AE, reperietur tempus <lb/>per primum dimidium AE minutorum 4, & &longs;e cun<lb/>dorum 14 <gap/> ac relinquetur proinde tempus per po&longs;te<lb/>rius dimidium FB minuti 1, at &longs;ecundorum 45 Ad <lb/>Tertium nihil e&longs;t, quod dicam, quandò nihil determi<lb/>nas, &longs;ed prouocas <expan abbr="&longs;ol&utilde;">&longs;olum</expan> ad experimentum, quod fieri ab <lb/>alio exoptes. </s>

<s>Ac videbatur quidem id <expan abbr="experiment&utilde;">experimentum</expan> abs <lb/>te præ&longs;ertim ex&longs;pectandum, cùm profitereris <emph type="italics"/>nouam <lb/>&longs;cientiam,<emph.end type="italics"/> &longs;eu <emph type="italics"/>demon&longs;trationem, qua ratio, men&longs;ura, modus, <lb/>ac potentia accelerationis motus in naturali de&longs;cen&longs;u grauium <lb/>determinaretur:<emph.end type="italics"/> idque aduer&longs;us eam, quam <emph type="italics"/>excogitatam à <lb/>Galileo p&longs;eudo-&longs;cientiam<emph.end type="italics"/> appellitares; &longs;ed nolo tamen <lb/>hac in re e&longs;&longs;e importunus; addoque &longs;olùm, vbi id ex<lb/>perimentum peractum fuerit, &longs;ucce&longs;&longs;eritque, certum <lb/>me propemodum e&longs;&longs;e, ex ijs, quæ hactenus peregi ip&longs;i <lb/>valdè affinibus, elicitum exinde iri, quod opinionem <lb/>fulciar, non tuam, &longs;ed ex Galileo hactenus expre&longs;&longs;am. </s>

<s>XLVII. </s>

<s>Iam ad finem properans, <emph type="italics"/>omittere<emph.end type="italics"/> te dicis, <lb/><emph type="italics"/>quæ etiam de Motu accelerato examinari po&longs;&longs;ent, vt, qu&ecedil;, qua<lb/>li&longs;que &longs;it cau&longs;&longs;a accelerationis in naturali de&longs;cen&longs;u grauium: <lb/>cur corpora, &longs;altem, quæ eiu&longs;dem figuræ, & homogenea &longs;int, <lb/>cuiu&longs;cumque, & quantumlibet in&ecedil;qualis ponderis illa fuerint, <lb/>deorsùm nihilominùs &ecedil;quali celeritate de&longs;cendant: aliàque <lb/>eiu&longs;mo li, qu&ecedil; tibi quidem in promptu &longs;int, & alio loco, ac <lb/>tempore opportuniùs forta&longs;&longs;e proferenda in publicum: &longs;ed in<lb/>terim h&ecedil;c pr&ecedil;libanda puta&longs;&longs;e, qu&ecedil; non mo ò ad reuincendos<emph.end type="italics"/><lb/>G<emph type="italics"/>alilei errores opportuna, &longs;ed ad veram quoque, ac germa<lb/>nam accelerati motus naturam aperiendam nece&longs;&longs;aria vide<lb/>rentur.<emph.end type="italics"/></s><s> Quo rursùs loco, nihil e&longs;t, quod addam, neque <lb/>cur importunè rogem, quamobrem non cen&longs;ueris <pb pagenum="86"/><expan abbr="&longs;ubiiciend&utilde;">&longs;ubiiciendum</expan> aliquid e&longs;&longs;e de quæ&longs;tionibus illis Phy&longs;icis <lb/>ac duabus præ&longs;ertim heic commemoratis; cùm id fe<lb/>cerit maximè &longs;perandum, qui titulus e&longs;t <emph type="italics"/>Phy&longs;ica demon<lb/>&longs;tratio<emph.end type="italics"/> præ&longs;criptus. </s>

<s>Scilicet tibi liberum fuit ex&longs;pecta<lb/>re tempus, quoddam opportunius; ac mihi &longs;anè op<lb/>pidò nimiùm pro tua comitate tribui&longs;ti, cùm faciens <lb/>editionis &longs;pem, id futurum inter&longs;erui&longs;ti, <emph type="italics"/>maximè, &longs;i <lb/>cognoueris i&longs;ta viris eruditis, mihique imprimis minimè di&longs;<lb/>plicui&longs;&longs;e.<emph.end type="italics"/></s><s> Ac intelligo quidem non fui&longs;&longs;e cur tibi pla<lb/>cerent, quæ de ii&longs;dem quæ&longs;tionibus in priore mearum <lb/>illarum Epi&longs;tolarum commentus &longs;um, ac cætera inter, <lb/>quod adnixus fui explicare Phy&longs;icam cau&longs;&longs;am, ob <lb/>quam cadens graue primo momento per vnam or<lb/>gyiam, cadit in &longs;ecundo per treis, in tertio per quin<lb/>que, &c. </s>

<s>Verùm ratio iam nulla &longs;ube&longs;t, quorsùm aut <lb/>quicquam repetam, aut obiectionem, &longs;i quampiam es <lb/>propo&longs;iturus præoccupem; cùm paratus aliunde &longs;im <lb/>& manus dare, & habere gratiam, quam maximam <lb/>voueo, meliora docenti. </s>

<s>Agno&longs;co interim, me in&longs;igni <lb/>quadam incuria illa confcrip&longs;i&longs;&longs;e, quæ leguntur poti&longs;<lb/>&longs;imùm à calce paginæ &longs;eptuage&longs;imæ ad caput &longs;exage<lb/>&longs;imæ tertiæ, vbi figuram explicans, quam ab initio hûc <lb/>retuli, ip&longs;os velocitatis gradus &longs;ic feci ex pari cum par<lb/>tibus &longs;patij, vt per eo&longs;dem triangulos repræ&longs;entatos <lb/>a&longs;&longs;ump&longs;erim; cùm debuerim potiùs per ip&longs;as triangu<lb/>lorum veluti ba&longs;eis parallelas repræ&longs;entare. </s>

<s>XLVIII. </s>

<s>Po&longs;tremò anacephalæo&longs;i concludens; <lb/><emph type="italics"/>Ex his enim,<emph.end type="italics"/> inquis, <emph type="italics"/>ni&longs;i vehementer fallor, manifestè iam <lb/>vides, & euidenter agno&longs;cis, quàm non rectè<emph.end type="italics"/> G<emph type="italics"/>alileus mo<lb/>tum æquabiliter acceleratum eum e&longs;&longs;e definierit, qui æqualibus<emph.end type="italics"/><pb pagenum="87"/><emph type="italics"/>temporibus, æqualia celeritatis augmenta acquirat: cùm Sole <lb/>clarius iam tibi &longs;it, eumdem motum, æqualibus temporibus, non <lb/>&ecedil;qualia, &longs;ed maiora &longs;emper, ac maiora recipere celeritatis aug<lb/>menta, in continua ratione dupla. </s>

<s>Vides item, & pari eui<lb/>dentiâ per&longs;picis, non minus erra&longs;&longs;e<emph.end type="italics"/> G<emph type="italics"/>alileum, cùm &longs;patia <lb/>&ecedil;qualibus temporibus emen&longs;a, eam inter &longs;e rationem ob<lb/>&longs;eruare voluit, quæ inter numeros omnis imparis ab vnitate <lb/>procedenteis reperitur; cùm eadem quoque spatia, clarè ac <lb/>manife<gap/> è ignoueris, &ecedil;qualibus temporibus, maiora &longs;emper <lb/>ac maiora percurri, in eadem continua ratione dupla. </s>

<s>Vides <lb/>porrò, ac penè palpas, quàm vana, atque inanis &longs;it noua illa, <lb/>& tantopere ab ip&longs;o<gap/>et auctore laudata, de Motu accelerato <lb/>p&longs;eudo &longs;cientia: cùm non ni&longs;i fal&longs;is, atque erroneis principiis <lb/>innitatur; & quam non immeritò ante annos duos mihi di&longs;<lb/>plicuerit, quòd tu quoque ii&longs;dem illis principiis nounullam fi<lb/>dem adhiberes.<emph.end type="italics"/> C<emph type="italics"/>ertiora nunc habes, & quibus intrepidé <lb/>a&longs;&longs;en&longs;um pr&ecedil;beas, re&longs;titutam &longs;cilicet motus accelerati defini<lb/>tionem & ab iniu&longs;ta Galilei oppugnatione vindicatam. </s>

<s>Ha<lb/>bes & veram, germanàmque in naturali de&longs;cen&longs;u grauium <lb/>accelerationis rationem, tam in temporibus, quàm in &longs;patijs <lb/>&ecedil;qualibus con&longs;ideratam. </s>

<s>Habes denique eam quoque ratio<lb/>nem, qu&ecedil; inter spatia &ecedil;qualibus temporibus emen&longs;a reperi<lb/>tur, indubitatis experientiis, certis, euidentibú&longs;que rationibus <lb/>demon&longs;tratam. </s>

<s>Qu&ecedil; &longs;i, vt &longs;pero, tibi accepta, probataque fue<lb/>rint, non exiguum huius oper&ecedil; pretium me con&longs;ecutum e&longs;&longs;e <lb/>arbitrabor.<emph.end type="italics"/></s><s> Ad hæc verò omnia, Optime virorum, <lb/>nihil regerere in animo e&longs;t: cùm illa &longs;atis, &longs;uperque <lb/>&longs;int, quæ circa &longs;ingula edi&longs;&longs;erui. </s>

<s>E&longs;t &longs;olùm, quòd <lb/>gratias agam vberes, pro in&longs;igni illo affectu, quem <lb/>ante duos annos in me te&longs;tari dignatus es, quemque <pb pagenum="88"/>expre&longs;&longs;i&longs;ti nunc etiam, pretium collocans operæ, <lb/>quam meam &longs;pera&longs;ti comprobationem. </s>

<s>Quòd &longs;i <lb/>videaris &longs;pe excidi&longs;&longs;e, dum reprobantem potiùs, quàm <lb/>approbantem habes me: at non excidi&longs;ti profectò, <lb/>cùm & &longs;pera&longs;tia ffarite tui reuerent <lb/>amanti&longs;&longs;imum virum; & me eum volui&longs;ti, vt interpre<lb/>tor, qui aliunde ius amicitiæ &longs;eruans illibati&longs;&longs;imum, <lb/>tibi, in veritatis gratiam, non erube&longs;cerem repugnare. <lb/></s>

<s>Et quàm, putas, &longs;æpe expetij po&longs;&longs;e tibi &longs;ub&longs;cribere, vt <lb/>foret non affectum magis, quàm opinionum con&longs;pi<lb/>ratio; verùm ip&longs;emet iudex eris, vbi meas nugas per<lb/>volveris, an-non &longs;altem di&longs;&longs;en&longs;erim cum aliqua &longs;pecie <lb/>probabilitatis. </s>

<s>Sic certe habe, fore me &longs;emper com<lb/>parati&longs;&longs;imum a&longs;&longs;entiendo, &longs;i quandò maior mihi ex <lb/>te &longs;imilitudo veri affulgeat, qui &longs;um interim, &longs;i quis <lb/>alius, comparati&longs;&longs;imus ob&longs;equendo. </s>

<s>Vale, Pari&longs;ijs, <lb/>Eidib. </s>

<s><emph type="center"/>DE PROPORTIONE,<emph.end type="center"/></s>

<s><emph type="center"/>QVA GRAVIA DECIDENTIA<emph.end type="center"/></s>

<s><emph type="center"/>accelerantur.<emph.end type="center"/></s>

<s><emph type="center"/>EPISTOLA SECVNDA.<emph.end type="center"/><lb/><gap desc="hr tag"/></s>

<s><emph type="center"/><emph type="italics"/>EIDEM.<emph.end type="italics"/><emph.end type="center"/></s>

<s>QVOD non improbâris, oprimè CASRÆE, <lb/>mandari typis meam Re&longs;pon&longs;ionem, &longs;eu <lb/>qualecumque Iudicium de tua illa Demon<lb/>&longs;tratione, circa accelerationem grauium <lb/>decidentium, cuius autographum ad te mi&longs;i, &longs;i modo <lb/>Vindicias, quas intercedente eodem nobili Senatore, <lb/>& amico &longs;ingulari, Franci&longs;co Luillerio, dedi&longs;ti ad me, <lb/>iuberem attexi: Ecce non alia conditione Typogra<lb/>pho annui, dum meam opellam exigeret, quàm vt <lb/>tuam &longs;imul accipiens, tuo de&longs;iderio faceret &longs;atis. </s>

<s>V&longs;us <lb/>&longs;um autem ea licentia, quam abs te factam memini, <lb/>committendi etiam Re&longs;pon&longs;ionem ad Epi&longs;tolam il<lb/>lam tuam, cuius aliquoties à te facta mentio; idque <lb/>tam in tuo, quàm in meo contextu, pro tuo arbitratu, <lb/>variatis perpaucis: & quod Vindicias attinet, omi-<pb pagenum="90"/>natus &longs;um, vt pro tuo candore, tuaque æquitate, lici<lb/>tum cen&longs;eres Exceptione vti (Notis &longs;cilicet interpo&longs;itis, <lb/>quibus controuer&longs;ia fieret explicatior (ac tum inte<lb/>gram facere Lectori adiudicationem. </s>

<s>Cùm certè, quòd <lb/>&longs;pectat ad me, tuæ Demon&longs;trationis vim non per<lb/>&longs;enti&longs;cam, ac tu, tamet&longs;i iam agno&longs;cas id Experimen<lb/>tum, cui, vt fundamento, innixam fecoras, collabi, <lb/>con&longs;cribis tamen, peti&longs;que Vindicias, aiens <emph type="italics"/>te ignotam <lb/>mihi veritatem maiori iam luce illu&longs;tratam aperire, & <lb/>quam quæ&longs;iui, optauique, ab errore vindicatam exhibere:<emph.end type="italics"/><lb/>incumbit &longs;anè nece&longs;&longs;itas, inquirendi quid illud &longs;it, <lb/>quod ob&longs;tet mihi tantoperè, ne tua Demon&longs;tratione <lb/>mouear; quove modo &longs;im adeò hebes, vt ne in tanta <lb/>quidem luce po&longs;itam à te veritatem videam. </s>

<s>Quin<lb/>etiam, cùm à capite ad calcem, quod aiunt, queraris, <lb/>&longs;upponere me extuis principiis, quæ ex illis non de<lb/>ducantur, ac affingere tibi quædam, quæ te imperitiæ <lb/>coarguant; teneor vel ex hoc maximè ad intertexen<lb/>dum velut Apologiam; vt cùm nihil habeam veritate, <lb/>&longs;inceritatéque antiquius, ac nihil minùs volüerim, <expan abbr="quã">quam</expan> <lb/>aut admittere quidpiam fal&longs;um, aut tibi quicquam <lb/>imponere; deuoueam, &longs;i quid tale mihi imprudenti <lb/>exciderit, aut &longs;altem declarem quid potuerit me ad id <lb/>efferendum mouere. </s>

<s>Nam vides alioquin habitum <lb/>me iri malæ fidei, improbumque virum, qualem non <lb/>haberi (Deum immortalem) quantum magis mea <lb/>intere&longs;t, quàm imperitum non reputari! Quanquam <lb/>ego &longs;anè longè &longs;emper abfui, vt imperitiam in te <lb/>cau&longs;arer, cuius magnam potiùs peritiam, virtutem<lb/>que reuereor; &longs;ed animo &longs;olùm præconcepi, fore, vt <pb pagenum="91"/>pro eo, quo te habui erga veritatem affectu, minimè <lb/>impatienter ferres, &longs;i in i&longs;ta tanta caligine rerum, di<lb/>cereris non in&longs;pexi&longs;&longs;e attentè &longs;atis aliquid, enuncians <lb/>videlicet ea, ex quibus quæpiam incommoda con&longs;e<lb/>qui deprehenderentur. </s>

<s>No&longs;ti etiam, quantum &longs;udâ<lb/>rim, vt in&longs;inuatione lenire id po&longs;&longs;em; ac &longs;peciatim <lb/>quantum laboris inter cætera &longs;u&longs;tinuerim, cùm articu<lb/>lo xxiv. </s>

<s>o&longs;tendenda tibi fuit fal&longs;itas tui illius Experi<lb/>menti. </s>

<s>Quin-etiam tamet&longs;i in hi&longs;ce Vindiciis conti<lb/>nuo veluti in&longs;ultu dicas pa&longs;&longs;im <emph type="italics"/>me grauiter errare; pec<lb/>care, decipi, &longs;uppo&longs;itionibus tantum fal&longs;is vti; præoccupato <lb/>animo, & non intelligentem e&longs;&longs;e; non e&longs;&longs;e in buius controuer<lb/>&longs;iæ ingre&longs;&longs;um penetralia; non penitiùs dicta à te, ip&longs;amque <lb/>naturam rei inspexi&longs;&longs;e,<emph.end type="italics"/> & quæ id genus &longs;imilia &longs;unt; om<lb/>nia tibi lubens condono, partim con&longs;cius meæ imbe<lb/>cillitatis, partim contentus libertatem Lectoribus per<lb/>mittere, vt diiudicent quicquid id e&longs;t rei. </s>

<s>Quod atti<lb/>net autem ad ea, quæ toties tibi à me affingi, impo<lb/>nique exaggeras, æquum e&longs;t profectò, vt eam inficias, <lb/>ac eam labem, qua &longs;entio me ad&longs;pergi, pro viribus <lb/>eluam. </s>

<s>Facio verò id etiam vel eo nomine maximè <lb/>inuitus, quòd ea mouenda iterùm &longs;int, quæ di&longs;plicui&longs;<lb/>&longs;e tibi videntur; &longs;ed nece&longs;&longs;itatem ip&longs;e hanc feci&longs;ti, ni&longs;i <lb/>contendi&longs;ti, vt me proderem, non rudem quidem, ac <lb/>ineptum, quorum nominum non puderet me; &longs;ed pro<lb/>fligatæ con&longs;cientiæ, & nullius candoris virum, qualis, <lb/>Deo propitio, neque &longs;im, neque vt habear, pati po&longs;&longs;im. <lb/></s>

<s>Sed ecce demùm tuas Vindicias, cum ne minimo qui<lb/>dem vllo &longs;en&longs;us, vocumque detrimento; vtcum que &longs;e<lb/>ponerem volens ho&longs;ce titulos, quibus me exornas, <pb pagenum="92"/>quo&longs;que non promereri me, quemadmodum &longs;entio, <lb/>&longs;ic ingenuè profiteor. </s>

<s><emph type="center"/><emph type="italics"/>VINDICI<emph.end type="italics"/>Æ <emph type="italics"/>DEM<emph.end type="italics"/>O<emph type="italics"/>NSTRATI<emph.end type="italics"/>O<emph type="italics"/>NIS<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>PHYSICÆ.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>De Proportione, qua grauia decidentia accelerantur.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Ad clarißimum Virum D. Petrum<emph.end type="italics"/> G<emph type="italics"/>a&longs;&longs;endum Cathedra<lb/>dralis Eccle&longs;iæ Dinien&longs;is Præpo&longs;itum dignißimum.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="italics"/>Vidi,<emph.end type="italics"/> C<emph type="italics"/>larißime Ga&longs;&longs;ende, ad eam Epi&longs;tolam, quam <lb/>de Motu accelerato ante paucas hebdomadas ad te direxi, <lb/>Respon&longs;ionem tuam, eamque accuratè, ac diligenter per<lb/>legi. </s>

<s>In qua &longs;anè non po&longs;&longs;um non probare quam-maximè <lb/>diligentiam, ac &longs;agacitatem tuam, in eius Experientiæ exa<lb/>mine, quæ totius Epistolæ fundamentum, & occa&longs;io etiam <lb/>fuit: ea quippe f&oelig;licitate rem perfeci&longs;ti, vt meritò tibi gra<lb/>tiæ habendæ &longs;int, quòd ea demùm per&longs;pexeris, ex quibus mul<lb/>tò certiùs tota de motu accelerato controuer&longs;ia dirimatur. <lb/></s>

<s>Qua in re, cùm partem mihi quoque nonnullam f&oelig;licitatis <lb/>huius facis, vt qui viam, ac methodum nouam ad illu&longs;tra<lb/>tionem tandiù de&longs;ideratæ veritatis certißimam, clarißimam<lb/>que exhibuerim, id pro ingenita tibi humanitate, con&longs;ueta<lb/>que vrbanitate facis.<emph.end type="italics"/> C<emph type="italics"/>æterùm, cùm in hoc præcipuo tuæ, <lb/>ac meæ Epistolæ argumento &longs;olertiam tuam, atque indu&longs;triam <lb/>pro innata animi mei ingenuitate vehementer probem, & <lb/>amicè deo&longs;culer, in cæteris tamen capitibus nec à me, nec <lb/>(opinor) à cæteris, obtinere poteris approbationem; in ijs <lb/>maxime, in quibus postr<gap/>ma parte Re&longs;pon&longs;ionis tuæ ea <lb/>mihi affingis, quæ nec mea &longs;int, nec ex meis legitimè de<lb/>duci poßint: vt &longs;cilicet ex iis, tanquam datis, ab&longs;urdam de<lb/>cretorum meorum omnium pugnam, & tanquam di&longs;&longs;en&longs;io-<emph.end type="italics"/><pb pagenum="93"/><emph type="italics"/>nem, eamque inter &longs;e&longs;e di&longs;cordiam, contrarietatemque con<lb/>cludas, quam ne rudioribus quidem harum rerum tyronibus <lb/>obuceres; & in iis tamentam pertinaci in&longs;tas indu&longs;tria, tan<lb/>taque vehementia depugnas, imò toties eadem multis pa<lb/>ginis, & maiore tuæ Epi&longs;tolæ parte inculcas, vt apud minùs <lb/>harum rerum peritos qui tuaplurimùm authoritate mouebun<lb/>tur, videri poßim mortalium omnium imperitißimus. </s>

<s>Et <lb/>&longs;anè, &longs;i id iure faceres, & ea dicerem, quæ mihi affingis, <lb/>aut eadem ex meis ceu verbis, ceu principiis legitima illatio<lb/>ne concluderes; haberes quidem pro mea ingenuitate confi<lb/>tenrem reum; &longs;ed &ecedil;terno quoque me &longs;ilentio addicerem, qui <lb/>etiam num hac ætate tam pueriliter balbutirem. </s>

<s>Sed cùm <lb/>euidens, persp<gap/>ctumque mihi &longs;it, nihil à me dictum, quod <lb/>&longs;ibi omni ex parte perfect ßimè non cohæreat; patieris pro <lb/>tua humanitate, Vir prudentißime, vt qua potero breuitate <lb/>tibi primùm, ac deinde cæteris, in iis pr&ecedil;&longs;ertim rebus &longs;atis<lb/>faciam, qu&ecedil; minus &longs;ibi coh&ecedil;rere putaueris; vbi primùm pau<lb/>ca quædam etiam examinauero, quæ pro<emph.end type="italics"/> G<emph type="italics"/>alilei defen&longs;ione <lb/>adducis.<emph.end type="italics"/></s>

<s>Hæc tua e&longs;t Præfatio, ob quam dicendorum quic<lb/>quam præoccupare nihil e&longs;t nece&longs;&longs;e; cùm repetiturus <lb/>eadem omnia &longs;is. </s>

<s>Quia verò deinceps Articulos &longs;ingu<lb/>los Epi&longs;tolæ meæ, &longs;iue Re&longs;pon&longs;ionis, ad Demon&longs;tratio<lb/>nem tuam, numeris di&longs;er<gap/>tos percurris; age meipiamus <lb/>à primis. </s>

<s><emph type="center"/>IN ARTICVLOS II. III. IV. V. </s>

<s>De Statu Controuer&longs;iæ.<emph.end type="center"/></s>

<s><emph type="italics"/>Atque imprimis, cùm initium Re&longs;pon&longs;ionis tuæ, v&longs;que ad <lb/>numerum<emph.end type="italics"/> VI. <emph type="italics"/>in explicando Controuer&longs;iæ<emph.end type="italics"/> S<emph type="italics"/>tatu penè totum <lb/>occupetur, nihil adhùc e&longs;t, in quo di&longs;&longs;entiamus.<emph.end type="italics"/></s><pb pagenum="94"/>

<s>Dicere vis &longs;anè circa explicandum vtriu&longs;que opi<lb/>nionis modum quatenus etiam opinionem, quam tu <lb/>defendis ita expo&longs;ui, vt ip&longs;e cam exponeres (tamet&longs;i <lb/>po&longs;teà me non ingre&longs;&longs;um in penetralia controuer&longs;iæ <lb/>dicas) alioquin enim circa rem ip&longs;am planum e&longs;t, <lb/>quantum di&longs;&longs;entiamus; cùm tu gradus velocitatis in <lb/>acceleratione grauium decidentium acqui&longs;itæ habere <lb/>&longs;e velis vt tran&longs;acta &longs;patia, non vt tempora; ego vnà <lb/>cum Galileo &longs;e vt tran&longs;acta tempora, non verò vt <lb/>&longs;patia habere opiner: ac tu defendas &longs;patia æqualibus <lb/>temporibus in dupla continuò ratione percurri; ego <lb/>&longs;patia decurri cen&longs;eam æqualibus temporibus iuxta <lb/>progre&longs;&longs;ionem numerorum imparium ab vnitate in<lb/>c&oelig;ptorum. </s>

<s>Porrò quia ad illu&longs;trationem totius <lb/>controuer&longs;iæ de&longs;iderari adhùc videtur ratio illius Ti<lb/>tuli, quo fuit libellus à te in&longs;criptus, <emph type="italics"/>Phy&longs;ica Demonstra<lb/>tio, qua ratio, men&longs;ura, modus, ac potentia accelerationis mo<lb/>tus in naturali de&longs;cen&longs;u grauium determinantur, Aduer&longs;us <lb/>nuper excogitatam à Galileo<emph.end type="italics"/> G<emph type="italics"/>alilei Florentino Philo&longs;opho, <lb/>ac Mathematico de eodem motu P&longs;eudo &longs;cientiam<emph.end type="italics"/> (&longs;iqui<lb/>dem non pauci tuo libro <emph type="italics"/>lege<emph.end type="italics"/> pellicto quæ&longs;ierunt ex me, <lb/>quamobrem tu illum Demon&longs;trationem indigita&longs;&longs;es, <lb/>quod non &longs;atis per&longs;picerent, qua forma con&longs;tare De<lb/>mon&longs;tratio po&longs;&longs;et) ideò videtur operæ-pretium rem <lb/>heic &longs;upplere; ac tantò magis, quantò iam etiam titu<lb/>lus e&longs;t tuus, <emph type="italics"/>Vindici&ecedil; Phy&longs;ic&ecedil; Demon&longs;trationis.<emph.end type="italics"/></s><s> Itaque, <lb/>vt Demon&longs;trationem, quantum quidem a&longs;&longs;equor, toto <lb/>ex opere eliciam, ea videtur huiu&longs;modi. </s>

<s><emph type="italics"/>Si in motu accelerato grauium decidentium velocitates <lb/>acqui&longs;it&ecedil; &longs;e habent, vt emen&longs;a &longs;patia, nece&longs;&longs;e e&longs;t spatia<emph.end type="italics"/><pb pagenum="95"/><emph type="italics"/>decurri temporibus æqualibus in ratione continuò dupla:<emph.end type="italics"/></s>

<s><emph type="italics"/>Atqui in motu accelerato grauium decidentium velocitates <lb/>acqui&longs;it&ecedil; &longs;e habent vt emen&longs;a spatia:<emph.end type="italics"/></s>

<s><emph type="italics"/>Igitur in motu accelerato grauium decidentium nece&longs;&longs;e e&longs;t <lb/>spatia decurri æqualibus temporibus in ratione continuò du<lb/>pla.<emph.end type="italics"/></s>

<s>Propo&longs;itionis con&longs;equutio probatur. </s>

<s><emph type="italics"/>Diui&longs;o &longs;patio in quotcumque æqualeis parteis lubuerit, &longs;i <lb/>in fine primæ partis vnus velocitatis gradus acqui&longs;itus &longs;it, in <lb/>fine &longs;ecundi acqui&longs;iti &longs;int duo, in fine tertij tres, & ita dein<lb/>ceps; oportet tempus, quo percurritur &longs;ecunda pars, æquale e&longs;&longs;e <lb/>tempori, quo percurritur dimidium inferius primæ partis, <lb/>quòd velocitas per illam acqui&longs;ita &longs;it dupla velocitatis acqui<lb/>&longs;itæ per hoc, vti & spatium duplum e&longs;t; ac deinde tempus, <lb/>quo percurruntur tertia, & quarta (tempus, inquam, aliun<lb/>de æquale tempori, quo &longs;igillatim percurrerentur triens, <lb/>& quadrans infimi eiu&longs;dem primæ partis) e&longs;&longs;e &longs;imiliter <lb/>æquale, quòd vt ambarum &longs;patium duplum e&longs;t &longs;patij &longs;ecun<lb/>dæ, ita dupla velocitas acqui&longs;ita per illas &longs;it: & iterùm tem<lb/>pus, quo percurruntur quinta, &longs;exta, &longs;eptima, octaua, pari <lb/>ratione e&longs;&longs;e æquale, quod vt &longs;patium illarum iunctim spatij <lb/>&longs;ecundæ, & tertiæ e&longs;t duplum, &longs;ic dupla velocitas &longs;it; atque ita <lb/>de cæteris:<emph.end type="italics"/></s>

<s><emph type="italics"/>Igitur, &longs;i in motu accelerato grauium decidentium veloci<lb/>tates acqui&longs;itæ &longs;e habent vt emen&longs;a &longs;patia; nece&longs;&longs;e e&longs;t spatia <lb/>decurri temporibus æqualibus in ratione continuò dupla.<emph.end type="italics"/></s>

<s>A&longs;&longs;umptio autem ita probatur. </s>

<s><emph type="italics"/>Con&longs;tat experientia clara, facili, & indubitata, &longs;i globus <lb/>quilibet a&longs;&longs;umatur, & Bilanx ita &longs;uspendatut, vt lance al<lb/>tera &longs;u&longs;tentata cum impo&longs;ito tanto pondere, quantum ip&longs;ius<emph.end type="italics"/><pb pagenum="96"/><emph type="italics"/>globi e&longs;t (quantumque e&longs;t, &longs;atis vt cum globo in altera lance <lb/>per aërem libera impo&longs;ito æquilibrium faciat) globus dein<lb/>ceps dimittatur in ip&longs;am lancem liberam: fore, vt dimi&longs;&longs;us <lb/>ex &longs;uæ vnius diametri altitudine globus attollat &longs;uo impetu <lb/>non modò lancem &longs;u&longs;tentatam cum æqualibrij pondere, &longs;ed <lb/>vnum pondus prætereà, &longs;uo itidem ponderi æquale, præcisè: <lb/>& dimi&longs;&longs;us ex duarum diametrorum altitudine, duo attollat <lb/>pondera, hoc e&longs;t duplum &longs;ui ponderis præcisè, & ex trium <lb/>altitudine, treis, &longs;eu triplum, &c.<emph.end type="italics"/></s>

<s><emph type="italics"/>Igitur, cùm tanta &longs;it velocitas cuiu&longs;que rei, quantus impe<lb/>tus, imò impetus velocitas &longs;it; habent &longs;e velocitates in motu <lb/>accelerato grauium decidentium acqui&longs;itæ vt emen&longs;a &longs;pa<lb/>tia.<emph.end type="italics"/></s>

<s>Confirmatur A&longs;&longs;umptio aduer&longs;us Galileum. </s>

<s><emph type="italics"/>Quia<emph.end type="italics"/> G<emph type="italics"/>alileus falsò definit motum æquabiliter accelera<lb/>tum illum, qui à quiete recedens æqualibus temporibus æqua<lb/>lia celeritatis momenta acquirit; & paralogi&longs;ticè probat mo<lb/>tum æquabiliter acceleratum non e&longs;&longs;e eum, qui æqualibus &longs;pa<lb/>tiis æqualia celeritatis augmenta acquirit (quandò id arguit <lb/>ex eo, quod totum, & pars eodem, aut æquali tempore per<lb/>currerentur: cùm tamen con&longs;tet dimidium tempore breuiore <lb/>percurri, quàm duplum) ac tum gratis &longs;ibi po&longs;tulat concedi <lb/>gradus velocitatis eiu&longs;dem mobilis &longs;uper diuer&longs;as planorum <lb/>inclinationes acqui&longs;itos tunc e&longs;&longs;e æqualeis, cùm eorumdem pla<lb/>norum eleuationes ponuntur æquales<gap/> tum ad id probandum <lb/>falsò a&longs;&longs;umit globum filo nunc longiore, nunc breuiore &longs;u&longs;pen<lb/>&longs;um, & ex eadem altitudine per inæqualeis arcus vibratum, <lb/>a&longs;&longs;urgere &longs;emper ad eandem altitudinem.<emph.end type="italics"/></s>

<s>Ac talis quidem formari pote&longs;t, vt mihi videtur, <lb/>tua Demon&longs;tratio, quantum, vt dixi, elicitur ex operis <pb pagenum="97"/>tui totius contextu; cuius & hæc pote&longs;t e&longs;&longs;e qua&longs;i Sum<lb/>ma; ordine licet retrogrado, ob analy&longs;in, qua fuit re<lb/>texendus. </s>

<s>Videlicet initium facis ab A&longs;&longs;umptionis <lb/>Confirmatione, dum prima parte operisin refutando <lb/>Galileo es totus; pro&longs;equeris deinde probando ean<lb/>dem A&longs;&longs;umptionem tuo Experimento, dum ip&longs;um <lb/>copiosè deducis, & exaggeras; ae tandem probas, vt <lb/>con&longs;equens Propo&longs;itionis deducatur ex po&longs;ito ante<lb/>cedente, dum &longs;tabilire fusè conaris illam &longs;patiorum <lb/>Rationem duplam; quæ etiam Conclu&longs;io e&longs;t De<lb/>mon&longs;trationis. </s>

<s>Nihil verò nece&longs;&longs;e heic e&longs;t adnotare <lb/>quemadmodum non modò A&longs;&longs;umptio &longs;it fal&longs;a; &longs;ed <lb/>etiam Propo&longs;itionis con&longs;equutio &longs;it nulla: cùm hoc &longs;it <lb/>totius controuer&longs;iæ opus. </s>

<s>Itaque hac luce præmi&longs;&longs;a, <lb/>& tuum contextum, vt in&longs;equamur, initium facia<lb/>mus ab ip&longs;a A&longs;&longs;umptionis confirmatione. </s>

<s><emph type="center"/>IN ARTICVLOS VI. VII. VIII. </s>

<s>De Motus <lb/>æquabiliter accelerari Definitione.<emph.end type="center"/></s>

<s><emph type="italics"/>At numero<emph.end type="italics"/> VI. <emph type="italics"/>iam reprehendis primùm, quòd aßigna<lb/>tam à<emph.end type="italics"/> G<emph type="italics"/>alileo motus accelerati definitionem minùs probem; <lb/>tum quòd eam quoque rationem, <expan abbr="quã">quam</expan> idem<emph.end type="italics"/> G<emph type="italics"/>alileus vulgò <lb/>receptam accelerati motus definitionem ab&longs;urditatis arguit, <lb/>paralogi&longs;mum e&longs;&longs;e contendam. </s>

<s>Jdeoque numero<emph.end type="italics"/> VII. G<emph type="italics"/>a<lb/>lilei definitionem inde numeris omnibus perfectam e&longs;&longs;e conclu<lb/>dis, quòd eà &longs;eruatâ rectè vniformis acceleratio intelligatur. <lb/></s>

<s>At imprimis istud non reprehendo; &longs;ed quòd &longs;uam illam <lb/>definitionem nouam nec &longs;ufficienter, nec ea, qua par e&longs;&longs;et, <lb/>ratione confirmauerit.<emph.end type="italics"/></s>

<s>Ni&longs;i tu illud reprehendis; non videbaris ergo dicere <pb pagenum="98"/><emph type="italics"/>debere fui&longs;&longs;e ab eo fal&longs;am accelerati motus definitionem <lb/>institutam.<emph.end type="italics"/></s><s> Quòd fueris autem cau&longs;atus ip&longs;um <emph type="italics"/>&longs;uam <lb/>illam Definitionem experientia certa, ac euidenti non con<lb/>firma&longs;&longs;e;<emph.end type="italics"/> agno&longs;ce quæ&longs;o tu-ne certiore, ac euiden<lb/>tiore <emph type="italics"/>tuam<emph.end type="italics"/> confirmâris. <emph type="italics"/>Tuam,<emph.end type="italics"/> inquam; namlicet eam <lb/>&longs;emper e&longs;&longs;e repetas <emph type="italics"/>vulgò receptam communemque;<emph.end type="italics"/> ec<lb/>qui <expan abbr="nã">nam</expan> tamen illi &longs;unt, qui eodem t<gap/><expan abbr="&utilde;">um</expan> modo definiunt? <lb/></s>

<s>Galileus certè eam non vt receptam, communemque <lb/>impugnauit, &longs;ed vt eam, quæ po&longs;&longs;et fortè ab aliquo ex<lb/>cogitari. </s>

<s>Verumtamen id obiter. </s>

<s><emph type="italics"/>Deinde, non minùs rectè aliter quoque vniformis accele<lb/>ratio haberi pote&longs;t, vt &longs;tatim con&longs;tabit: Satis-ne igitur Gali<lb/>lei definitio inde perfecta concluditur, quòd eà &longs;eruatâ vnifor<lb/>mis acceleratio habeatur?<emph.end type="italics"/></s>

<s>Ita profectò, &longs;i per eam con&longs;tet, quid &longs;it motum <lb/>accelerari, & accelerari æquabiliter; neque id vulgari, <lb/>&longs;iue potiùs tua, de qua dicis mox con&longs;titurum, perinde <lb/>præ&longs;tetur. </s>

<s><emph type="italics"/>Vt autem probes,<emph.end type="italics"/><lb/><figure id="fig23"></figure><lb/><emph type="italics"/>quàm rectè iuxta Galilei <lb/>mentem, acceleratio illa <lb/>motus habeatur, iu<lb/>bes concipere duas li<lb/>neas<emph.end type="italics"/> AB, <emph type="italics"/>&<emph.end type="italics"/> AC, <lb/><emph type="italics"/>angulum con&longs;tituentes in<emph.end type="italics"/><lb/>A, <emph type="italics"/>& tertiam<emph.end type="italics"/> VX <emph type="italics"/>per <lb/>anguli apicem<emph.end type="italics"/> A <emph type="italics"/><expan abbr="ince-dent&etilde;">ince<lb/>dentem</expan>, & cùm prioribus <lb/>duabus angulos vtrim<lb/>que æqualeis con&longs;tituentem: hanc, &longs;eruatâ &longs;emper eadem<emph.end type="italics"/><pb pagenum="99"/><emph type="italics"/>angulorum æqualitate, ita fluentem, ac de&longs;cenden<lb/>tem concipi postulas, vt etiam intelligamus partem inter <lb/>lineas<emph.end type="italics"/> AB, AC, <emph type="italics"/>interceptam continuò ea ratione augeri, <lb/>vt notatis in<emph.end type="italics"/> AB, <emph type="italics"/>&<emph.end type="italics"/> AC, <emph type="italics"/>partibus æqualibus<emph.end type="italics"/> AE, EG, <lb/>GI, IL, <emph type="italics"/>&longs;emper interceptarum parallelarum incrementa <lb/>haberi æqualia aduertamus. </s>

<s>Nempe vt<emph.end type="italics"/> AG <emph type="italics"/>dupla est <lb/>ip&longs;ius<emph.end type="italics"/> AE, <emph type="italics"/>&longs;ic<emph.end type="italics"/> GF <emph type="italics"/>dupla est ip&longs;ius<emph.end type="italics"/> ED: <emph type="italics"/>& eadem ratione<emph.end type="italics"/><lb/>IH <emph type="italics"/>eiu&longs;dem<emph.end type="italics"/> ED <emph type="italics"/>e&longs;t tripla, &<emph.end type="italics"/> LK <emph type="italics"/>quadrupla, atque <lb/>ita deinceps. </s>

<s>Ex quibus ita concludis:<emph.end type="italics"/> Quare a&longs;&longs;umptis <lb/>partibus æqualibus temporis per parteis æqualeis lineæ <lb/>AC repræ&longs;entatis, notum e&longs;t momenta, &longs;eu incremen<lb/>ta velocitatis per parallelas repræ&longs;entatæ æqualia ac<lb/>quiri &longs;ub huiu&longs;modi partibus. <emph type="italics"/>Hæc &longs;anè vera &longs;unt; <lb/>&longs;ed recordare verißimè quoque à te dictum numero<emph.end type="italics"/> IV. <emph type="italics"/>pun<lb/>ctum<emph.end type="italics"/> A <emph type="italics"/>po&longs;&longs;e non tantum pro initio temporis haberi, &longs;ed etiam <lb/>pro initio spatij, & (vt item addis) pro initio velocitatis.<emph.end type="italics"/></s>

<s>Recordor; &longs;ed adnoto &longs;imul habui&longs;&longs;e me punctum <lb/>A, pro initio temporis quidem æquabiliter &longs;luentis, <lb/>prout comparatur ad lineam AC (aut AB) in parteis <lb/>æqualeis diui&longs;am; pro initio verò &longs;patij in longum de<lb/>currendi, prout comparatur ad aream AKL in trian<lb/>gulos æqualeis di&longs;tinctam; ac pro initio velocitatis <lb/>continenter acquirendæ, prout comparatur cum linea <lb/>parteis æqualeis continuò ad&longs;ci&longs;cente, quov&longs;que c&oelig;<lb/>pta à puncto A, euadat KL. </s>

<s><emph type="italics"/>Vt igitur punctum<emph.end type="italics"/> A, <emph type="italics"/>nunc habes pro initio temporis, <lb/>& parteis æqualeis<emph.end type="italics"/> AE, EG, GI, IL, <emph type="italics"/>pro partibus <lb/>æqualibus temporis; concipe etiam vicißim idem punctum<emph.end type="italics"/> A <lb/><emph type="italics"/>initium e&longs;&longs;e &longs;patij, cuius parteis æqualeis æqualia item &longs;eg<lb/>menta<emph.end type="italics"/> AE, EG, GI, IL, <emph type="italics"/>de&longs;ignent. </s>

<s>Quo po&longs;ito, tam<emph.end type="italics"/><pb pagenum="100"/><emph type="italics"/>notum erit, quàm anteà momenta, &longs;eu incrementa velocitatis <lb/>per parallelas<emph.end type="italics"/> ED, GE, IH <emph type="italics"/>&<emph.end type="italics"/> LK <emph type="italics"/>repræ|entatæ. </s>

<s>æqualia <lb/>&longs;ub huiu&longs;modi partibus acquiri. </s>

<s>Cùm igitur in vtraque <lb/>hypothe&longs;i eadem omninò velocitatis acceleratio habeatur, cur <lb/>prior à te constituta perfectam omnibus numeris<emph.end type="italics"/> G<emph type="italics"/>alilei de<lb/>finitionem o&longs;tendat; vulgatam autem defi utionem po&longs;terior <lb/>hypothe&longs;is pari ratione perfectam non euincat?<emph.end type="italics"/></s>

<s>Cau&longs;&longs;am in&longs;inuaui tum mox, tum verbis illis, quæ <lb/>præmi&longs;eram, <emph type="italics"/>Quippe memini&longs;&longs;e, aut potiùs adnota&longs;&longs;e dili<lb/>genter oportet agi heic de motu æquabiliter accelerato, &longs;iue <lb/>cuius celeritas continenter, vniformiterque incre&longs;cat, neque <lb/>vllum &longs;it momentum con&longs;equentis temporis, in quo motus non <lb/>&longs;it velocior, quàm in quouis antecedente, & in quo non eadem <lb/>ratione ip&longs;a velocitas augeatur.<emph.end type="italics"/></s><s> Nempe memini <emph type="italics"/>Tempo<lb/>ris,<emph.end type="italics"/> ob rationem po&longs;teà deductam, vbi tu primùm de <lb/>eo egi&longs;ti, admonendo fui&longs;&longs;e originem mali, quòd in <lb/>definitione vulgari, &longs;eu tua nulla e&longs;&longs;et facta <expan abbr="m&etilde;tio">mentio</expan> tem<lb/>poris, &longs;ine quo tamen neque celeritas, neque accele<lb/>ratio (& maximè quidem vniformis) intelligi po&longs;&longs;it. <lb/></s>

<s>Obieci illeic, <emph type="italics"/>Si velocitas attendatur &longs;olùm penes &longs;patia, <lb/>debere &longs;emper id mobile, quod decem percurrerit &longs;tadia, dici <lb/>moueri celeriter, & &longs;emper id, quod vnicum percurrerit, tar<lb/>dè, cum contingere tamen poßit, vt quod percurrit vnicum, <lb/>moueatur decuplò velociùs, quàm illud, quod percurrit decem.<emph.end type="italics"/><lb/>Addo heic &longs;olùm; &longs;i AC &longs;it &longs;patium, & mobile di&longs;ce<lb/>dens ab A acceleretur v&longs;que ad E per parteis integri <lb/>minuti; & motu non interrupto accelerari pergat ab <lb/>E in G, &longs;ed per parteis integræ horæ; ac rursùs motu <lb/>non interrupto accelerari pergat à G in I, &longs;ed per par<lb/>teis integri &longs;ecundi; rur&longs;u&longs;que etiam non interrupto <pb pagenum="101"/>motu, accelerari pergat ab I, in L, &longs;ed per parteis in<lb/>tegri die<gap/>: quæ&longs;o, dices-ne huiu&longs;modi accelerationem <lb/>e&longs;&longs;e vn formem? </s>

<s>Et ecce ea tamen futura e&longs;t continens; <lb/>ac ip&longs;i gradus velocitatis repræ&longs;entati iuxta te paralle<lb/>lis ED, GF, IH, LK, cum interceptis omnibus, ha<lb/>bituri &longs;unt inter &longs;e, eandem rationem, quam ip&longs;æ par<lb/>tes &longs;pati, repræ entatæ iuxta te partibus lineæ AC. <lb/></s>

<s>Quòd &longs;i id reputes ab&longs;urdum; ab&longs;urdum quoque vi<lb/>deri debet metiri accelerationem, ac vniformem po<lb/>ti&longs;&longs;imùm, penes &longs;patium, non penes tempus: atque <lb/>idcircò lineam AC comparatam ad eas parallelas pro <lb/>velocitatibus habitas, non pro tempore, &longs;ed pro &longs;patio <lb/>habere. </s>

<s>Enim verò, vt expre&longs;&longs;iùs dicam quamobrem lineæ <lb/>DE, FG, & parallelæ cæteræ accipi non po&longs;&longs;int pro <lb/>gradibus velocitatis, &longs;i partes lineæ AC accipiantur pro <lb/>&longs;patij, non pro temporis partibus, ac &longs;imul in&longs;inuem <lb/>quid di&longs;criminis circa repræ&longs;entationem per eandem <lb/>figuram, inter vtramque hypothe&longs;in &longs;it, rem ecce <lb/>paucis ita deduco. </s>

<s>Si DE &longs;it velocitatis gradus, qui per <lb/>additamenta continua à puncto A &longs;ecundum trian<lb/>gulum ADC, acqui&longs;itus &longs;it, dum mobile AE percur<lb/>rit; quæro quî euadat hic gradus, vbi deinceps mobi<lb/>le pergendo decurrit EG? </s>

<s>An per<gap/>i&longs;&longs;e illum dicemus? <lb/></s>

<s>Non &longs;ane: quoniam alioquin mobili perueniente ex <lb/>A in G non reperiretur acqui&longs;itus in G, ni&longs;i vnus velo<lb/>citatis gradus; quatenus etiam per te, &longs;eu ex vulgari de<lb/>finitione, additamenta ex E in G æqualia &longs;unt addita<lb/>mentis ex A in E, nec pote&longs;t proinde ab v&longs;que E ac<lb/>qui&longs;itus e&longs;&longs;e, ni&longs;i gradus vnus, v. </s>

<s>FP æqualis ip&longs;i DE <pb pagenum="102"/>acqui&longs;ito ab v&longs;que A. </s>

<s>Et quamvis tu &longs;is inferiùs di<lb/>cturus velocitatem acqui&longs;itam ex E in G duplam e&longs;&longs;e <lb/>acqui&longs;itæ in E (nempe dum &longs;tatuis primum gradum <lb/>acquiri à &longs;olo medio ip&longs;ius AE) & &longs;ic velle debeas <lb/>gradum acqui&longs;itum in E, &longs;eu DE perire; quoniam re<lb/>periri in G, ni&longs;i duos gradus non vis: cùm &longs;i acqui&longs;itus <lb/>in E remaneret, futuri e&longs;&longs;ent tres: vide nihilominùs <lb/>quid hoc loco &longs;equatur. </s>

<s>Nam &longs;i pereunte gradu DE, <lb/>duo gradus, quos vis reperiri in G, vt puta FP, & <lb/>PG, acquirendi &longs;int per &longs;olum &longs;patium EG, factis vi<lb/>delicet augmentis &longs;ecundum triangulum, qui ducta <lb/>linea ex E in F &longs;it EFG, nece&longs;&longs;e e&longs;t, accelerationis <lb/>æquabilitas interrumpatur pror&longs;us in E; & cùm ibi <lb/>acceleratio ad &longs;uum redierit principium, non &longs;it dein<lb/>ceps futura tanta, quanta fuerit in E, ni&longs;i in medio <lb/>&longs;patij EG. </s>

<s>Itaque gradus velocitatis DE acqui&longs;itus <lb/>ex A in E non perit, &longs;ed manet; & cum mobile pro<lb/>inde peruenit ad G, talis gradus euadit PG, ac illi ad<lb/>iunctus reperitur FP acqui&longs;itus interim per augmen<lb/>ta facta &longs;ecundum triangulum DFP. </s>

<s>Quæro deinde, an gradus velocitatis DE manens, <lb/>dum mobile percurrit EG, otio&longs;us &longs;it, an aliquid agat? <lb/></s>

<s>Non dices &longs;anè otio&longs;um e&longs;&longs;e; alioquin enim mobile <lb/>tempore nihilo breuiore perueniret ex E in G, quàm <lb/>ex A in E, vt putà tran&longs;latum æquali &longs;olùm velocita<lb/>te. </s>

<s>Igitur agit aliquid. </s>

<s>Requiro, quantum? </s>

<s>hoc e&longs;t, <lb/>Si concipiamus mobile, po&longs;tquàm peruenit ad E, non <lb/>accipere amplius vlla augmenta, qualia acquiri dixi<lb/>mus &longs;ecundum triangulum DFP, &longs;ed moueri &longs;olùm <lb/>æquabiliter velocitate acqui&longs;ita DE: requiro quanto <pb pagenum="103"/>tempore mobile &longs;it peruenturum ad G? </s>

<s>An dices <lb/>&longs;olùm quanto tempore peruenerit ex A in E? Atqui, <lb/>vt faceret, oporteret velocitatem non totam permane<lb/>re, &longs;ed &longs;en&longs;im deminur, vt &longs;i deminutio fieret &longs;ecun<lb/>dum triangulum DPE: quippe hoc &longs;olùm modo <lb/>tempus po&longs;&longs;et æquale fieri, dum nimirum velocitas &longs;ie <lb/>decre&longs;ceret ad v&longs;que P, vt ab v&longs;que A reciprotè incre<lb/>ui&longs;&longs;et. </s>

<s>Quo ca&longs;u neque mobile æquabiliter moue<lb/>retur; neque peruenienti in G &longs;upere&longs;&longs;et ampliùs vlla <lb/>velocitas: neque proinde, &longs;i velocitate hac decre&longs;cente <lb/>intelligamus acquiri velocitatem &longs;ecundum triangu<lb/>lum DFP, acqui&longs;ita erit in G velocitas alia, quàm FP <lb/>ip&longs;ius DE æqualis, non dupla. </s>

<s>Igitur mobile percur<lb/>rens EG velocitate &longs;ola DE percurreret ip&longs;um tem<lb/>pore breuiore, quàm percurri&longs;&longs;et AE. </s>

<s>Quanto igitur? <lb/></s>

<s>Omninò dimidio. </s>

<s>Siquidem cùm velocitas DE non <lb/>foret deminuta, &longs;ed mobili perueniente ad G, reperi<lb/>retur adhùc integra, vt puta effecta PG, ideò vim <lb/>&longs;uam exprimeret &longs;ecundum totum quadrangulum <lb/>DG, hoc e&longs;t &longs;ecundum duos triangulos triangulo <lb/>ADE &longs;igillatim æqualeis; &longs;icque velocitas bis illud po&longs;<lb/>&longs;et &longs;ecundum quadrangulum DG, quod po&longs;&longs;et &longs;emel <lb/><expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> <expan abbr="triangul&utilde;">triangulum</expan> ADE: atque adeò mobile perueni<lb/>ret duplò citius (quod e&longs;t dimidium temporis) ex E in <lb/>G velocitate DE manente eadem, quam ex A in E, <lb/>velocitate eadem DE incre&longs;cente à nihilo &longs;ui. </s>

<s>Atque <lb/>ex hoc e&longs;t, quare adnotem, gradum, qui acquiritur, & <lb/>gradum, qui manet, e&longs;&longs;e inæqualeis; ac manentem di<lb/>ci po&longs;&longs;e duplò maiorem, quatenùs e&longs;t duplò poten<lb/>tior, &longs;eu duplo fortiùs ampliú&longs;que agens. </s><pb pagenum="104"/>

<s>Intelligamus iam, dum mobile percutrit EG, & <lb/>velocitas DE manens promouetur &longs;ecundum qua<lb/>drangulum DG, quov&longs;que euadat PG, nouum in<lb/>terim velocitatis gradum acquiri &longs;ecundum triangu<lb/>lum DFP, quov&longs;que euadat FP: nece&longs;&longs;e e&longs;t prorsùs <lb/>ob nouam velocitatem additam percurri EG tempore. <lb/></s>

<s>breuiore, quàm &longs;it dimidium temporis, quo decur&longs;um. <lb/></s>

<s>fuerit AE. Quanto-nam ergo? </s>

<s>Sanètriente. </s>

<s>Nam vt <lb/>velocitas &longs;ecundum quadrangulum DG, dupla ve<lb/>locitatis &longs;ecundum triangulum ADE diminuit tem<lb/>pus ad dimidium; ita velocitas &longs;ecundum trapezion <lb/>DFGE, triplum eiu&longs;dem trianguli, diminuit ad v&longs;<lb/>que trientem: Adeò vt, &longs;i tempus, quo decur&longs;um <lb/>fuerit AE, &longs;upponatur, vt à te fit, minutorum v. </s>

<s>&longs;ex, <lb/>tempus, quo decurretur EG, futurum &longs;it minutorum <lb/>duorum. </s>

<s>Cæterùm præter iam obiecta alibi incom<lb/>moda, tum illud quoque heinc &longs;equitur, Quòd &longs;i <lb/>EG &longs;ecunda pars &longs;patij percurratur triente eius tem<lb/>poris, quo decur&longs;a fuerit prima AE, futurum &longs;it, vt <lb/>tempore &longs;ecundo percurrantur partes non modò &longs;e<lb/>cunda, &longs;ed etiam tertia, quarta, quinta, &longs;exta, &longs;eptima, <lb/>& penè octaua; quandò qua ratione &longs;ecundum &longs;pa<lb/>tium percurritur triente, eadem tertium percurretur <lb/>quinta eiu&longs;dem temporis parte; quartum &longs;eptima, <lb/>quintum nona, &longs;extum vndecima, &longs;eptimum decima<lb/>tertia, octauum quintadecima, & hæc fragmenta &longs;i<lb/>mùl iuncta vnum integrum proximè conficient. <lb/></s>

<s>Hoc autem fal&longs;um qu dem e&longs;t, & tu ip&longs;e longè abes, <lb/>vt fatearis &longs;ed vides tamen, vt fuerit ex ea po&longs;itione <lb/>deductam, qua vis parteis lineæ AC e&longs;&longs;e parteis &longs;patij, <pb pagenum="105"/>& parallelas DE, FG e&longs;&longs;e gradus velocitatis. </s>

<s>Vides ergo quantum repugnet po&longs;itio huiu&longs;modi; <lb/>ac peruidere &longs;imul potes, quantum inter&longs;it di&longs;eriminis <lb/>inter hypothe&longs;in vtramque. </s>

<s>Nam in ea quidem, <lb/>quam &longs;equor, cùm partes lineæ AC, fiant partes <lb/>temporis, linea DE optimè repræ&longs;entat velocitatem <lb/>aqui&longs;itam in fi<gap/>e primi, & &longs;imul triangulum ADE op<lb/>timè repræ&longs;entat vnum &longs;patium, dum ea acquiritur, <lb/>tran&longs;actum: FG verò optimè repræ&longs;entat velocita<lb/>tem acqui&longs;itam in fine &longs;ecundi; & &longs;imul trapezion <lb/>DFGE optimè repræ&longs;entat tribus triangulis tria &longs;pa<lb/>tia peracta, quorum vnum debeatur gradui FP, prout <lb/>interim acquifito, & alij duo gradui PG, prout per<lb/>&longs;eueranti ab v&longs;que puncto E. </s>

<s>At in ea, quam tu &longs;e<lb/>queris, neque habes, quò referas tempus, cuius etiam <lb/>tua definitio non meminit<gap/> neque cùm plures &longs;patij <lb/>partes æquali tempore percurrantur, illarum di&longs;tin<lb/>ctionem habes, vt ad eas referas gradus inæqualeis ve<lb/>locitatis. </s>

<s>Addo autem, quædam præclarè ex mea <lb/>hypothe&longs;i intelligi, quibus nihil &longs;imile ex tua. </s>

<s>Veluti <lb/>Primò, Quemadmodum omnes velocitatis gradus <lb/>&longs;emel acqui&longs;iti inuariati maneant, & &longs;ingulis tempo<lb/>ribus æquipolleant con&longs;tanter duobus gradibus, hoc <lb/>e&longs;t duobus &longs;patijs æqualibus primo percurrendis &longs;uf<lb/>ficiant; vt de&longs;ignatur continua &longs;erie quadrangulo<lb/>rum æqualium, DG, PI, QL, itemque FQ, <lb/>RM, &c. </s>

<s>Deinde, Quemadmodum primo tempore <lb/>vnicum &longs;patium percurratur, quatenus vnicus e&longs;t gra<lb/>dus, qui acquiritur, & nullus interim, qui permaneat: <lb/>In &longs;ecundo autem &longs;int tria, quorum vnum quidem per <pb pagenum="106"/>recens acqui&longs;itum percurratur, & alij duo per primum <lb/>per&longs;euerantem: In tertio quinque, quorum vnum per <lb/>tunc acqui&longs;itum, & ex alijs quatuor, duo per primum, <lb/>duo per &longs;ecundum per&longs;eueranteis: In quarto &longs;eptem, <lb/>quorum vnum itidem per tunc acqui&longs;itum, & ex alijs, <lb/>duo per primum, duo per &longs;ecundum, duo per tertium <lb/>per&longs;eueranteis, atque ita de cæteris. </s>

<s>Ad hæc, Quem<lb/>admodum proinde æqualibus temporibus æqualia <lb/>fiant additamenta, &longs;eu æquales gradus velocitatis ac<lb/>quirantur, & interim tamen decur&longs;us &longs;patiorum &longs;ecun<lb/>dum &longs;eriem numerorum ab vnitate inc&oelig;ptorum <lb/>fiat. </s>

<s><emph type="italics"/>Adde quòd ad vniformen motus accelerationem minimè <lb/>nece&longs;&longs;arium e&longs;t, vt acqui&longs;ita æqualibus temporibus velocitatis <lb/>incrementa æqualia &longs;int (vt paßim &longs;upponere videris) &longs;ed <lb/>&longs;atis e&longs;t, &longs;i continuò maiora in quacumque ratione<emph.end type="italics"/> G<emph type="italics"/>eome<lb/>trica acquirantur: cùm notum &longs;it omnibus progreßiones <lb/>Geometricas non minùs vniformeis e&longs;&longs;e, quàm Arithmeticas. <lb/></s>

<s>Ex quibus planè efficitur, definitionem accelerati motus <lb/>quamcúmque inde veram, perfectamque non probari, quòd <lb/>ea ratione concepta &longs;it, qua vniformis acceleratio exprima<lb/>tur.<emph.end type="italics"/></s>

<s>Id, quod dicis videri me &longs;upponere, reuerâ &longs;uppo<lb/>no: & quod ais <emph type="italics"/>notum omnibus progreßiones Geometricas <lb/>non minùs e&longs;&longs;e vniformeis, quàm Arithmeticas,<emph.end type="italics"/> mihi &longs;al<lb/>tem notum non e&longs;t (<emph type="italics"/>qualemcumque me habiturus &longs;is<emph.end type="italics"/>) vt <lb/>neque capio id, quod ais, <emph type="italics"/>ad vniformem motus acceleratio<lb/>nem &longs;atis e&longs;&longs;e, &longs;i incrementa velocitatis continuò maiora in <lb/>quacumque ratione Geometrica acquirantur.<emph.end type="italics"/></s><s> Sed nempe <lb/>videris tu mihi <emph type="italics"/>vniformitatem<emph.end type="italics"/> cum <emph type="italics"/>conformitate<emph.end type="italics"/> confun-<pb pagenum="107"/>dere; & quia videtur <emph type="italics"/>conformitas<emph.end type="italics"/> idem &longs;onare, quod <lb/><emph type="italics"/>proportio,<emph.end type="italics"/> confundere quoque cum <emph type="italics"/>proportione vnifor<lb/>mitatem:<emph.end type="italics"/> cùm videatur tamen <emph type="italics"/>Vniformitas<emph.end type="italics"/> relatio e&longs;&longs;e <lb/>identitatis, ob vnum, eundemque tenorem, in vna, <lb/>atque eademre; <emph type="italics"/>Proportio<emph.end type="italics"/> autem e&longs;&longs;e potiùs &longs;imilitu<lb/>dinis relatio, quæ in rebus alioquin diuer&longs;is, &longs;iue di&longs;&longs;i<lb/>tis reperiatur. </s>

<s>Ex hoc quippe e&longs;t, cur dicatur inter <lb/>fontem, & radicem, non <emph type="italics"/>vniformitas,<emph.end type="italics"/> &longs;ed <emph type="italics"/>proportio<emph.end type="italics"/> e&longs;<lb/>&longs;e: & in colore pennarum cycni, non <emph type="italics"/>proportio,<emph.end type="italics"/> &longs;ed <lb/><emph type="italics"/>vniformitas:<emph.end type="italics"/> ac eodem ex capite e&longs;t, cur in progre&longs;&longs;io<lb/>ne Geometrica rationem vnius ad quàtuor, quatuor ad <lb/>&longs;exdecim, &longs;exdecim ad &longs;exaginta quatuor, dicamus <lb/>e&longs;&longs;e <emph type="italics"/>proportionem,<emph.end type="italics"/> non verò vniformitatem; & in pro<lb/>gre&longs;&longs;ione Arithmetica vnius duorum, trium, quatuor, <lb/>vel duorum, quatuor, &longs;ex, octo; vel trium &longs;ex, nouem, <lb/>duodecim, &c. <emph type="italics"/>vniformitatem<emph.end type="italics"/> e&longs;&longs;e, & non <emph type="italics"/>proportionem<emph.end type="italics"/><lb/>dicamus. </s>

<s>Heinc igitur e&longs;t, quorsùm videar non iniu<lb/>riâ &longs;upponere accelerationem motus, vt <emph type="italics"/>vniformis,<emph.end type="italics"/> &longs;eu <lb/>æquabilis &longs;it, debere Arithmetica progre&longs;&longs;ione ince<lb/>dere, & ea quidem &longs;ecundum impareis ab vnitate nu<lb/>meros, putà vnum, tria, quinque, &longs;eptem, &c. </s>

<s>a&longs;&longs;um<lb/>pta; cùm tu, licet Geometricarum &longs;im plici&longs;&longs;imam, du<lb/>plam nempe, elegeris reperire in ea vniformitatem, <lb/>&longs;eu æquabilitatem non po&longs;&longs;is: &, &longs;i reperire velis ali<lb/>quam, Arithmeticam v&longs;urpare cogaris, eam nempe, <lb/>quæ &longs;ecundum vnitates e&longs;t, veluti dum ais gradus ve<lb/>locitatis &longs;ic acquiri, vt &longs;int in fine primi &longs;patij vnus, in <lb/>&longs;ine &longs;ecundi duo, in fine tertij tres, &c. </s>

<s>Quamobrem <lb/>autem dicas definitionem, de qua agitur, <emph type="italics"/>veram, per<lb/>fectamque non probari, quòd ea ratione concepta &longs;it, qua<emph.end type="italics"/><pb pagenum="108"/><emph type="italics"/>vniformis acceleratio exprimatur:<emph.end type="italics"/> non video quorsùm <lb/>re&longs;pexeris; cùm videam heic agi de motu, cuius vni<lb/>formis &longs;it acceleratio. </s>

<s><emph type="italics"/>Sed ex his porrò etiam vides, quàm non rectè vulgatam <lb/>accelerati motus definitionem inde numero<emph.end type="italics"/> VIII. <emph type="italics"/>reprehen<lb/>das, quòd ea ratione concepta &longs;it, qua vniformis acceleratio <lb/>non exprimatur. </s>

<s>Modò enim vtdisti puncto<emph.end type="italics"/> A <emph type="italics"/>pro initio <lb/>&longs;patij con&longs;tituto, cuius partes æquales æqualibus &longs;egmentis<emph.end type="italics"/><lb/>EG, GI, IL <emph type="italics"/>de&longs;ignentur, non tantum recti vniformem <lb/>quampiam, &longs;ed eandem planè velocitatis accelerationem ha<lb/>beri: vt iam ampliùs inquirere tibi non liceat, quomodo ex <lb/>vulgata motus accelerati definitione, qua<emph.end type="italics"/> is dicitur, qui <lb/>æqualibus &longs;patijs æqualia velocitatis augmenta acqui<lb/>rat, <emph type="italics"/>motum concipere liceat æquabiliter acceleratum. </s>

<s>Iam <lb/>enim habes concipi pror&longs;us eodem modo, quo tu illum con-<emph.end type="italics"/><lb/><figure id="fig24"></figure><lb/><emph type="italics"/>cipis, atque exprimis ex data<emph.end type="italics"/> G<emph type="italics"/>a<lb/>lilei definitione. </s>

<s>Nam quòd eodem <lb/>numero<emph.end type="italics"/> VIII. <emph type="italics"/>de&longs;cripto nouo trian<lb/>gulo<emph.end type="italics"/> APB <emph type="italics"/>accelerationis augmen<lb/>tum minoribus triangulis inter pa<lb/>rallelas<emph.end type="italics"/> CL, DM, EO, <emph type="italics"/>&c. <lb/></s>

<s>con&longs;titutis metiendum putas, non <lb/>rectè id facis. </s>

<s>Vt enim velocitas <lb/>acqui&longs;ita per &longs;patium<emph.end type="italics"/> AC <emph type="italics"/>de&longs;igna<lb/>tur per lineam<emph.end type="italics"/> CL, <emph type="italics"/>velocitas ac<lb/>qui&longs;ita in<emph.end type="italics"/> D, <emph type="italics"/>exprimitur linea<emph.end type="italics"/><lb/>DN: <emph type="italics"/>& velocitas acqui&longs;ita in<emph.end type="italics"/> E, <lb/><emph type="italics"/>repræ&longs;entatur linea<emph.end type="italics"/> EQ, <emph type="italics"/>& ita <lb/>de cæteris. </s>

<s>Cur enim celeritatis <lb/>augmenta hoc loco triangulis, in &longs;uperiore autem figura<emph.end type="italics"/><pb pagenum="109"/><emph type="italics"/>lineis metienda edicis? </s>

<s>Constat autem lineas<emph.end type="italics"/> CL, ND, <lb/>EQ, <emph type="italics"/>&c. </s>

<s>vniformi augmento accre&longs;cere, & e&longs;&longs;e, vt<emph.end type="italics"/> AC <emph type="italics"/>ad<emph.end type="italics"/><lb/>CL, <emph type="italics"/>ita<emph.end type="italics"/> AD <emph type="italics"/>ad<emph.end type="italics"/> DN, <emph type="italics"/>&<emph.end type="italics"/> AE <emph type="italics"/>ad<emph.end type="italics"/> EQ, <emph type="italics"/>&c. </s>

<s>Non <lb/>rectè igitur cen&longs;es augmentum velocitatis vniforme e&longs;&longs;e non <lb/>po&longs;&longs;e, &longs;i spatijs æqualibus cre&longs;cat æqualiter, & tota illa noui <lb/>istius trianguli difformis &longs;tructura sponte corruit.<emph.end type="italics"/></s>

<s>Heic idem dicendum, quod & paulò antè, quate<lb/>nus parteis lineæ AB contendis habendas pro parti<lb/>bus &longs;patij, quæ comparentur cum parallelis habitis <lb/>pro gradibus velocitatis, nulla habita temporis ratio<lb/>ne. </s>

<s>Quod autem quæris, <emph type="italics"/>Cur hoc loco celeritatis aug<lb/>menta triangulis in &longs;uperiore autem figura lineis metienda <lb/>edixerim?<emph.end type="italics"/> Cau&longs;&longs;am ex eo potes intelligere, quòd cùm <lb/>tu duos gradus NM, & MD, v. </s>

<s>æqualeis facias, <lb/>qua&longs;i acqui&longs;itos ex L, & C, &longs;ecundum duos triangulos <lb/>LNM, & CMD (tamet&longs;i inæquales &longs;int, & MD ex <lb/>LC manente factus, duobus æquiualeat) ideò quem <lb/>defectum exprimere non licuit lineâ ND, exprimere <lb/>placuerit trapezio LD. Nimirùm, cùm velocitas <lb/>ND creetur partim ex LC, promota in MD &longs;ecun<lb/>dum quadrangulum, partim ex additamentis ip&longs;i fa<lb/>ctis &longs;ecundum triangulum LNM; tu ex velocitate hac <lb/>detrahis integrum triangulum LMC: &longs;icque ex tri<lb/>bus &longs;uper&longs;unt tantum partes velocitatis duæ, quas vt <lb/>&longs;imul iunct is repræ&longs;entarem, triangulum à te factum <lb/><expan abbr="vacu&utilde;">vacuum</expan> &longs;upplcui, tran&longs;lato LNM in MCL: cópo&longs;itoque <lb/>inde quadrangulo, locum ip&longs;um trianguli tran&longs;lati re<lb/>liqui inanem. </s>

<s>Fandem autem ob cau&longs;&longs;am relicti &longs;unt <lb/>duo trianguli manes ad ordinem tertium tres ad quar<lb/>tum, &c. </s>

<s>Exindeque e&longs;t, cur <emph type="italics"/>difformis<emph.end type="italics"/> quidem, &longs;ed <pb pagenum="110"/>iuxta te tamen con&longs;titutus triangulus &longs;it; neque pro<lb/>pterea cius &longs;tructura, quatenus e&longs;t tuis decretis confor<lb/>mis, &longs;ponte corruat. </s>

<s>Addam-ne, cùm lineâ AC <lb/>b<gap/>cta in S, ductáque lineâ SL contendas ip&longs;e ex <lb/>deductis articulo XXXV, & &longs;equentibus progre&longs;&longs;ionem <lb/>tuam illam duplum incipere ab S, & mobile tam citò <lb/>peruenire ex C in D, quàm ex S in C, &longs;icque ob <lb/>duplum &longs;patium velocitatem acqui&longs;itam in D e&longs;&longs;e du<lb/>plam velocitatis acqui&longs;itæ in C, atque adeò e&longs;&longs;e ad il<lb/>lam vt lineam DN ad lineam CL: addam-ne in<lb/>quam, & triangulum &longs;ieri exinde adhuc deformius, <lb/>& comparationem hanc tuam peruerti, cùm adeò <lb/>fal&longs;um &longs;it dicere, vt SC, ad CL, ita SD ad DN? </s>

<s>An<lb/>non vel ex hoc capite agno&longs;cere potes, a&longs;&longs;umptis li<lb/>neis CL, DN, & parallelis cæteris pro incrementis <lb/>velocitatis, non licere vniformitatem, æquabilitatem<lb/>ve accelerationis tueri? </s>

<s><emph type="center"/>IN ARTICVLOS IX. X. XI. XII. </s>

<s>De Paralogi&longs;mo, qui <lb/>Galileo Definitionem &longs;puriam impugnanti <lb/>obiicitur.<emph.end type="center"/></s>

<s><emph type="italics"/>Po&longs;tquàm autem<emph.end type="italics"/> G<emph type="italics"/>alilei definitionem confirmare, & <lb/>communem aliorum de&longs;truere conatus es, aggrederis numero <lb/>x. </s>

<s>eam rationem, qua idem Galileus communiorem motus <lb/>vniformiter accelerati definitionem ab&longs;urditatis arguit, à <lb/>paralogi&longs;mo excu&longs;are: &longs;ed fru&longs;tra huius cau&longs;&longs;æ pairocinium <lb/>&longs;u&longs;cipis, cùm nec eam obtinere, nec &longs;atis plau&longs;ibiliter eam de<lb/>fendere poßis. </s>

<s>Hæc porrò e&longs;t<emph.end type="italics"/> G<emph type="italics"/>alilei ratio.<emph.end type="italics"/></s><s> Si accelera<lb/>tio motus in de&longs;cen&longs;u grauium æqualibus &longs;patiis, <lb/>æqualia &longs;umeret velocitatis incrementa, e&longs;&longs;ent velo-<pb pagenum="111"/>citates inter &longs;e, vt emen&longs;a &longs;patia: at quoties velocitates <lb/>inter &longs;e &longs;unt, vt emen&longs;a &longs;patia, debent nece&longs;&longs;ariò ea <lb/>&longs;patia aut eodem, aut æquali tempore percurri. </s>

<s>Si igi<lb/>tur velocitas acqui&longs;ita per totam AC, eam rationem <lb/>habeat ad velocitatem acqui&longs;itam per AB, <lb/><figure id="fig25"></figure><lb/>quam &longs;patium AC, ad &longs;patium AB, nece&longs;&longs;e e&longs;t, <lb/>vt totum &longs;patium AC eodem, aut æquali tem<lb/>pore decurratur, quo &longs;patium AB ab&longs;oluitur. <lb/></s>

<s>Impo&longs;&longs;ibile e&longs;t autem, vt corpus de&longs;cendens per <lb/>AC, eodem, aut æquali tempore percurrat to<lb/>tam AC, quo percurrit partem eius AB, ni&longs;i mo<lb/>tus fiat in in&longs;tanti. </s>

<s>Tam impo&longs;&longs;ibile e&longs;t igitur, <lb/>vt velocitates in de&longs;cen&longs;u grauium inter &longs;e &longs;int, vt <lb/>emen&longs;a &longs;patia, quàm impo&longs;&longs;ibile e&longs;t motum illum fie<lb/>ri in in&longs;tanti. <emph type="italics"/>Hanc ego rationem Paralogi&longs;mum dico, tu <lb/>contendis e&longs;&longs;e veram Demon&longs;trationem. </s>

<s>Vitium ego tan<lb/>quam intelligenti breuiùs fortè indicaui: at præoccupato cer<lb/>tè aliunde animo, non &longs;ufficienter illud detexi. </s>

<s>Exactiùs igi<lb/>tur (vt po&longs;tulas) &longs;ingulas huius Ratiocinationis propo&longs;itiones <lb/>hoc loco perpendemus. </s>

<s>Prima h&ecedil;c e&longs;t,<emph.end type="italics"/> Si acceleratio motus <lb/>in de&longs;cen&longs;u grauium æqualibus &longs;patiis æqualia &longs;umeret <lb/>velocitatis incrementa, e&longs;&longs;ent velocitates inter &longs;e, vt <lb/>emen&longs;a &longs;patia. <emph type="italics"/>Nunc age, quis huius propo&longs;itionis &longs;en&longs;us <lb/>e&longs;&longs;e videtur? </s>

<s>Duplicem enim patitur, & quidem valdè di<lb/>uer&longs;um, quorum alter verus, alter fal&longs;us &longs;it; & ni&longs;i po&longs;teriore <lb/>hoc &longs;en&longs;u illam po&longs;t<emph.end type="italics"/> G<emph type="italics"/>alileum v&longs;urpes, concludis omninò ni<lb/>hil. </s>

<s>Prior &longs;en&longs;us i&longs;te e&longs;t, Si acceleratio motus in de&longs;cen&longs;u <lb/>grauium æqualibus spatiis æqualia &longs;umat velocitatis augmen<lb/>ta; nece&longs;&longs;e e&longs;t, vt hæc eadem augmenta quibu&longs;libet spatij <lb/>partibus acqui&longs;ita eandem inter &longs;erationem ob&longs;eruent, quàm<emph.end type="italics"/><pb pagenum="112"/><emph type="italics"/>emen&longs;a &longs;patia, & hic &longs;en&longs;us verus ac nece&longs;&longs;arius e&longs;t. </s>

<s>Si <lb/>enim intriangulo æqualia spatia de&longs;ignentur<emph.end type="italics"/> AD, DE, EF, <lb/><emph type="italics"/>&c. </s>

<s>& in<emph.end type="italics"/> D <emph type="italics"/>acqui&longs;itus &longs;upponatur vnus<emph.end type="italics"/><lb/><figure id="fig26"></figure><lb/><emph type="italics"/>gradus, & in<emph.end type="italics"/> E <emph type="italics"/>duo, & tres in<emph.end type="italics"/> F, <emph type="italics"/>manife&longs;tum <lb/>e&longs;t duos gradus, ad quos acceleratio perueni&longs;&longs;e <lb/>ponitur in<emph.end type="italics"/> E, <emph type="italics"/>e&longs;&longs;e ad vnum gradum acqui&longs;i<lb/>tum in<emph.end type="italics"/> D, <emph type="italics"/>vt &longs;patium<emph.end type="italics"/> AE <emph type="italics"/>ad spatium<emph.end type="italics"/> AD; <lb/><emph type="italics"/>& &longs;imiliter gradus treis, qui in<emph.end type="italics"/> F <emph type="italics"/>&longs;upponun<lb/>tur terminare celeritatis augmentum, e&longs;&longs;e ad <lb/>gradum vnum ip&longs;ius<emph.end type="italics"/> D, <emph type="italics"/>vel ad duos ip&longs;ius<emph.end type="italics"/> E, <lb/><emph type="italics"/>vt<emph.end type="italics"/> AF, <emph type="italics"/>ad<emph.end type="italics"/> AD, <emph type="italics"/>vel<emph.end type="italics"/> AE. <emph type="italics"/>Et hoc quidem <lb/>&longs;en&longs;u, &longs;i primam illam<emph.end type="italics"/> G<emph type="italics"/>alilei v&longs;urpares, vera omninò e&longs;&longs;et, <lb/>ac nece&longs;&longs;aria, &longs;ed A&longs;&longs;umptio, quæ &longs;ub&longs;umitur, fal&longs;a e&longs;&longs;et at<lb/>que impoßibilis; nempe hæc.<emph.end type="italics"/></s><s> At quoties velocitates inter <lb/>&longs;e &longs;unt vt emen&longs;a &longs;patia (<emph type="italics"/>in &longs;en&longs;u proximè aßignato<emph.end type="italics"/>) de<lb/>bent nece&longs;&longs;ariò ea &longs;patia aut eodem, aut æquali tem<lb/>pore percurri: <emph type="italics"/>Sicque iam hac ex parte<emph.end type="italics"/> G<emph type="italics"/>alilei licet ratio<lb/>cinatio corruit. </s>

<s>Sed alius item e&longs;&longs;e pote&longs;t primæ illius Propo<lb/>&longs;itionis &longs;en&longs;us, vt &longs;eilicet quoties acceleratio velocitatis in de&longs;<lb/>cen&longs;u grauium æqualibus &longs;patiis æqualia incrementa acquirit, <lb/>integræ velocitates &longs;ecundum &longs;e totas, & qua&longs;libet &longs;ui parteis <lb/>analogas aeceptæ, & con&longs;iderata, & non tantum acqui&longs;itæ <lb/>partibus &longs;patii æqualibus incrementa, eam ab initio ad finem <lb/>inter &longs;e rationem ob&longs;eruent, quam emen&longs;a &longs;patia. </s>

<s>Qui &longs;en<lb/>&longs;us à priore longè diuer&longs;us est, & à te non intenditur modò; <lb/>&longs;ed di&longs;tinctè quoque eodem numero x. </s>

<s>exprimitur. </s>

<s>Ais enim.<emph.end type="italics"/><lb/>Rem certè in hunc modum concipio. </s>

<s>Intelligatur <lb/>AC, diui&longs;a in duodecim parteis æqualeis, ac proinde <lb/>eius dimidium AB, &longs;eu ip&longs;i æqualeis DE in <gap/>x; &longs;int<lb/>que primùm duo mobilia, quorum vnum de&longs;cendat <pb pagenum="113"/>ex A, ver&longs;us C, eodem momento, quo aliud ex D, <lb/>ver&longs;us E; notum e&longs;t, &longs;i vtrumque quidem fer<lb/><figure id="fig27"></figure><lb/>retur non accelerato, &longs;ed æquabili motu, <lb/>euenturum e&longs;&longs;e, vt velocitate illius ex&longs;i&longs;tente <lb/>dupla ad velocitatem i&longs;tius, illud perueniret <lb/>in C, eodem momento, quo i&longs;tud in E; <lb/>quoniam &longs;patium ab illo &longs;uperatum foret <lb/>vbique ad &longs;patium ab i&longs;to &longs;uperatum, du<lb/>plum; hoc e&longs;t, forent ab illo &longs;uperatæ duæ <lb/>partes, cùm ab i&longs;to vna: ab illo quatuor, cùm ab hoc <lb/>duæ, &c. </s>

<s>quatenus &longs;patia &longs;e haberent vbique, vt velo<lb/>citates; hoc e&longs;t, velocitas per totam AC, e&longs;&longs;et vbique <lb/>dupla velocitatis per totam DE. </s>

<s>At verò, quoniam <lb/>heic agitur de motu non æquabili, &longs;ed continenter <lb/>accelerato; ita di&longs;cedant rursùs mobilia eodem tem<lb/>pore, vnum ab A, aliud à D, vt &longs;uccre&longs;centibus conti<lb/>nuò velocitatis gradibus, illud perueniendo in C, ac<lb/>qui&longs;ierit duodecim, hoc perueniendo in E, &longs;ex: <emph type="italics"/>Tum <lb/>interrogas,<emph.end type="italics"/> Quid impediat, quò minùs illud perueniat <lb/>in C, eodem tempore, quo i&longs;tud in E? <emph type="italics"/>Ego verò re&longs;<lb/>pondeo, nihil certè impedire, &longs;i tales e&longs;&longs;ent, quales de&longs;cribis <lb/>velocitate: taleis autem &longs;ine dubio de&longs;cribis, qualeis in prima <lb/>illa<emph.end type="italics"/> G<emph type="italics"/>alilei propo&longs;itione &longs;ignificari putas. </s>

<s>At hoc &longs;en&longs;u hypo<lb/>thetica illa Galilei propo&longs;itio fal&longs;a e&longs;t, euidenterque impoßi<lb/>bilis: cùm nulla prorsùs ratione con&longs;equens inferi poßit ex <lb/>antecedente. </s>

<s>Hoc enim e&longs;t Antecedens,<emph.end type="italics"/> Acceleratio ve<lb/>locitatis in de&longs;cen&longs;u grauium per totam AC, ita con<lb/>tinua &longs;ucce&longs;&longs;ione cre&longs;cit, vt primùm in B acqui&longs;itus <lb/>&longs;upponatur vnus aliquis velocitatis gradus; & vlteriùs <lb/>procedente motu, & continuò incre&longs;cente celeritate, <pb pagenum="114"/>duo iam in C velocitatis gradus habeantur. <emph type="italics"/>Istad <lb/>certè e&longs;t antecedens, & nihil aliud aiunt ij, qui à<emph.end type="italics"/> G<emph type="italics"/>alileo ab<lb/>&longs;urditatis arguuntur. </s>

<s>Iam ergo vide, vtrum ex hoc antece<lb/>dente, rectè tuum illud, & Galilei Con&longs;equens inferatur:<emph.end type="italics"/> Ergo <lb/>velocitas de&longs;cen&longs;us per totam AC ab initio ad finem, <lb/>& &longs;ecundum qua&longs;libet eius parteis con&longs;iderata, perpe<lb/>tuò dupla e&longs;t eius velocitatis, qua idem graue per AB <lb/>de&longs;cendit. <emph type="italics"/>Siue enim<emph.end type="italics"/> AB <emph type="italics"/>coniunctam toti<emph.end type="italics"/> AC, <emph type="italics"/>con&longs;ide<lb/>res, &longs;iue vt &longs;eparatam, qualis e&longs;t<emph.end type="italics"/> DE, <emph type="italics"/>&longs;emper velocitas de&longs;<lb/>cen&longs;us per<emph.end type="italics"/> AC, <emph type="italics"/>quandiù percurritur prior eius pars<emph.end type="italics"/> AB, <emph type="italics"/>nec <lb/>&longs;ui-ip&longs;ius, nec velocitatis per<emph.end type="italics"/> DE, <emph type="italics"/>dupla e&longs;t, vt falsò a&longs;&longs;umis, <lb/>&longs;ed planè eadem, aut æqualis omninò est. </s>

<s>Nempe volumus, <lb/>& nece&longs;&longs;ariò exigimus (quod ip&longs;a quoque rei natura po&longs;tu<lb/>lat) vt motus, qui per totam<emph.end type="italics"/> AC, <emph type="italics"/>& per partem<emph.end type="italics"/> AB, <emph type="italics"/>&longs;iue <lb/>per æqualem<emph.end type="italics"/> DE, <emph type="italics"/>eadem planè velocitate incipiat, & eadem <lb/>velocitate progrediatur per totam<emph.end type="italics"/> AB, <emph type="italics"/>& per ip&longs;am<emph.end type="italics"/> DE: <lb/><emph type="italics"/>ex<emph.end type="italics"/> B <emph type="italics"/>verò ita velocitas augeatur, vt tandem in<emph.end type="italics"/> C <emph type="italics"/>dupla in<lb/>ueniatur eius, qua fuit in<emph.end type="italics"/> B, <emph type="italics"/>vel in<emph.end type="italics"/> E. H<emph type="italics"/>æc enim nostra, <lb/>& communis aliorum &longs;uppo&longs;itio e&longs;t, & primæ propo&longs;itionis à<emph.end type="italics"/><lb/>G<emph type="italics"/>alileo a&longs;&longs;umptæ antecedens; &longs;i tamen aduer&longs;um nos, & non <lb/>potiùs aduer&longs;us Chimeras, & Tragalaphos depugnet. </s>

<s>At <lb/>ex eo antecedente tuumillud, &<emph.end type="italics"/> G<emph type="italics"/>alilei con&longs;equens nece&longs;&longs;a<lb/>ria illatione non priùs inferetur, quàm aliud quodlibet ex <lb/>vero fal&longs;um eruatur. </s>

<s>Prima igitur<emph.end type="italics"/> G<emph type="italics"/>alilei Propo&longs;itio, eo <lb/>&longs;en&longs;u, quo ab ip&longs;o v&longs;urpatur, & à te intelligitur, fal&longs;a e&longs;t, <lb/>atque impoßibilis; ideóque tota eius ratiocinatio, non demon<lb/>&longs;tratio, &longs;ed merus Paralogi&longs;mus e&longs;t.<emph.end type="italics"/></s>

<s>An videri potes operosè quidem, &longs;ed nequicquam <lb/>tamen explicare conatum, vt Paralogi&longs;mum o&longs;tendas, <lb/>quem quanta moderatione potueram non fui&longs;&longs;e à te <pb pagenum="115"/>o&longs;ten&longs;um innueram; bonitatem tuam implorando, &longs;i <lb/>fortè liceret mihi dicere, videri po&longs;&longs;e cuipiam, te eum <lb/>potiùs e&longs;&longs;e, qui incideres in Paralogi&longs;mum? </s>

<s>Quippe <lb/>huiu&longs;modi de re &longs;ola hæc verba habueras, quæ non <lb/>pigebit repetere, <emph type="italics"/>Vt &longs;i graue de&longs;cendens per AB, tem<lb/>pus quodcumque in&longs;umat, puta quadrantem: ac deinde BC <lb/>ip&longs;i AB æquale, dimidio quadrante percurrat: quis neget in<emph.end type="italics"/><lb/>C <emph type="italics"/>duplam haberi velocitatem eius, quæ fuit in B? Et-tamen <lb/>idem graue totam AC, & dimidium eius AB eodem tem<lb/>pore non percurreret.<emph.end type="italics"/></s><s> Scilicet i&longs;thæc ip&longs;a &longs;unt, ob quæ <expan abbr="c&utilde;">cum</expan> <lb/>ego dixerim, videri te <emph type="italics"/>Rem controuer&longs;am pro principio <lb/>a&longs;&longs;umere:<emph.end type="italics"/> ais iam te fui&longs;&longs;e breuiter loquutum, quod pu<lb/>târis me <emph type="italics"/>intelligentem<emph.end type="italics"/> &longs;atis, vt paucis multa caperem: <lb/>nunc autem, quia contigit &longs;ecus, & &longs;altem virum <emph type="italics"/>animo <lb/>præoccupatum<emph.end type="italics"/> es alloquutus, e&longs;&longs;e rem exactiùs, fu&longs;iu&longs;<lb/>que dicendam. </s>

<s>Age itaque tu adeò humanus, vt te hu<lb/>ius meæ hebetudinis, præoccupationi&longs;que mi&longs;e<lb/>reat, patere &longs;altem lentè incedam, viamque pertentem; <lb/>&longs;i quà po&longs;&longs;im te con&longs;equi. </s>

<s>Cùm tu quæ pauca Gali<lb/>leus hac de re habet, reduxeris ad &longs;yllogi&longs;ticam quan<lb/>dam formam; videtur mihi po&longs;&longs;e non incommodè, vt <lb/>res di&longs;tinctiùs percipiatur, ea fieri A&longs;&longs;umptio, quæ tibi <lb/>Propo&longs;itio e&longs;t, ea Propo&longs;itio, quæ A&longs;&longs;umptio, & Syllo<lb/>gi&longs;mus proinde &longs;ic in&longs;titui. </s>

<s><emph type="italics"/>Quoties velocitates &longs;untinter &longs;e, vt emen&longs;a spatia, de<lb/>bent nece&longs;&longs;ariò ea spatia aut eodem, aut æquali tempore per<lb/>curri.<emph.end type="italics"/></s>

<s><emph type="italics"/>At, &longs;i acceleratio motus in de&longs;cen&longs;u grauium æqualibus <lb/>&longs;patiis æqualia &longs;umeret velocitatis incrementa, e&longs;&longs;ent velocita<lb/>tes inter &longs;e, vtemen&longs;a spatia.<emph.end type="italics"/></s><pb pagenum="116"/>

<s><emph type="italics"/>Igitur, &longs;i acceleratio motus in de&longs;cen&longs;u grauium æquali<lb/>bus spatiis æqualia &longs;umeret velocitatis incrementa, deberent <lb/>nece&longs;&longs;ariò ea &longs;patia aut eodem, aut æquali tempore percurri.<emph.end type="italics"/></s>

<s>Tu Propo&longs;itionem (nomine A&longs;&longs;umptionis) <emph type="italics"/>fal&longs;am <lb/>ac impoßibilem<emph.end type="italics"/> dicis: &longs;ed tuo nimirum illo &longs;en&longs;u;) de <lb/>quo dicendum con&longs;equenter) nam alio quidem, quem <lb/>diuer&longs;um ais, & Galileo, mihique tribuis, admittere <lb/>verum, nece&longs;&longs;ariumque cogeris, ob meum illud ratio<lb/>cinium, cuius aliquam recita&longs;ti partem. </s>

<s>Nihil verò <lb/>ex eo repeto; cùm nemo non &longs;tatim peruideat po&longs;&longs;e <lb/>Propo&longs;itionem accipi in duplici ca&longs;u, Vno, &longs;i motus <lb/>non acceleratus, &longs;ed æquabilis &longs;it; Altero, &longs;i acceleratus, <lb/>&longs;ed æquabili tamen progre&longs;&longs;ione. </s>

<s>Si primo enim, <lb/>&longs;int duo mobilia, quorum alterum &longs;it velocius, & per<lb/>currere debeat &longs;patium duplò longius, quod &longs;it, verbi <lb/>cau&longs;sâ, duo &longs;tadia; manife&longs;tum e&longs;t duo ab illo &longs;tadia, <lb/>& vnum ab alio, eodem, aut æquali tempore percurri. <lb/></s>

<s>Sin verò &longs;ecundo, duo mobilia &longs;int, quorum motus <lb/>continenter &longs;ic acceleretur, vt celeritas vnius &longs;it conti<lb/>nenter, &longs;eu tempore toto, aut ei&longs;dem &longs;altem partibus <lb/>celeritatis alterius dupla, & &longs;patium percurrendum &longs;it <lb/>&longs;imiliter duplum, veluti rursùs duo &longs;tadia: manife&longs;tum <lb/>iterum e&longs;t, duo ab illo &longs;tadia, & vnum ab alio, eodem, <lb/>aut æquali tempore percurri. </s>

<s>Ac Propo&longs;itionem qui<lb/>dem ego &longs;ic&longs;tabilio. </s>

<s>Re&longs;tat, vt tu proponas ca&longs;um, <lb/>qui exceptionem faciat, ac non e&longs;&longs;e veram vniuersè <lb/>demon&longs;tres. </s>

<s>Porrò nullum habes, præter tuum &longs;en<lb/>&longs;um, &longs;eu ip&longs;am quæ&longs;tionem, atque conclu&longs;ionem, de <lb/>qua controuer&longs;iam Galileo facis; neque vllum tibi ad <lb/>eum conuincendum argumentum &longs;uppetit, quàm ip&longs;a <pb pagenum="117"/><gap/>dhûc controuer&longs;ia: Id enim manife&longs;tum fit, tum ex <lb/>verbis illis, quæ paulò antè recitaui, tum ex illis, quæ <lb/>habesiam, fa&longs;ioribus quidem, &longs;ed ei&longs;dem tamen. </s>

<s>Quia <lb/>verò tu ad A&longs;&longs;umptionem (Propo&longs;itionis nomine) hæc <lb/>refers; age quid id &longs;it peruideamus. </s>

<s>A&longs;&longs;umptio e&longs;t, <emph type="italics"/>Si acceleratio motus in de&longs;cen&longs;u gra<lb/>uium æqualibus &longs;patiis æqualia &longs;umeret velocitatis incremen<lb/>ta, e&longs;&longs;ent velocitates inter &longs;e, vt emen&longs;a spatia.<emph.end type="italics"/></s><s> Tu illam <lb/>explanaturus duplicem ip&longs;i &longs;en&longs;um attribuis. <emph type="italics"/>Et prior <lb/>quidem i&longs;te est,<emph.end type="italics"/> inquis, <emph type="italics"/>&longs;i acceleratio motus in de&longs;cen&longs;u gra<lb/>uium æqualibus &longs;patijs æqualia &longs;umat velocitatis augmenta, <lb/>nece&longs;&longs;e est, vt hæc eadem augmenta quibu&longs;libet spatij parti<lb/>bus acqui&longs;ita, eandem inter &longs;e rationem ob&longs;eruent, quàm <lb/>emen&longs;a &longs;patia.<emph.end type="italics"/></s><s> At ego non &longs;um Oedipus, pote&longs;que ip&longs;e <lb/>cau&longs;&longs;ari te non affari intelligentem: &longs;iquidem non ita <lb/>&longs;um &longs;olers, vt per&longs;picere valeam, quid diuer&longs;itatis, aut <lb/>explanationis, &longs;en&longs;us hic, quem facis &longs;pecialem, <lb/>contineat. </s>

<s>Po&longs;terior, <emph type="italics"/>vt &longs;cilicet,<emph.end type="italics"/> inquis, <emph type="italics"/>quoties accelera<lb/>tio velocitatis in de&longs;cen&longs;u grauium æqualibus spatiis æqualia <lb/>incrementa acquirit, integræ velocitates &longs;ecundum &longs;e totas, & <lb/>qua&longs;libet &longs;ui parteis analogas acceptæ, & con&longs;ideratæ, & non <lb/>tantum acqui&longs;ita partibus &longs;patii æqualibus incrementa, ea <lb/>ab initio ad finem inter &longs;e rationem ob&longs;eruent, quam emen&longs;a <lb/>&longs;patia.<emph.end type="italics"/> Hæc paulò ob&longs;curiùs, fortè propter illud, <emph type="italics"/>& <lb/>non tantum acqui&longs;ita partibus spatii æqualibus incrementa,<emph.end type="italics"/><lb/>quod ad priorem &longs;en&longs;um attinens, cen&longs;ui&longs;ti hui<gap/> <expan abbr="inter-&longs;erend&utilde;">inter<lb/>&longs;erendum</expan>. </s>

<s>Sed vtcumque &longs;it; cùm tu &longs;en&longs;um hunc eun<lb/>dem cum eo facias, quem ais à me exprimi di&longs;tinctè; ea <lb/>de cau&longs;&longs;a ip&longs;um in confe&longs;&longs;o habeo. </s>

<s>Iam cùm &longs;it A&longs;<lb/>&longs;umptio hypothetica, & duas proinde parteis <expan abbr="cõtineat">contineat</expan>. <pb pagenum="118"/><expan abbr="quar&utilde;">quarum</expan> altera Antecedens, altera Con&longs;equens dicatur, <lb/>tu &longs;ic vtramque à conditione (vt Dialectici loquuntur) <lb/>ab&longs;oluis, vt priorem &longs;en&longs;um antecedenti tribuas, & <lb/>po&longs;ter orem con&longs;equenti; ac po&longs;tquàm antecedens ex<lb/>pre&longs;&longs;i&longs;ti in linea (expre&longs;&longs;um priùs in triangulo, dum ex<lb/>plicares priorem &longs;en&longs;um) arguas non inferri ex eo legi<lb/>timè con&longs;equens, expre&longs;&longs;um iuxta po&longs;teriorem. </s>

<s>Tu <lb/>igitur tale facis Antecedens. </s>

<s><emph type="italics"/>Acceleratio velocitatis in de&longs;cen&longs;u grauium per<emph.end type="italics"/><lb/><figure id="fig28"></figure><lb/><emph type="italics"/>totam AC, ita continua &longs;ucceßione cre&longs;cit, vt pri<lb/>mùm in B acqui&longs;itus &longs;upponatur vnus aliquis ve<lb/>locitatis gradus, & vlteriùs procedente motu, & <lb/>continuò incre&longs;cente celeritate duo iam in C velo<lb/>citatis gradus habeantur.<emph.end type="italics"/></s>

<s>Ac tum, po&longs;tquàm dixi&longs;ti illos, quià Ga<lb/>lile o arguuntur, nihil aliud dicere, videre <lb/>me iubes, vtrum ex tali Antecedente, rectè inferatur <lb/>tale Con&longs;equens. </s>

<s><emph type="italics"/>Ergo velocitas de&longs;cen&longs;us per totam AC ab initio ad fi<lb/>nem, & &longs;ecundum qua&longs;libet eius parteis con&longs;iderata perpetuò <lb/>dupla e&longs;t eius velocitatis, qua idem graue per AB de&longs;cen<lb/>dit.<emph.end type="italics"/></s>

<s>Itaque, cùm neges &longs;equelam, vt aiunt, hypotheticæ <lb/>A&longs;&longs;umptionis, & in illa cardo negotij ver&longs;etur, Ad<lb/>moneo dumtaxat circa Antecedens videri loco <emph type="italics"/>Veloci<lb/>tatis,<emph.end type="italics"/> reponendam voculam <emph type="italics"/>Motus,<emph.end type="italics"/> & te aut debui&longs;&longs;e <lb/>in&longs;erere, aut &longs;altem debere iam &longs;upponere aduerbium <lb/><emph type="italics"/>æquabiliter,<emph.end type="italics"/> aut <emph type="italics"/>vniformiter,<emph.end type="italics"/> proximè ip&longs;um verbum <lb/><emph type="italics"/>cre&longs;cit,<emph.end type="italics"/> &longs;iue potius <emph type="italics"/>fit<emph.end type="italics"/> (ni&longs;i non <emph type="italics"/>velocitatis acceleratio,<emph.end type="italics"/> &longs;ed <lb/><emph type="italics"/>velocitas<emph.end type="italics"/> &longs;impliciter &longs;cribatur) itemque proxime vocem <pb pagenum="119"/><emph type="italics"/>celeritate:<emph.end type="italics"/> adeo proinde, vt Antecedens aut &longs;it, aut intel<lb/>ligatur huiu&longs;modi. </s>

<s><emph type="italics"/>Acceleratio motus in de&longs;cen&longs;u grauium per totam A<emph.end type="italics"/>C <lb/><emph type="italics"/><gap/>a continua &longs;ucceßione æquabiliter fit, vt primùm in B <lb/>acqui&longs;itus &longs;upponatur vnus aliquis velocitatis gradus, & vl<lb/>terius procedente motu, & continuò incre&longs;cente æquabiliter <lb/>celeritate, duo iam in C velocitatis gradus habeantur.<emph.end type="italics"/></s>

<s>Quippe heic agitur de Motu, cuius acceleratio fiat, <lb/>&longs;eu celeritas, velocitas-ve incre&longs;cat &longs;ucce&longs;&longs;ione conti<lb/>nua, non quacumque, &longs;ed æquabili. </s>

<s>Nam illa qui<lb/>dem acceleratio, quam antè obiiciebam po&longs;&longs;e accipi, <lb/>primò &longs;ecundum parteis minuti, deinde &longs;ecundum <lb/>parteis horæ, tum &longs;ecundum parteis &longs;ecundi, tandem <lb/><expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> parteis diei, aut quæuis alia huiu&longs;modi; talis, <lb/>inquam, acceleratio continua &longs;ucce&longs;&longs;ione fieret, atta<lb/>men difformi, inæquabili, qualemque ip&longs;e non es ad<lb/>mi&longs;&longs;urus, cùm ab initio v&longs;que controuer&longs;iæ &longs;tatueris <lb/>definiti <emph type="italics"/>motum æquabiliter acceleratum eum, qui æqualibus <lb/>spatijs æqualia celeritatis augmenta acquirat.<emph.end type="italics"/></s><s> Circa Con&longs;e<lb/>quens, moneo &longs;olùm te aut debui&longs;&longs;e in&longs;erere, aut iam <lb/>debere &longs;upponere mentionem partium <emph type="italics"/>analogarum;<emph.end type="italics"/><lb/>qua&longs;i nimirùm e&longs;&longs;e debeat, aut &longs;altem intelligi huiu&longs;<lb/>modi Con&longs;equens. </s>

<s><emph type="italics"/>Ergo velocitas de&longs;cen&longs;us per totam A<emph.end type="italics"/>C <emph type="italics"/>ab initio ad fi<lb/>nem, & &longs;ecundum qua&longs;libet eius parteis con&longs;iderata perpetuò <lb/>dupla e&longs;t velocitatis de&longs;cen&longs;us eiu&longs;dem mobilis per totam AB <lb/>ab initio ad finem, & &longs;ecundum qua&longs;libet eius parteis, parti<lb/>bus ip&longs;ius AC analogas, con&longs;ideratæ.<emph.end type="italics"/></s>

<s>Id &longs;cilicet ip&longs;e iam edixeras po&longs;teriorem exprimens <lb/>&longs;en&longs;um; & per&longs;picuum e&longs;t inæqualeis lineas, quæ ac-<pb pagenum="120"/>ceptæ fuerint &longs;ecundum &longs;e totas in ratione aliqua, po&longs;<lb/>&longs;e deinceps illegitimè comparari &longs;ecundum parteis, <lb/>&longs;i facto æquali partium numero non prima vnius ad <lb/>primam alterius, &longs;ed ad decimam referatur, & vniuersè <lb/>quælibet ad quamlibet ordinis non &longs;ui. </s>

<s>Hi&longs;ce præmi&longs;&longs;is, videndum e&longs;t, quo iure tu&longs;eque<lb/>lam neges, & mon&longs;tres con&longs;equens non rectè, ac para<lb/>logi&longs;ticè inferri ex antecedente. </s>

<s>Nam nece&longs;&longs;itas qui<lb/>dem inferendi ex eo manife&longs;ta e&longs;t, quod Acceleratio <lb/>fieri, aut velocitas cre&longs;cere non po&longs;&longs;it æquabiliter per <lb/>totam AC, neque &longs;imiliter per totam AB, quin &longs;i ve<lb/>locitas in C dupla &longs;it velocitatis in B, quælibet partes <lb/>analogæ acceptæ per totam AC, duplæ &longs;int ad analo<lb/>gas per totam AB: atque ita, quin velocitas mobilis <lb/>de&longs;cendentis per AC &longs;it perpetuò dupla velocitatis <lb/>eiu&longs;dem mobilis de&longs;cendentis per AB. </s>

<s>Quod &longs;anè <lb/>adeò e&longs;t manife&longs;tum, vt neip&longs;e quidem negare id po<lb/>tueris, po&longs;tquàm ob&longs;erua&longs;ti comparatam primùm à <lb/>me lineam AC diui&longs;am in duodecim parteis cum <lb/>linea AC diui&longs;a in &longs;ex, tanquam cum &longs;eparata, exi&longs;ten<lb/>teque, intelligentiæ cau&longs;sâ DE, ac &longs;ubinde intellexi<lb/>&longs;ti e&longs;&longs;e omninò nece&longs;&longs;arium, vt idem mobile, &longs;i velo<lb/>eitatem in B, &longs;implam, in C verò duplam acquirat, <lb/>reperiatur &longs;imul in fine primæ, & in fine &longs;ecundæ <lb/>duodenarum partium; in fine tertiæ, & in fine &longs;extæ; <lb/>in fine &longs;extæ, & in fine duodecimæ; propter analogiam <lb/>&longs;implicium partium lineæ AB, & duplicium lineæ AC. <lb/>Ecquid-nam ergo iuris iam habes, vt perneges con&longs;e<lb/>quutionem? </s>

<s>Scilicet his verbis illud explicas, <emph type="italics"/>&longs;iue <lb/><gap/>im AB vt coniunctam toti AC con&longs;ideres, &longs;iue vt<emph.end type="italics"/><pb pagenum="121"/><emph type="italics"/>&longs;eparatam, qualis e&longs;t<emph.end type="italics"/> DE, <emph type="italics"/>&longs;emper velocitas de&longs;cen&longs;us per<emph.end type="italics"/><lb/>AC, <emph type="italics"/>quandiù percurritur prior eius pars<emph.end type="italics"/> AB, <emph type="italics"/>nec &longs;ui-ip&longs;ius, <lb/>nec velocitatis per<emph.end type="italics"/> DE <emph type="italics"/>dupla e&longs;t, vt falsò a&longs;&longs;umis, &longs;ed planè <lb/>eadem aut æqualis omninò e&longs;t.<emph.end type="italics"/></s>

<s>Hui tamen! &longs;iccine exactius, magi&longs;que <lb/><figure id="fig29"></figure><lb/>&longs;ufficienter mihi Paralogi&longs;mum iam de<lb/>tegis, & proptereáne ægrè fers te mihi <lb/>(<expan abbr="|c&utilde;">|cum</expan> intelligentem putares) indica&longs;&longs;e bre<lb/>uiùs ratiocinationis Galileanæ vitium? <lb/><emph type="italics"/>Semper,<emph.end type="italics"/> inquis, <emph type="italics"/>velocitas de&longs;cen&longs;us per<emph.end type="italics"/> AC, <lb/><emph type="italics"/>quandò percurritur prima eius pars<emph.end type="italics"/> AB, <emph type="italics"/>nec <lb/>&longs;ui ip&longs;ius, nec velocitatis per<emph.end type="italics"/> DE <emph type="italics"/>dupla e&longs;t.<emph.end type="italics"/><lb/>Enimverò, non quæritur, vtrum reipsâ dupla &longs;it, &longs;ed <lb/>an duplam e&longs;&longs;e tuo ex principio con&longs;equatur. </s>

<s>Nam <lb/>noui quidem ego fal&longs;um e&longs;&longs;e Con&longs;equens; &longs;ed verè ta<lb/>men con&longs;equi ex Antecedente, admi&longs;&longs;o o&longs;tendo. </s>

<s>Dicis <lb/><emph type="italics"/>me id falsò a&longs;&longs;umere;<emph.end type="italics"/> ego verò non falsò a&longs;&longs;umo, qui <lb/>ne a&longs;&longs;umo quidem, &longs;ed &longs;olum con&longs;equi demon&longs;tro, vt<lb/>cumque po&longs;tquàm id demon&longs;traui, &longs;ub&longs;umere deinde <lb/>po&longs;&longs;im, vt o&longs;tendam te tibi repugnare, quòd <expan abbr="c&utilde;">cum</expan> fatea<lb/>ris AC, & AB inæqualibus percurri temporibus, prin<lb/>cipium tamen id defendas, ex quo fateri &longs;imul cogaris <lb/>eodem, aut æquali tempore percurri. </s>

<s>Itaque cùm <lb/>heic non agatur de veritate Con&longs;equentis, &longs;ed de ne<lb/>ce&longs;&longs;itate, qua con&longs;equitur, ac tu deberes o&longs;tendere <lb/>nece&longs;&longs;ariò non con&longs;equi, & declarare in quo peceá<lb/>rim, inferendo fore velocitatem per totam AC du<lb/>plam velocitatis per totam AB, nihil aliud habes, <lb/><expan abbr="quã">quam</expan>, <emph type="italics"/>non e&longs;&longs;e duplam.<emph.end type="italics"/></s><s> Quod perinde e&longs;t, ac &longs;i te ponen<lb/>te illud Antecedens, <emph type="italics"/>Plato e&longs;t lapis,<emph.end type="italics"/> ego inferam i&longs;tud <pb pagenum="122"/>Con&longs;equens, igitur <emph type="italics"/>Plato &longs;en&longs;u caret:<emph.end type="italics"/> & te negante <lb/>con&longs;equutionem, illam ex eo probem, <emph type="italics"/>quòd lapis &longs;en&longs;u <lb/>careat:<emph.end type="italics"/> ac tum dicas Con&longs;equens <emph type="italics"/>non rectè inferri;<emph.end type="italics"/> & <lb/>compul&longs;us ad id probandum, nihil tamen aliud <lb/>quàm hoc dicas, <emph type="italics"/>Plato enim &longs;en&longs;u non caret, vt falsò, <lb/>a&longs;&longs;umis, &longs;ed planè &longs;en&longs;u præditus e&longs;t.<emph.end type="italics"/></s><s> Videlicet quæ&longs;tio <lb/>non erit de veritate Con&longs;equentis, nam ego quoque <lb/>Platonem &longs;en&longs;u carere fal&longs;um reputabo: &longs;ed de nece&longs;<lb/>&longs;itate con&longs;equutionis, quam tu infirmare deberes, ne <lb/>euerteret tuum Antecedens; neque ego falsò a&longs;&longs;u<lb/>mam, carere Platonem &longs;en&longs;u, qui ne a&longs;&longs;umam quidem: <lb/>&longs;ed nece&longs;&longs;ariò &longs;olummodò, & vt conclu&longs;ionem dedu<lb/>cam; tamet&longs;i <expan abbr="deduct&utilde;">deductum</expan> a&longs;&longs;umere po&longs;&longs;im, vt o&longs;tendam te <lb/>contradicere tibi ip&longs;i, tanquam coactum a&longs;&longs;erere Pla<lb/>tonem &longs;en&longs;u de&longs;titui, quem a&longs;&longs;eras præditum &longs;en&longs;u. </s>

<s>Pergis porrò, <emph type="italics"/><expan abbr="N&etilde;pe">Nempe</expan> volumus, & nece&longs;&longs;ariò exigimus (quod <lb/>ip&longs;a quoque rei natura po&longs;tulat) vt motus, qui per totam<emph.end type="italics"/><lb/>AC, <emph type="italics"/>& per partem<emph.end type="italics"/> AB, <emph type="italics"/>&longs;iue per æqualem<emph.end type="italics"/> DE, <emph type="italics"/>eadem <lb/>planè velocitate incipiat, & eadem velocitate progrediatur, <lb/>per totam<emph.end type="italics"/> AB, <emph type="italics"/>& per ip&longs;am<emph.end type="italics"/> DE, <emph type="italics"/>ex<emph.end type="italics"/> B <emph type="italics"/>verò ita velocitas <lb/>augeatur, vt tandem in<emph.end type="italics"/> C <emph type="italics"/>dupla inueniatur eius, quæ fuit in<emph.end type="italics"/><lb/>B, <emph type="italics"/>vel in<emph.end type="italics"/> E. At, optime Vir, quod vis quidem, & <lb/>exigis, vt <emph type="italics"/>c&oelig;ptus ex A motus,<emph.end type="italics"/> &longs;iue progre&longs;&longs;urus &longs;it v&longs;que <lb/>ad C, &longs;iue de&longs;iturus in B, <emph type="italics"/>eadem planè velocitate incipiat, <lb/>& progrediatur v&longs;que ad B,<emph.end type="italics"/> idip&longs;um e&longs;t, quod po&longs;tulat <lb/>ip&longs;a quoque rei natura (vtcumque po&longs;teà cau&longs;&longs;eris me <lb/>non in&longs;pexi&longs;&longs;e illam penitiùs.) Quod autem vis, & <lb/>exigis, vt velocitas ex B ita augeatur, vt tandem in <lb/>C dupla inueniatur eius, quæ fuit in B, idip&longs;um iam <lb/>e&longs;t, quod o&longs;ten&longs;um e&longs;t tantùm auer&longs;ari Naturam, <pb pagenum="123"/>quantùm auer&longs;atur motum in&longs;tantancum. </s>

<s>Quam<lb/>obrem, non &longs;ufficit tibi, vt velis, atque exigas velo<lb/>citat<gap/>m in C duplam e&longs;&longs;e velocitatis in B, &longs;ed re&longs;tat, <lb/>vt illud, &longs;i po&longs;lit, o&longs;tendas. </s>

<s>Quomodo verò id vnquam <lb/>po&longs;&longs;is, ni&longs;i volendo, & exigendo, vt quod quæritur, <lb/>tibi concedatur, atque adeò petendo, vt loquuntur, <lb/>principium? </s>

<s>Idip&longs;um e&longs;t, quod te feci&longs;&longs;e, circa relata <lb/>verba, obieci articulo XI. & quod tamen iam repetis <lb/>con&longs;tanter. </s>

<s>Quippe eò quoque te iam adegit, quem <lb/>exi&longs;tima&longs;ti te po&longs;&longs;e di&longs;tinguere priorem &longs;en&longs;um, à <lb/>po&longs;teriore valde diuer&longs;um. </s>

<s>Nam po&longs;tquàm dixi&longs;ti <lb/><expan abbr="e&utilde;">eum</expan> &longs;en&longs;um <emph type="italics"/>verum e&longs;&longs;e, ac nece&longs;&longs;arium,<emph.end type="italics"/> i&longs;thæc <lb/><figure id="fig30"></figure><lb/>verba tua &longs;equuntur, <emph type="italics"/>Si enim in triangulo <lb/>æqualia spatia de&longs;ignentur<emph.end type="italics"/> AD, DE, EF, <lb/><emph type="italics"/>&c. </s>

<s>& in<emph.end type="italics"/> D <emph type="italics"/>acqui&longs;itus &longs;upponatur vnus <lb/>gradus, & in<emph.end type="italics"/> E <emph type="italics"/>duo, & tres in<emph.end type="italics"/> F; <emph type="italics"/>manife<lb/>&longs;tum e&longs;t d<gap/>os gradus, ad quos acceleratio per<lb/>ueni&longs;&longs;e ponitur in<emph.end type="italics"/> E, <emph type="italics"/>e&longs;&longs;e ad vnum gradum <lb/>acqui&longs;itum in<emph.end type="italics"/> D, <emph type="italics"/>vt spatium<emph.end type="italics"/> AE, <emph type="italics"/>ad spa<lb/>tium. </s>

<s>AD.<emph.end type="italics"/></s><s> Deprehendere enim &longs;tatim <lb/>licet, quemadmodum idip&longs;um &longs;upponas, quod pror<lb/>sùs controuertitur: nempe in E e&longs;&longs;e duos gradus, vbi <lb/>vnus fuerit in D. </s>

<s>Ni&longs;i verò hoc e&longs;t; quid nam tandem <lb/>e&longs;t, quod dicunt petere principium? </s>

<s>Subinnueram <lb/>ego articulo eodem id mouere te, quòd velocitas ac<lb/>qui&longs;ita in C (re&longs;umendo nempelineam ABC) &longs;it re<lb/>uerâ maior, quàm acqui&longs;ita in B; &longs;ed tu attendere <lb/>nolui&longs;ti ex eo, quòd &longs;it maior, non &longs;equi tamen e&longs;&longs;e <lb/>duplam; ratus &longs;cilicet te penitiùs in&longs;pexi&longs;&longs;e rei natu<lb/>ram, ac eo principio &longs;emper abductus, de quo tota e&longs;t <pb pagenum="124"/>controuer&longs;ia; itemque opinione illa, quod in trian<lb/>gulo, lineæ ba&longs;i parallelæ repræ&longs;entare gradus veloci<lb/>tates valeant, &longs;i partes cruris alterutrius ip&longs;is re&longs;pon<lb/>dentes repræ&longs;entent &longs;patia; non aduertendo, quî i&longs;ti <lb/>gradus inæquales &longs;int, & à &longs;eip&longs;is differant, dum <lb/>acquiruntur, & dum manent; & quid incommodi ex <lb/>hac repræ&longs;entatione trahatur. </s>

<s>Videtur &longs;altem occa&longs;io <lb/>dubitandi fieri debui&longs;&longs;e, po&longs;tquàm admonitus à me, <lb/>fal&longs;um deprehendi&longs;ti id Experimentum, cui &longs;oli in<lb/>nixus, prounciâras velocitatem duplam e&longs;&longs;e ex du<lb/>pla altitudine; ac &longs;altem ob&longs;erua&longs;ti globum cadentem <lb/>ex A in C, hoc e&longs;t ex altitudine duarum <lb/><figure id="fig31"></figure><lb/>&longs;ui diametrorum, non eleuare cum oppo&longs;ita <lb/>lance duplum eius ponderis, quod eleuat ex <lb/>A in B, hoc e&longs;t ex altitudine vnius: &longs;ed res e&longs;t <lb/>po&longs;teà fu&longs;iùs dicenda. </s>

<s>Heic &longs;olùm moneo, <lb/>quod &longs;ubdis <emph type="italics"/>tuam, & communem aliorum &longs;uppo&longs;i<lb/>tionem e&longs;&longs;e primæ Propo&longs;itionis<emph.end type="italics"/> (&longs;eu &longs;uperioris A&longs;<lb/>&longs;umptionis) G<emph type="italics"/>alilei Antecedens,<emph.end type="italics"/> e&longs;&longs;e <expan abbr="illã">illam</expan> quidem <lb/>tuam, aliorumque &longs;uppo&longs;itionem, ip&longs;amque fal&longs;am, <lb/>ac impo&longs;&longs;ibilem; &longs;ed à Galileo tamen hypotheticè &longs;o<lb/>lùm v&longs;urpari, & Antecedens fieri, vt quid ex ea incom<lb/>modi nece&longs;&longs;ariò &longs;equatur, demon&longs;tret. </s>

<s>Vnde & <lb/>quod ais, <emph type="italics"/>ni&longs;i aduer&longs;us<emph.end type="italics"/> C<emph type="italics"/>himæras, & Tragelaphos depugnet,<emph.end type="italics"/><lb/>vides quonam &longs;en&longs;u accipiendum &longs;it; & quod &longs;upere&longs;t, <lb/>ip&longs;e iam agno&longs;cis, an eius rationem <emph type="italics"/>merum e&longs;&longs;e Paralo<lb/>gi&longs;mum<emph.end type="italics"/> probâris vllo argumento. </s>

<s><emph type="italics"/>Quòd &longs;i tamen præoccupatus contrariis decretis animus <lb/>tuus, <expan abbr="nond&utilde;">nondum</expan> clarißimam veritatis huius lucem plenè per&longs;picit, <lb/>ac penitùs agno&longs;cit,<emph.end type="italics"/> C<emph type="italics"/>oncipe in triangulo ABC partes lineæ<emph.end type="italics"/><pb pagenum="125"/><emph type="italics"/>AC non iam spatij parteis æqualeis de&longs;ignare, &longs;ed temporis. <lb/></s>

<s>Tunc ex tuis, & Galilei principijs facilè agno&longs;ces velocita<lb/>tem in E, hoc e&longs;t in fine &longs;ecundi temporis acqui&longs;itans, veloci<lb/>tat<gap/>s in D acqui&longs;itæ duplam e&longs;&longs;e, perpetuóque<emph.end type="italics"/><lb/><figure id="fig32"></figure><lb/><emph type="italics"/>velocitates, & tempora in eadem e&longs;&longs;e ratione. <lb/></s>

<s>Hoc autem con&longs;tituto, tuis ego, &<emph.end type="italics"/> G<emph type="italics"/>alilei <lb/>armis ita aduer&longs;um te in&longs;urgo.<emph.end type="italics"/></s>

<s>Et verò opperior. </s>

<s><emph type="italics"/>Si velocitatis incrementa tempori bus æqua<lb/>libus acqui&longs;ita eam inter &longs;e rationem ob&longs;erua<lb/>rent, quam tempora, nece&longs;&longs;ariò ip&longs;æ quoque <lb/>velocitates perpetuò e&longs;&longs;ent inter &longs;e, vt tempora, <lb/>e&longs;&longs;etque, exempli gratiâ, velocitas duobus temporibus æquali<lb/>bus acqui&longs;ita velocitatis primo tempore acqui&longs;itæ dupla.<emph.end type="italics"/></s>

<s>Scilicet i&longs;ta tibi e&longs;t hypothetica Propo&longs;itio. </s>

<s>A&longs;&longs;um<lb/>tio &longs;equitur. </s>

<s><emph type="italics"/>At quoties velocitas quælibet alterius e&longs;t dupla, nece&longs;&longs;e e&longs;t, <lb/>vt eodem, aut æquali tempore à velocitate dupla &longs;patium <lb/>decurratur duplum eius, quod percurritur à velocitate &longs;ubdu<lb/>pla.<emph.end type="italics"/></s>

<s>Conclu&longs;ionem &longs;ubtices; nam quod &longs;equitur e&longs;t <lb/>qua&longs;i Sub&longs;umptum. </s>

<s>Quæ&longs;o te verò, ecquam nam <lb/>po&longs;&longs;es exinde deducere, con&longs;tante Syllogi&longs;mo ex ter<lb/>minis quatuor; neque tertio termino, vt decuit in hy<lb/>pothe&longs;i, vnà cum Propo&longs;itionis aut antecedente, aut <lb/>con&longs;equente a&longs;&longs;umpto. </s>

<s>Huiu&longs;modi enim videtur <lb/>fui&longs;&longs;e debere A&longs;&longs;umptio. </s>

<s><emph type="italics"/>At quoties velocitas quælibet est alterius dupla, velocita<lb/>tis incrementa temporibus æqualibus acqui&longs;ita eam inter &longs;e <lb/>rationem ob&longs;eruant, quam tempora.<emph.end type="italics"/></s><pb pagenum="126"/>

<s>Ac tum Conclu&longs;io fui&longs;&longs;et. </s>

<s><emph type="italics"/>Igitur &longs;i velocitas quælibet e&longs;&longs;et alterius dupla, nece&longs;&longs;ariò <lb/>ip&longs;æ quóque velocitates perpetuò e&longs;&longs;ent inter &longs;e, vt tempora, <lb/>e&longs;&longs;etque, exempli gratiâ, velocitas duobus temporibus acqui&longs;i<lb/>ta velocitatis primo tempore acqui&longs;itæ dupla.<emph.end type="italics"/></s>

<s>Agno&longs;cis autem ecquid nam aduer&longs;um me heinc <lb/>concludatur. </s>

<s>Sed de A&longs;&longs;umptione tamen tua, <expan abbr="tanquã">tanquam</expan> <lb/>habenda e&longs;&longs;et legitima, vt dicam, ea, vt po&longs;&longs;it quadam<lb/>tenus cum propo&longs;itione cohærere, nece&longs;&longs;e e&longs;t ita &longs;up<lb/>pleatur. </s>

<s><emph type="italics"/>Quoties velocitas quælibet<emph.end type="italics"/> duobus temporibus acqui<lb/>&longs;ita <emph type="italics"/>alterius<emph.end type="italics"/> primo tempore acqui&longs;itæ <emph type="italics"/>est dupla; nece&longs;&longs;e <lb/>e&longs;t, vt eodem, aut æquali tempore<emph.end type="italics"/> (hoc e&longs;t aggregato duo<lb/>rum temporum) <emph type="italics"/>à velocitate dupla &longs;patium decurratur du<lb/>plum eius, quod percurritur<emph.end type="italics"/> (tempore n<gap/>mpe vno, &longs;eu pri<lb/>mo) <emph type="italics"/>à velocitate &longs;ubdupla.<emph.end type="italics"/></s>

<s>Tunc autem addo e&longs;&longs;e nece&longs;&longs;e, vt percurratur &longs;pa<lb/>tium non modo duplum, &longs;ed & quadruplum primi: &longs;i <lb/>velocitas quidem acqui&longs;ita æquabiliter fuerit (qualis <lb/>illa e&longs;t, qua de agimus) quatenus dum &longs;ecundus veloci<lb/>tatis gradus tempore &longs;ecundo acquiritur, & per ip&longs;um <lb/>par &longs;patium illi, quod decur&longs;um fuit tempore primo, <lb/>percurritur, percurruntur &longs;imùl duo alia per gradum <lb/>velocitatis primo tempore acqui&longs;itum, ac in vigore <lb/>per&longs;euerantem, veluti iam antè declaratum e&longs;t. </s>

<s>Sed <lb/>ecce Sub&longs;umis. </s>

<s><emph type="italics"/>Si igitur primo tempore AD, spatium PM percurra<lb/>tur à velocitate &longs;ubdupla primo illo toto tempore acqui&longs;ita, <lb/>eodem tempore &longs;imul percurretur &longs;patium PN &longs;patii PM <lb/>duplum à velocitate dupla toto tempore AE acqui&longs;ita.<emph.end type="italics"/></s><pb pagenum="127"/>

<s>Cùm <emph type="italics"/>dicis eodem tempore,<emph.end type="italics"/> hoc e&longs;t <emph type="italics"/>primo,<emph.end type="italics"/> vnde quæ&longs;o <lb/>a&longs;&longs;umis? </s>

<s>Nam in A&longs;&longs;umptione quidem non <lb/><figure id="fig33"></figure><lb/>di&longs;tinxeras v<gap/>rius velocitatis re&longs;pectu idem, <lb/>aut æquale acciperes, & procliue fuit, vt <lb/>acciperes re&longs;pectu duplæ, cui re&longs;ponderent <lb/>duo tempora, &longs;iue, vt expre&longs;&longs;i, aggregatum <lb/>temporum duorum, vnde & &longs;ub&longs;umendum <lb/>fuit. </s>

<s><emph type="italics"/>Si primo tempore AD, &longs;patium PM per<lb/>curratur à velocitate &longs;ubdupla, futurum vt toto <lb/>tempore AE<emph.end type="italics"/> (&longs;iue duobus temporibus, aut aggregato <lb/>duorum) <emph type="italics"/>percurratur spatium PN &longs;patij PM duplum.<emph.end type="italics"/></s>

<s>Quo ca&longs;u rursùs addo futurum, vt non modò du<lb/>plum, &longs;ed etiam quadruplum percurratur. </s>

<s><emph type="italics"/>Sicque eodem tempore ab eodem mobili percurretur totum <lb/>spatium PN, & eius dimidium PM, quod e&longs;t impoßibile, <lb/>ni&longs;i motus fieret in in&longs;tanti.<emph.end type="italics"/></s>

<s><emph type="italics"/>Eodem,<emph.end type="italics"/> hoc e&longs;t, <emph type="italics"/>primo,<emph.end type="italics"/> nullatenus &longs;equitur; <emph type="italics"/>eodem,<emph.end type="italics"/> id <lb/>e&longs;t, <emph type="italics"/>aggregato<emph.end type="italics"/> duorum, ita vt totum &longs;patium PN per<lb/>curratur duobus, & dimidium PM illorum primo, &longs;e<lb/>quitur quidem, &longs;ed addendum, percurri in&longs;uper alia <lb/>duo &longs;patia: quæ duo aliis iuncta, motu, qui fiat &longs;uc<lb/>ce&longs;&longs;iue, non in <expan abbr="in&longs;tãti">in&longs;tanti</expan>, percurrantur. </s>

<s>Enimverò, vt Sub<lb/>&longs;umptum tuo &longs;en&longs;u probes, & te perinde, atque me, <lb/>mutatis &longs;o ùm terminis, ratiocinari planum facias, hi&longs;<lb/>ce verbis pro&longs;equeris. </s>

<s><emph type="italics"/>Nam, vt modo ratiocinandi tuo etiam vtar, &longs;umpto quo<lb/>piam alio &longs;patio<emph.end type="italics"/> RO, <emph type="italics"/>spatio<emph.end type="italics"/> PM <emph type="italics"/>æquali; concipiantur duo <lb/>mobilia, quorum vnum per<emph.end type="italics"/> PN <emph type="italics"/>eodem momento moueri in<lb/>cipiat velocitate dupla, quo alterum per<emph.end type="italics"/> RO <emph type="italics"/>de&longs;cendit velo-<emph.end type="italics"/><pb pagenum="128"/><emph type="italics"/>citate &longs;ubdupla: tum nece&longs;&longs;e fuerit, vt quibu&longs;libet temporis <lb/>momentis continuò partes spatii<emph.end type="italics"/> PM <emph type="italics"/>duplo maiores percur<lb/>rantur, quàm &longs;int partes &longs;patii<emph.end type="italics"/> RO, <emph type="italics"/>quæ ab alio mobili ii&longs;<lb/>dem momentis &longs;ubdupla velocitate decurruntur. </s>

<s>Quo igi<lb/>tur tempore mobile lentius &longs;patium<emph.end type="italics"/> RO <emph type="italics"/>totum percurrerit, <lb/>eodem alterum mobile duplò velocius &longs;patium<emph.end type="italics"/> PN <emph type="italics"/>etiam <lb/>ab&longs;oluerit. </s>

<s>Et quoniam, te iudice, alia ratio non e&longs;t, &longs;iue spa<lb/>tium<emph.end type="italics"/> RO, <emph type="italics"/>aut<emph.end type="italics"/> PM, <emph type="italics"/>à toto &longs;patio<emph.end type="italics"/> PN <emph type="italics"/>&longs;eiunctum, &longs;iue ei<lb/>dem coniunctum &longs;upponatur, nece&longs;&longs;arium planè fuerit, vt <lb/>etiam ab vno, eodemque mobili, vno, eodemque tempore to<lb/>tum spatium<emph.end type="italics"/> PN, <emph type="italics"/>& eius dimidium<emph.end type="italics"/> PM <emph type="italics"/>percurratur; <lb/>quod certum est e&longs;&longs;e impoßibile, ni&longs;i motus fieret in in&longs;tanti. <lb/></s>

<s>Hæc ratiocinatio, variatis tantum terminis, de quibus contro<lb/>uer&longs;ia e&longs;t, tota (vt vides) tua est.<emph.end type="italics"/></s>

<s>Imò, non tantum meam agno&longs;co, &longs;ed inuariatis <lb/>etiam terminis, & qualem omninò aduer&longs;um te dedu<lb/>xi, agno&longs;co; adeò vt mirer ip&longs;um te, illam aduer&longs;um <lb/>te comparatam, non variatis terminis retorquere in <lb/>me, &longs;ed mutato nomine, v&longs;urpare aduer&longs;us teip&longs;um. <lb/></s>

<s>Nam, vt mutares terminos, de quibus, vt ais, contro. <lb/></s>

<s>uer&longs;ia e&longs;t, debueras idip&longs;um, quod ego ratiocinando <lb/>habui pro <emph type="italics"/>Spatio,<emph.end type="italics"/> habere pro <emph type="italics"/>Tempore,<emph.end type="italics"/> quod pro <emph type="italics"/>Tempo<lb/>re,<emph.end type="italics"/> habere pro <emph type="italics"/>Spatio,<emph.end type="italics"/> cùm alterum alter arguamus, <lb/>quòd velocitas exæquetur à me quidem <emph type="italics"/>Tempori,<emph.end type="italics"/> à te <lb/>verò <emph type="italics"/>Spatio.<emph.end type="italics"/></s><s> Sic autem accepta linea PM pro tempo<lb/>re AD, & PN pro tempore AB, pro&longs;equi potu<gap/>es <lb/>hoc modo. </s>

<s><emph type="italics"/>Nam vt modo ratiocinandi tuo etiam vtar, &longs;umpto quo<lb/>piam alio tempore<emph.end type="italics"/> RO, <emph type="italics"/>tempori<emph.end type="italics"/> PM <emph type="italics"/>æquali, con<gap/>mus <lb/>duo mobilia, quorum vnum per<emph.end type="italics"/> PN <emph type="italics"/>eodem &longs;patio moueri<emph.end type="italics"/><pb pagenum="129"/><emph type="italics"/>incipiat velocitate dupla, quo alterum per<emph.end type="italics"/> RO <emph type="italics"/>de&longs;cendit <lb/>velocitate &longs;ubdupla; tum nece&longs;&longs;e fuerit, vt quibu&longs;libet &longs;pa<lb/>tij partibus continuò momenta temporis<emph.end type="italics"/> PM <emph type="italics"/>duplò matora <lb/>percurrantur, quam &longs;int momenta temporis<emph.end type="italics"/> RO, <emph type="italics"/>quæ ab <lb/>aliò mobili ii&longs;dem partibus &longs;ubdupla velocitate decurruntur. <lb/></s>

<s>Quo igitur spatio mobile lentius tempus<emph.end type="italics"/> RO <lb/><figure id="fig34"></figure><lb/><emph type="italics"/>totum percurrerit, eodem alterum mobile duplò <lb/>velocius tempus<emph.end type="italics"/> PN <emph type="italics"/>etiam ab&longs;oluerit. </s>

<s>Et quo<lb/>niam te iudice alia ratio non est, &longs;iue tempus<emph.end type="italics"/><lb/>RO, <emph type="italics"/>aut<emph.end type="italics"/> PM <emph type="italics"/>à toto tempore<emph.end type="italics"/> PN <emph type="italics"/>&longs;eiunctum, <lb/>&longs;iue eidem coniunctum &longs;upponatur: nece&longs;&longs;arium <lb/>planè fuerit, vt etiam ab vno, eodemque mobili, <lb/>vno eodemque &longs;patio totum tempus<emph.end type="italics"/> PN, <emph type="italics"/>& <lb/>eius dimidium<emph.end type="italics"/> PM <emph type="italics"/>percurratur, quod certum <lb/>e&longs;t e&longs;&longs;e impoßibile, ni&longs;i motus fieret in puncto.<emph.end type="italics"/></s>

<s>Hoc &longs;anè modo fui&longs;&longs;es ratiocinatus <emph type="italics"/>variatis tan<lb/>tum terminis,<emph.end type="italics"/> ac facere mihi quandam re&longs;pondendi ne<lb/>ce&longs;&longs;itatem vi&longs;us fui&longs;&longs;es. </s>

<s>Nunc autem, cùm terminos <lb/>controuer&longs;os non varies, ac nihil concludas aduer&longs;um <lb/>me, &longs;ed illud omninò, atque eodem modo, quod e&longs;t <lb/>aduer&longs;us te conclu&longs;um: e&longs;t planè cur mirer &longs;ic captare <lb/>te ex teip&longs;o triumphum. </s>

<s>Nam & cum alioquin ita <lb/>habes. </s>

<s><emph type="italics"/>Hæc ratiocinatio, variatis tantum terminis de quibus <lb/>controuer&longs;ia e&longs;t, tota, vt vides, tua e&longs;t; quam &longs;i vt legitimam <lb/>admittis, tuis ip&longs;e plagis conclu&longs;us es: &longs;in autem reiicis, & ab<lb/>&longs;urdamagno&longs;cis, non rectè facis, dum nullo modo dißimilem, <lb/>tanquam demon&longs;trationem defendis, & hanc eius loco tibi <lb/>repo&longs;itam Paralogi&longs;mum iam e&longs;&longs;e, & non ni&longs;i eadem diftin<lb/>ctione di&longs;&longs;ol<gap/>dum fateri teneris.<emph.end type="italics"/></s><pb pagenum="130"/>

<s>Cùm, inquam, &longs;ic habes, per&longs;picis omninò, quo <lb/>iure me dicas iis plagis conclu&longs;um, quibus tu potiùs à <lb/>me irretitus teip&longs;um implicueris magis: aut-quàm <lb/>meritò Paralogi&longs;mum cen&longs;eas, quod ratiocinium priùs <lb/>probâris, & nunc tanti putaueris, vt tuum inde ratio<lb/>cinum duxeris e&longs;&longs;e confirmandum. </s>

<s>Et pergis qui<lb/>dem, </s>

<s><emph type="italics"/>Nempe aliud e&longs;t æqualibus &longs;iue spatiis, &longs;iue temporibus <lb/>æqualia velocitatis augmenta acquiri, eaque eandem inter &longs;e <lb/>rationem &longs;eruare, quam æqualia&longs;iue spatia, &longs;iue tempora ob<lb/>&longs;eruant; & aliud velocitates ip&longs;as integras &longs;ecundum &longs;e totas, <lb/>& &longs;ingulas earum parteis analogas ab initio ad finem totius <lb/>motus inter &longs;e comparatas, in eadem e&longs;&longs;e ratione, quæ inter <lb/>æqualia &longs;iue tempora, &longs;iue spatia emen&longs;a reperiatur. </s>

<s>Pri<lb/>mum illud verum e&longs;&longs;e nihil repugnat, at &longs;ecundum istud fal<lb/>&longs;um, & impoßibile est; quod &longs;i rectè<emph.end type="italics"/> G<emph type="italics"/>alileus aduerti&longs;&longs;et, <lb/>Paralogi&longs;mum nobis pro demon&longs;tratione non obtru&longs;i&longs;&longs;et.<emph.end type="italics"/></s>

<s>Verumtamen, ne confunde quæ&longs;o tempora cum <lb/>&longs;patiis; cum ais aliud e&longs;&longs;e <emph type="italics"/>æqualibus &longs;iue &longs;patiis, &longs;iue tem<lb/>poribus, &c.<emph.end type="italics"/></s><s> Siquidem & facta ratiocinatione nihil <lb/>conclu&longs;i&longs;ti contra tempora, vt te puta&longs;ti concludere; <lb/>&longs;ed &longs;olùm contra &longs;patia, quatenus à me fuerant impe<lb/>tita: & tempora aliunde cum velocitatibus comparata <lb/>nullam agno&longs;cunt di&longs;tinctionem, qualem te putas in<lb/>uehere: cùm & totæ velocitates, & ip&longs;arum partes, &longs;eu <lb/>augmenta eandem &longs;emper proportionem cum tempo<lb/>ribus, partibu&longs;que corum analogis &longs;eruent. </s>

<s>Quin<lb/>etiam, quod &longs;pectat ad &longs;patia, declaratum iam e&longs;t, <lb/>quàm irrito conamine &longs;ic di&longs;tinguas, quatenus de mo<lb/>tu non quomodocumque, &longs;ed æquabiliter accelerato <pb pagenum="131"/>agitur; &longs;tupendumque e&longs;t, te in eo hærere, quòd Gali<lb/>leus non aduerterit fal&longs;um, ac impo&longs;&longs;ibile e&longs;&longs;e, quod <lb/>&longs;ecundum ais, hoc e&longs;t, <emph type="italics"/>velocitates ip&longs;as integras, &c.<emph.end type="italics"/> &longs;i<lb/>quidem i&longs;tud e&longs;&longs;e fal&longs;um, impo&longs;&longs;ibileque non modò <lb/>aduertit, &longs;ed etiam o&longs;tendit, quod tu recu&longs;as aduertere, <lb/>con&longs;equi ex ea, quam tu &longs;equeris, opinione. </s>

<s>Recu&longs;as, <lb/>inquam, & ita habes, qua&longs;i idip&longs;um pro principio vero, <lb/>atque nece&longs;&longs;ario à &longs;e credito v&longs;urpauerit; ac interim <lb/>fui&longs;&longs;e ab eo Paralogi&longs;mum obtru&longs;um ais, quem nuilla<lb/>tenus o&longs;tendi&longs;ti, & prof<gap/>&longs;&longs;us o&longs;tendere, incidi&longs;ti ip&longs;e in <lb/>Paralogi&longs;mum. </s>

<s><emph type="italics"/>Sed aliam quoque Propo&longs;itionem, optime<emph.end type="italics"/> G<emph type="italics"/>a&longs;&longs;ende, non <lb/>minùs fal&longs;am, atque impoßibilem numero xi. </s>

<s>in fine mihi af<lb/>fingis; dum ais m<gap/>ad vulgatam motus accelerati definitionem <lb/>con&longs;equenter loquentem, velle in de&longs;cen&longs;u per totum spatium <lb/>AC bifariam diui&longs;um in B, partem BC tran&longs;curri<emph.end type="italics"/><lb/><figure id="fig35"></figure><lb/><emph type="italics"/>in dimidio eius temporis, quo percurritur AB; ex <lb/>qua fal&longs;a &longs;uppo&longs;itione, &longs;equenti numero vnum In<lb/>commodum, & ad finem Respon&longs;ionis tuæ alia plura <lb/>longè ab&longs;urdißima deducis, quæ tanquam con&longs;ectaria <lb/>ex meis principiis, ac decretis nece&longs;&longs;ariò illata mihi <lb/>obiectas.<emph.end type="italics"/> V<emph type="italics"/>team igitur Propo&longs;itionem &longs;emel tracte<lb/>mus, eius examen in commodiorem locum re&longs;erua<lb/>bimus.<emph.end type="italics"/></s>

<s>Cùm tu Caput magni momenti per&longs;tringas adeò <lb/>obiter; non po&longs;&longs;um ego non &longs;altem duo, aut tria quæ<lb/>dam adnotare. </s>

<s>Quî enim Imprimis intactum præ<lb/>teream, quod <emph type="italics"/>me affingere tibi<emph.end type="italics"/> ais <emph type="italics"/>Propo&longs;itionem fal&longs;am; <lb/>ac impo&longs;ßibilem, dum aio te ad vulgatam motus definitionem <lb/>con&longs;equenter loquentem, velle in de&longs;cen&longs;u per totum &longs;patium<emph.end type="italics"/><pb pagenum="132"/><emph type="italics"/>A<emph.end type="italics"/>C, <emph type="italics"/>bifariam diui&longs;um in B, partem BC tran&longs;curri <gap/><lb/>dimidio eius temporis, quo percurritur AB?<emph.end type="italics"/> Etenim, quæ<lb/>&longs;o tuam fidem, an tua, an alterius fuerint, quæ &longs;unt iam <lb/>&longs;uperiùs verba recitata? </s>

<s>Su&longs;ceperas ip&longs;e o<gap/>tendendum <lb/>in illa Galilei A&longs;&longs;umptione Paralogi&longs;mum, & præmi<lb/>&longs;eras, <emph type="italics"/>non vno modo tantum, &longs;ed pluribus intelligi po&longs;&longs;e, <lb/>quomodo velocitates &longs;int inter &longs;e, vt emen&longs;a spatia; licet <lb/>eadem spatia, neque eodem, neque æquali tempore percur<lb/>rantur:<emph.end type="italics"/> ac tum deligens modum vnum, qui præ cæte<lb/>ris id præ&longs;taret, atque idcircò <gap/>&longs;&longs;umptionem Paralo<lb/>gi&longs;mi conuinceret, i&longs;thæc met &longs;ub<gap/>eci&longs;ti verba, <emph type="italics"/>Vt <gap/><lb/>graue de&longs;cendens per AB, tempus quodcumque in&longs;umat, putà <lb/>quadrantem; ac deinde BC ip&longs;i AB æquale dimidio qua<lb/>drante percurrat; quis neget in<emph.end type="italics"/> C <emph type="italics"/>duplam haberi velocita<lb/>tem eius, quæ fuit in B? </s>

<s>Et tamen idem graue totam AC, <lb/>& dimidium eius AB eodem tempore non percurreret.<emph.end type="italics"/><lb/>Subinde autem qua&longs;i re ab&longs;olutè cófecta pro&longs;equutus <lb/>es, <emph type="italics"/>A&longs;&longs;umptio igitur Galilei fal&longs;a e&longs;t, & totæ eius ratiocinatio <lb/>merus Paralogi&longs;mus.<emph.end type="italics"/></s><s> Quæ&longs;o ergo te, quid tibi affinxi? <lb/></s>

<s>Agno&longs;cis tua verba, an non? <emph type="italics"/>Propo&longs;itionem,<emph.end type="italics"/> inquis, <emph type="italics"/>fal<lb/>&longs;am, ac impoßibilem?<emph.end type="italics"/> E&longs;to verò, illam iam fal&longs;am, ac <lb/>impo&longs;&longs;ibilem agno&longs;eas; at tunc &longs;altem veram, atque <lb/>nece&longs;&longs;ariam habui&longs;ti, cùm illa &longs;ola v&longs;us fueris ad o&longs;ten<lb/>dendum Paralogi&longs;mum. </s>

<s>Nam &longs;i fal&longs;am quidem tunc <lb/>quoque, ac impo&longs;&longs;ibilem habui&longs;ti, quomodo proba&longs;ti <lb/>id, quod intend<gap/>ti? </s>

<s>Et, &longs;i &longs;en&longs;i&longs;ti po&longs;&longs;e eam tibi, tan<lb/>quam fal&longs;am, ac impo&longs;&longs;ibilem negari, quanam proui<lb/>dentia ip&longs;am communi<gap/>&longs;ti? </s>

<s>An o&longs;ten&longs;urus Paralogi&longs;<lb/>mum, volui&longs;ti &longs;ponte te exhibere paralogi&longs;tam ridi<lb/>culum, vt puta non alio principio, quam fal&longs;o, atque <pb pagenum="133"/>impo&longs;&longs;ibili vtcns, & quo pernegato, nudus, ac iner<lb/>ms, cùm te tamen tantopere o&longs;tenta&longs;&longs;es, reperireris<gap/><lb/>Sed qualemcumque habueris: &longs;altem ego &longs;um bona fi<lb/>de v&longs;us, neque affinxi quicquam tibi; cùm non aliam <lb/>tibi Propo&longs;itionem tribuerm, ni&longs;i, quam tu ip&longs;e pro <lb/>principio ad conuincendum Galileum v&longs;urpaueris, <lb/>quamque iam etiam fal&longs;am, impo&longs;&longs;ibilemque dicere <lb/>non po&longs;&longs;is, quin arguas te nihil confeci&longs;&longs;e, &longs;ed ope<lb/>ram planè lu&longs;i&longs;&longs;e, in Galileum cùm in&longs;ulta&longs;ti: ac per<lb/>peram fui&longs;&longs;e glortatum its verbis, <emph type="italics"/>A&longs;&longs;umptio igitur Ga<lb/>lilei fal&longs;a e&longs;t, & tota eius ratiocinatio merus Paralogi&longs;mus.<emph.end type="italics"/><lb/>An dices Propo&longs;itionem fui&longs;&longs;e conditionalem? </s>

<s>Si di<lb/>cas, eadem e&longs;t ruina. </s>

<s>Siquidem facta conditionis ap<lb/>po&longs;itione, &longs;uppo&longs;itio aut vera tibi, ac nece&longs;&longs;aria, aut <lb/>fal&longs;a, ac impo&longs;&longs;ibilis fuit. </s>

<s>Si prius, vides contradictio<lb/>nem, qua fal&longs;am iam, ac impo&longs;&longs;ibilem agno&longs;cis; &longs;i po<lb/>&longs;teriùs, vides ludibrium, cui te fui&longs;ti expo&longs;iturus. </s>

<s>An <lb/>dices te po&longs;teà cen&longs;ui&longs;&longs;e difficile determinatu e&longs;&longs;e, <lb/>quod tempus per primam, quod per &longs;ecundam de&longs;<lb/>cen&longs;us partem in&longs;umatur; ac ideò c&oelig;ni&longs;&longs;e compara<lb/>tionem non ab v&longs;que initio, &longs;ed ab ip&longs;o &longs;olùm me<lb/>dio primæ partis? </s>

<s>Si dicas, declaras te quidem &longs;ubdu<lb/>bita&longs;&longs;e po&longs;tmodùm, an hoc fortè principium non e&longs;&longs;et <lb/>verum, nece&longs;&longs;ariumque: &longs;ed concedendum e&longs;t inte<lb/>rim, te, cùm ip&longs;um heic v&longs;urpa&longs;ti, aut non habui&longs;&longs;e ip<lb/>&longs;um fal&longs;um, ac impo&longs;&longs;ibile; aut vltrò voluiffe exhibere <lb/>te Sophi&longs;ten planè ex&longs;ibilandum: quod ab&longs;it tamen vt <lb/>cen&longs;eam. </s>

<s>Vtcumque &longs;it, &longs;altem ego nihil affinxi. </s>

<s>De<lb/>inde, quod dixerim <emph type="italics"/>te fui&longs;&longs;e con&longs;equenter ad definitionem <lb/>vulgatem loq<gap/>tum,<emph.end type="italics"/> nihil &longs;anè; affinxi; cùm nece&longs;&longs;e <pb pagenum="134"/>omninò &longs;it, v<gap/> velocitatibus, ac &longs;pati<gap/>s eadem &longs;e ratio<lb/>ne habentibus, vbicumque a&longs;&longs;umpto æquali &longs;patio <lb/>v<gap/>itas <gap/>&longs;t dupla, ibi &longs;it præc sè temporis dimidium; <lb/>& plan<gap/> proinde &longs;equatur, vt a&longs;&longs;umpta linea BC æqua<lb/><gap/>p&longs;i A<gap/> cum velocitate decur&longs;us dupla, &longs;i AB qui<lb/>dem depu<gap/> certo tempore, vt quadrante horæ, ip&longs;a <lb/>BC percurratur octante, &longs;eu dimidio quadrantis. </s>

<s>Po<lb/><gap/> conqueteris <emph type="italics"/>me ex hac fal&longs;a &longs;uppo&longs;itione <lb/>deducere <gap/> &longs;equente vnum <gap/>ncommodum<emph.end type="italics"/> (vt putà da<lb/>to <gap/> &longs;emel fuerit pars AB, tempus <lb/><gap/> nulla mtione po&longs;&longs;e, ni&longs;i fu<lb/><gap/> <emph type="italics"/>ac<gap/>ad: finem Respon&longs;ionis <lb/><gap/> long <gap/> qu<gap/> tanquam con&longs;ectaria ex tuis <lb/>principiis, ac decretis <gap/>&longs;&longs;ariò illata tibi obiectem:<emph.end type="italics"/> verum <lb/><gap/> quamobrem tanti momenti <lb/><gap/> pr<gap/>uolandum, præter<lb/><gap/>bendo <gap/>, præ<gap/> retractandi ip&longs;um, &longs;eu attin<lb/>gendi vel deuiter, ob examen propo&longs;itionis re&longs;erua<lb/>tum in commodiore<gap/> locum. </s>

<s>Sed vtcumque &longs;it, re<lb/>puta<gap/>e: non potes, abunde e&longs;&longs;e, quòd propo&longs;itionem, <lb/>exiqua <gap/> iam, ac impo&longs;&longs;ibilem <lb/>ha<gap/>as; c<gap/>m & ob&longs;tent quæ mox obieci de impugna<lb/>to Paralogi&longs;mo, & comperiaris non &longs;atisfeci&longs;&longs;e, cùm <lb/><gap/>em. </s>

<s>In ommodum ite<gap/> obieci articulo xlij. </s>

<s>tan<lb/>quam con&longs;equens ex tuo decreto cum hac propo&longs;i<lb/>tione congruo, de &longs;patiis emen&longs;is, temporibus æqua<lb/>libus, in ratione continuò dupla. </s>

<s>Priu&longs;quam hæc de Paralogi&longs;mo, quem Galileo ob<lb/>ieci&longs;ti, dimi<gap/>am, memini&longs;&longs;e iuuatobie ci&longs;&longs;e me tibi arti<lb/>culis XXXVI, & XXXVIII. fui&longs;&longs;e tenon &longs;ecus ratiocina-<pb pagenum="135"/>tum, quàm Galileum: atque idcircò &longs;i ille quidem Pa<lb/>ralogi&longs;mum admi&longs;erit, incidi&longs;&longs;e te, recidi&longs;&longs;eque <lb/><figure id="fig36"></figure><lb/>in cundem: ac o&longs;tendere vel ex ea &longs;ola ratiocina<lb/>tione tua, quæ relata e&longs;t articulo XXXIII. quemad<lb/>modum ex tuis principiis demon&longs;trare liceat, <emph type="italics"/>&longs;i <lb/>velocitates &longs;icut &longs;patia &longs;int,<emph.end type="italics"/> fore <emph type="italics"/>vt totum, & pars <lb/>eodem, aut æquali tempore percurrantur.<emph.end type="italics"/> A&longs;&longs;umptâ <lb/>ergo, quæ illeic, lineâ, ideò probas <emph type="italics"/>&longs;patium<emph.end type="italics"/> DE, <lb/><emph type="italics"/>eodem tempore tran&longs;curri, quo<emph.end type="italics"/> SD; quia <emph type="italics"/>cùm<emph.end type="italics"/> AD <lb/><emph type="italics"/>dupla &longs;it ip&longs;ius<emph.end type="italics"/> AS, <emph type="italics"/>&<emph.end type="italics"/> AE <emph type="italics"/>ip&longs;ius<emph.end type="italics"/> AD, <emph type="italics"/>nece&longs;&longs;e &longs;it ve<lb/>locitatem in<emph.end type="italics"/> D <emph type="italics"/>duplam e&longs;&longs;e velocitatis in<emph.end type="italics"/> S, <emph type="italics"/>& veloci<lb/>tatem in<emph.end type="italics"/> E <emph type="italics"/>velocitatis in<emph.end type="italics"/> D. </s>

<s>Cùm & aliunde, <emph type="italics"/>velo<lb/>citas per totam<emph.end type="italics"/> DE <emph type="italics"/>dupla &longs;it velocitatis per totam<emph.end type="italics"/><lb/>SD; quatenus <emph type="italics"/>quodlibet &longs;patium inc&oelig;ptum ab<emph.end type="italics"/> A, <lb/><emph type="italics"/>& terminatum inter<emph.end type="italics"/> D, <emph type="italics"/>&<emph.end type="italics"/> E, <emph type="italics"/>duplum e&longs;t alterius <lb/>&longs;patii, quod &longs;it item inc&oelig;ptum ab<emph.end type="italics"/> A, <emph type="italics"/>& terminatum <lb/>inter<emph.end type="italics"/> S, <emph type="italics"/>&<emph.end type="italics"/> D; Dico aut te inde nihil conclude<lb/>re, aut &longs;ic licere argumentari. </s>

<s><emph type="italics"/>Si<emph.end type="italics"/> DE, <emph type="italics"/>&<emph.end type="italics"/> SD, <emph type="italics"/>eodem tempore percurruntur, quia veloci<lb/>tas à<emph.end type="italics"/> D <emph type="italics"/>in<emph.end type="italics"/> E, <emph type="italics"/>dupla e&longs;t velocitatis ab<emph.end type="italics"/> S <emph type="italics"/>in<emph.end type="italics"/> D. </s>

<s>Igitur, <emph type="italics"/>AD, & A<emph.end type="italics"/>S, <emph type="italics"/>eodem tempore percurrentur, quia <lb/>velocitas, ab A in D dupla e&longs;t velocitatis ab A in<emph.end type="italics"/> S. </s>

<s>Et &longs;imiliter, <emph type="italics"/>AE, & AD eodem tempore percurrentur; <lb/>quia velocitas ab<emph.end type="italics"/> A <emph type="italics"/>in<emph.end type="italics"/> E, <emph type="italics"/>dupla e&longs;t velocitatis ab<emph.end type="italics"/> A <emph type="italics"/>in<emph.end type="italics"/> D. </s>

<s>Ac rur&longs;us, quia vt velocitas per totam DE dupla <lb/>e&longs;t velocitatis per totam SD, ita velocitas per totam <lb/>SD debet e&longs;&longs;e dupla velocitatis per totam PS, & ve<lb/>locitas per totam PS, velocitatis per aliud vlterius di<lb/>midium, acita porrò, quantum licebit &longs;ubdiuidere ad <lb/>v&longs;que punctum A, &longs;icque demum velocitas per totam <pb pagenum="136"/>AE repenetur dupla velocitatis per totam AD, & ve<lb/>locitas per totam AD velocitatis per totam AS; Dico <lb/>aut te nihil concludere, aut &longs;ic licere ratiocinari. </s>

<s>Si <emph type="italics"/>DE, &<emph.end type="italics"/> SD <emph type="italics"/>eodem tempore percurruntur, quia velo<lb/>citas per totam<emph.end type="italics"/> DE, <emph type="italics"/>dupla e&longs;t velocitatis per totam<emph.end type="italics"/> SD. </s>

<s>Igitur, <emph type="italics"/>AD, &<emph.end type="italics"/> AS <emph type="italics"/>eodem tempore percurrentur, quia <lb/>velocitas per totam<emph.end type="italics"/> AD <emph type="italics"/>dupla e&longs;t velocitatis per totam<emph.end type="italics"/> AS. </s>

<s>Et &longs;imiliter, AE <emph type="italics"/>&<emph.end type="italics"/> DA <emph type="italics"/>eodem tempore percurrentur, <lb/>qui velocitas per totam<emph.end type="italics"/> AE, <emph type="italics"/>dupla e&longs;t veloci tatis per to<lb/>tam<emph.end type="italics"/> AD. </s>

<s>Quo, & non aliomodo Galileus, & ego ratiocina<lb/>ti &longs;umus. </s>

<s>Adderem concludi eodem planè modo, per<lb/>curri AF triplum, AG quadruplum, &c. </s>

<s>tempore eo<lb/>dem, quo eandem AD; verùm res deductu perfacilis <lb/>e&longs;t, iuxta ea quæ pari ratione deducis &longs;equentibus <lb/>articulis; & e&longs;t iam aliunde tempori parcendum. </s>

<s><emph type="center"/>IN ARTICVLOS XIII. XIV. XV. XVI. XVII. XVIII. </s>

<s>De <lb/>Po&longs;tulato Galilei, Circa motum &longs;uper æque altis, <lb/>non æquè inclinatis planis.<emph.end type="center"/></s>

<s><emph type="italics"/>Tran&longs;eo igitur ad numerum xiv. </s>

<s>in quo cùm initio, at<lb/>que in fine<emph.end type="italics"/> G<emph type="italics"/>alilei Po&longs;tulatum veri&longs;imile potiùs, quàm aut per <lb/>&longs;e euidens, aut ex euidentibus demon&longs;tratum, cum eodem<emph.end type="italics"/> G<emph type="italics"/>a<lb/>lileo agno&longs;cis, candide omninò facis: &longs;ed id planè &longs;ufficit, vt <lb/>cætera quoque, quæ ab eodem Galileo ex illo Po&longs;tulato inferun<lb/>tur, veri&longs;imilia tantum, & minimè demon&longs;trata cen&longs;eantur: <lb/>eumque proinde nobis de motu accelerato, non &longs;cientiam (vt <lb/>eam vocat) &longs;ed opinionem tantum tradidi&longs;&longs;e, quod &longs;olùm con<lb/>cludo.<emph.end type="italics"/></s><pb pagenum="137"/>

<s>At concludere &longs;imùl debes, aut in ip&longs;a Scientiæ <lb/>voce <expan abbr="hære&longs;cend&utilde;">hære&longs;cendum</expan>; aut &longs;i ip&longs;i non licuit vocem v&longs;urpare, <lb/>cùm &longs;e nouam &longs;cientiam inuchere profe&longs;&longs;us e&longs;t; licere <lb/>adhûc minùs tibi, qui illam P&longs;eudo-&longs;cientiam vocans, <lb/>profiteris te veram, ac certam in eius locum &longs;ub&longs;ti<lb/>tuere; quatenus tradita ab illo experimentis innititur, <lb/>quæ nullius hactenus fal&longs;itatis conuicta &longs;int; tua iis <lb/>&longs;uffulcitur, quæ conuicta &longs;int nullius e&longs;&longs;e veritatis. </s>

<s><emph type="italics"/>Quæ verò de Libro Torricellij posteà adiungis (et&longs;i ea non <lb/>viderim) partim vera, partim fal&longs;a, aut &longs;altem incerta e&longs;&longs;e <lb/>non dubito. </s>

<s>Duas certè eius Propo&longs;itiones primas ego quo<lb/>que de globis euidenter demonstro; at quomodo ex prioribus <lb/>illis duabus Propo&longs;itionibus po&longs;teriores inferantur, &longs;atis non <lb/>video, ni&longs;i<emph.end type="italics"/> G<emph type="italics"/>alilei principia &longs;upponantur. </s>

<s>Cùm enim globi <lb/>pondere æquales<emph.end type="italics"/> E, <emph type="italics"/>&<emph.end type="italics"/><lb/><figure id="fig37"></figure><lb/>F <emph type="italics"/>planis<emph.end type="italics"/> AC, <emph type="italics"/>&<emph.end type="italics"/> CD <lb/>(<emph type="italics"/>vel<emph.end type="italics"/> CB) <emph type="italics"/>in&longs;i&longs;tentes, <lb/>momenta ad de&longs;cen&longs;um <lb/>retineant in reciproca, <lb/>& permutata ratione planorum, ob eamque cau&longs;&longs;am momen<lb/>ta ip&longs;ius<emph.end type="italics"/> E, <emph type="italics"/>&longs;int ad momenta ip&longs;ius<emph.end type="italics"/> F, <emph type="italics"/>vt<emph.end type="italics"/> CB (<emph type="italics"/>&longs;iue<emph.end type="italics"/> CD) <emph type="italics"/>ad<emph.end type="italics"/><lb/>CA; <emph type="italics"/>non apparet vnde euidenter concludi poßit<emph.end type="italics"/> E, <emph type="italics"/>qui pau<lb/>cioribus momentis deor&longs;um voluitur, & magis à motu perpen<lb/>diculari di&longs;trahitur, eundem nihilominus gradum velocitatis <lb/>acquirere in<emph.end type="italics"/> A, <emph type="italics"/>quem globus<emph.end type="italics"/> F <emph type="italics"/>in<emph.end type="italics"/> B <emph type="italics"/>acqui&longs;ierit. </s>

<s>Nam quod <lb/>ais tarditatem motus spatij longitudine compen&longs;ari, conie<lb/>ctando quidem a&longs;&longs;eris; at (quod ad Po&longs;tulati per &longs;e, & ex <lb/>terminis minimè euidentis nece&longs;&longs;arium e&longs;&longs;et) nulla id ratione <lb/>demonstras.<emph.end type="italics"/></s>

<s>Quod de Propo&longs;itionibus Torricellij ais, cogno&longs;ces <pb pagenum="138"/>id pleniùs, de quo dubitas, vbi legeris earum proba<lb/>tiones. </s>

<s>Quod autem ais <emph type="italics"/>me coniectando, non vlla ratione <lb/>demon&longs;trando tarditatem motus &longs;patij longitudine compen&longs;ari <lb/>dixi&longs;&longs;e:<emph.end type="italics"/> adiicere debes, nihil fui&longs;&longs;e nece&longs;&longs;e præter ip&longs;am, <lb/>non coniect <expan abbr="irã">iram</expan>, &longs;ed <expan abbr="euidentiã">euidentiam</expan> proponere: cùm te con<lb/>tendente <emph type="italics"/>globum per plana æque-alta, &longs;ed inæqualiter in<lb/>clinata pareis velocitatis gradus in fine decen&longs;us non acquirere;<emph.end type="italics"/><lb/>ac non demon&longs;trante, &longs;ed dumtaxat notum dicente, <lb/><emph type="italics"/>tantò minoribus momentis de&longs;cendere globum per planum, <lb/>quantò minus accliue fuerit:<emph.end type="italics"/> excepi, <emph type="italics"/>non videre me, quomodo <lb/>id concluderes, quatenùs non a&longs;&longs;umeres planum, quantò mi<lb/>nùs accliue e&longs;t, tantò e&longs;&longs;e quoque prolixius. </s>

<s>Etenim notum <lb/>quidem e&longs;&longs;e acquiri minores velocitatis gradus in minùs de<lb/>cliui, quod &longs;it decliutori æquale: at &longs;i, vt minus decliue, ita <lb/>etiam prolixius &longs;it, notum quoque e&longs;&longs;e velocitatem in fine illius <lb/>quæ&longs;itam e&longs;&longs;e po&longs;&longs;e æqualem velocitati in fine decliuioris ac<lb/>qui&longs;itæ, prolixitate nempe de&longs;cen&longs;us paruitatem incremento<lb/>rum velocitatis compen&longs;ante Pro&longs;equeris.<emph.end type="italics"/></s>

<s><emph type="italics"/>Multa etiam totis numeris xv. </s>

<s>adducis, ve <lb/>experimentum<emph.end type="italics"/> G<emph type="italics"/>alilei de<emph.end type="italics"/> P<emph type="italics"/>endulorum vibratione, & ad <lb/>æqualem altitudinem a&longs;cen&longs;u defenda<gap/>, &longs;ed fateris tamen, quod <lb/>contendo, pendula eiu&longs;modi neque ad eandem, vnde ip&longs;a demi&longs;<lb/>&longs;a &longs;unt, altitudinem a&longs;cendere, neque ad æqualem &longs;emper, &longs;i <lb/>ex punctis ad lineam horizontalem diuer&longs;imodè comparatis, <lb/>&longs;uspendantur; huiu&longs;que etiam rei, ac diuer&longs;itatis cau&longs;&longs;as, at<lb/>que impedimenta inquiris, quæ &longs;i abe&longs;&longs;ent, tum eadem pendu<lb/>la ad æqualem perpetuò altitudinem præcisè con&longs;cen&longs;ura <lb/>diuinas, non autem demon&longs;tras.<emph.end type="italics"/></s>

<s>At beatus &longs;um &longs;altem, &longs;i non ab&longs;que aliqua, & cui <lb/>nih lrefragetur, veri&longs;imili ratione, diuinem. </s><pb pagenum="139"/>

<s><emph type="italics"/>Sed, vt tu ip&longs;e agno&longs;cis, demon&longs;trationes quæro, non veri&longs;i<lb/>militudines, aut &longs;u&longs;piciones.<emph.end type="italics"/></s>

<s>Tu verò & optimè facis, & beatior me longè es, &longs;i <lb/>demon&longs;trationes adinuenias, nec ea amplexeris, quæ <lb/>apertè fal&longs;a cùm &longs;int, ne veri&longs;imilitudinis quidem, aut <lb/>&longs;u&longs;picionis nomen mereantur. </s>

<s><emph type="italics"/>Quòd autem in Confirmationem adducis quatuor globos <lb/>quatuor distinctis filis &longs;ic appen&longs;os, vt primi longitudo &longs;it <lb/>vnius pedis, &longs;ecundi quatuor, tertij nouem, quarti &longs;exdecim: <lb/>ai&longs;que eos, &longs;i ex quapiam altitudine &longs;imul dimittantur, &longs;uas <lb/>inter &longs;e vibrationes ita componere, vt dum quartus globus <lb/>vnam perficiet, tertius duas, &longs;ecundus treis, & primus quatuor <lb/>ab&longs;oluat. </s>

<s>Hæc, inquam, & quæ inde colligis, nec certiora <lb/>&longs;unt, nec exactiùs cum experientia congruunt, quàm ea, qui<lb/>bus confirmandis a&longs;&longs;umpta &longs;unt. </s>

<s>Et&longs;i enim in paucis ali<lb/>quibus vibrationibus ea ratio vtcúmque ob&longs;eruari videatur; <lb/>breut tamen interrumpitur, vt &longs;æpius à me experientia <lb/>combrobatum est; cuius etiam rationem indicat, qui noua<emph.end type="italics"/><lb/>G<emph type="italics"/>alilei placita Gallicè reddidit lib.<emph.end type="italics"/> 1. <emph type="italics"/>artic.<emph.end type="italics"/> 17. <emph type="italics"/>vbi ip&longs;e quo<lb/>que &longs;e expertum e&longs;&longs;e a&longs;&longs;erit, vibrationes omneis eiu&longs;dem pen<lb/>duli æquali tempore perpetuò non ab&longs;olui: quod tamen nece&longs;<lb/>&longs;arium e&longs;&longs;et, vt con&longs;en&longs;us ille vibrationum diutiùs perma<lb/>neret.<emph.end type="italics"/></s>

<s>Illud de Pendulis experimentum ita certum e&longs;t, vt <lb/>fal&longs;um nunquam deprehenderim, quoties a&longs;&longs;umun<lb/>tur, & quandiù manent longitudinum exqui&longs;itè ea<lb/>rumdem. </s>

<s>Nam quia non ponderis, &longs;ed longitudinis <lb/>variatio vibrationum celeritatem, aut tarditatem va<lb/>riat, ideò ni&longs;i quatuor illa pendula a&longs;&longs;umantur exqui<lb/>&longs;itè longitudinum præ&longs;criptarum, fiet &longs;en&longs;im, vt quod <pb pagenum="140"/>pendulum &longs;atis exqui&longs;itè con&longs;onare videbatur cum <lb/>cæteris, vibrationum euariet, aut accelerando, &longs;i vel <lb/>tantillum breuius æquo fuerit, aut retardando, &longs;i tan<lb/>tillum prolixius. </s>

<s>Et aliunde quia filum, ni&longs;i metalli<lb/>cum &longs;it, diducitur &longs;en&longs;im, prolixiu&longs;que euadit, dum <lb/>partim tortum detorquetur, partim pondere pertra<lb/>ctum tenuatur; idcircò inde quoque fit, vt ni&longs;i cauea<lb/>tur, ne fiat variatio, longitudinis, vibrationes, quæ per <lb/>initia con&longs;onanter inter &longs;e fiebant, decre&longs;cant &longs;en&longs;im, <lb/>ac denique di&longs;crepare deprehendantur. </s>

<s>Heinc &longs;emper <lb/>mihi con&longs;titit, quod pendulum primò di&longs;crepare acce<lb/>lerando animaduerti, fui&longs;&longs;e aliquantulum æquo bre<lb/>uius; quod remorando, aliquantò prolixius: vt pro<lb/>inde non mirer & tibi; & authori, <expan abbr="qu&etilde;">quem</expan> citas, deprehen<lb/>&longs;am fui&longs;&longs;e aliquam vibrationum incon&longs;tantiam, & in<lb/>æqualitatem. </s>

<s>Cæterùm res ip&longs;a in &longs;e e&longs;t omninò cer<lb/>ta: & vel ex eo, quod deprehendi&longs;ti vibrationes &longs;al<lb/>tem peraliquod tempus ita con&longs;onare, vt pendulum <lb/>&longs;exdecim pedum vibrationem &longs;emel dumtaxat perage<lb/>ret, dum pendulum nouem, perageret bis, pendulum <lb/>quatuor, ter: pendulum vnius, quater; potui&longs;ti intelli<lb/>gere, quàm hæc egregiè congruant cum iis, quibus <lb/>confirmandis fuere v&longs;urpata; cum tu interim tale nihil <lb/>in tuæ &longs;ententiæ confirmationem profere po&longs;&longs;is. </s>

<s><emph type="italics"/>Opponis numero xviij. </s>

<s>non &longs;atis àme refelli, aut erroris <lb/>argui ea experimenta, quibus<emph.end type="italics"/> G<emph type="italics"/>alileus accelerationem motus <lb/>in de&longs;cen&longs;u grauium tam per aërem, quàm per plana quælibet <lb/>inclinata confirmat: nihil <gap/>ue à me ad luci expostulas, præter <lb/>experiundi modum di&longs;&longs;ici<gap/>em varii&longs;que erroribus o<gap/> noxium. <lb/></s>

<s>Nimirum eo loco id &longs;olùm efficere volui, vt quilibet intellige-<emph.end type="italics"/><pb pagenum="141"/><emph type="italics"/>ret, minùs mirum videri, &longs;i Galileus errauerit: cùm non ni&longs;i <lb/>experimento its erroribus obnoxio v&longs;us fuerit, qui nullâ dili<lb/>gentiâ vitaripo&longs;&longs;e videantur. </s>

<s>Satis autem eadem illa expe<lb/>rimenta erroris po&longs;tmodùm reuincenda videbantur, &longs;i longé <lb/>aliam accelerationis rationem in de&longs;cen&longs;u grauium interuenire <lb/>demon&longs;trarem.<emph.end type="italics"/></s>

<s>Non repugna&longs;&longs;em, &longs;i demon&longs;tra&longs;&longs;es; at demon&longs;tra&longs;<lb/>&longs;e non con&longs;titit. </s>

<s><emph type="center"/>IN ARTICVLOS XIX. XX. XXI. XXII. </s>

<s>De <lb/>Experimentis circaictum; impetum-ve grauium <lb/>cadentium; ad explorandum impetu&longs;-ne, vt <lb/>&longs;patium incre&longs;cat.<emph.end type="center"/></s>

<s><emph type="italics"/>Reprehendis item numero xix, quod nulla &longs;peciali Expe<lb/>rientia confirmem, quod experientià con&longs;tare affirmo, nempe<emph.end type="italics"/><lb/>Corpus graue quodcumque ex qualibet altitudine per <lb/>aërem cadens, & percutiens vt libet, perpetuò ex alti<lb/>tudine dupla duplò ampliùs, & ex tripla, quadruplave <lb/>di&longs;tantia, triplò, quadruploque fortiùs percutere. <lb/><emph type="italics"/>Nempe vide bam &longs;atis manifestum e&longs;&longs;e id eodem Experimento <lb/>comprobari po&longs;&longs;e, quo idip&longs;um po&longs;tmodum o&longs;ten&longs;urus eram in <lb/>globo. </s>

<s>Non fuit igitur cum operæ, ac temporis iactura du<lb/>plex ingerenda Experientia, vbi plu&longs;quam abundè &longs;ufficere <lb/>potuit vnica.<emph.end type="italics"/></s>

<s>Hactenus de Confirmatione tuæ illius A&longs;&longs;umptio<lb/>nis, quam &longs;uperiùs retulimus, vbi de Controuer&longs;iæ <lb/>Statu. </s>

<s>Sequitur videamus quid habeas de impugna<lb/>ta Probatione, ad quam &longs;pectabat Primum membrum <lb/>Po&longs;terioris partis Operis totius. </s>

<s>Quippe ratus te euer<lb/>ti&longs;&longs;e funditus Galilei &longs;cientiam, ac profe&longs;&longs;us te illi <pb pagenum="142"/>veram, certamque &longs;ub&longs;tituere, ducendum cen&longs;ueras <lb/>initium ab ip&longs;a Experientia, tanquam à germano eius <lb/>fundamento. </s>

<s>Quandoquidem porrò his me affatus <lb/>verbis fueras, <emph type="italics"/>Primùm ego te, optime<emph.end type="italics"/> G<emph type="italics"/>a&longs;&longs;ende, ad claras, <lb/>facileis, atque indubitatas Experientias prouoco, & in ijs ar<lb/>bitrum te, ac iudicem habere vehementer gaudeo. </s>

<s>Prima peti<lb/>tur ex impetu, quo globus, aut graue aliud corpus quodcumque <lb/>per <expan abbr="a&etilde;rem">aerrem</expan> sponte naturæ deorsùm cadit, ac percutit, &c.<emph.end type="italics"/><lb/>Quis heic loci non ex&longs;pecta&longs;&longs;et plu&longs;quàm vnicam <expan abbr="Ex-perientiã">Ex<lb/>perientiam</expan>? </s>

<s>Quis exi&longs;tima&longs;&longs;et te ex vnica facere primam, <lb/>& &longs;ecundam? </s>

<s>Quis non credidi&longs;&longs;et à te, ni&longs;i omneis, ni&longs;i <lb/>plurimas, &longs;altem plureis vnâ peractas, ob illud, <emph type="italics"/>corpus <lb/>graue quodcumque?<emph.end type="italics"/> Certè, cùm &longs;tatim repetens, <emph type="italics"/>con&longs;tare <lb/>facilè experientiâ<emph.end type="italics"/> dixi&longs;&longs;es <emph type="italics"/>corpus graue quodcumque ex <lb/>qualibet altitudine per <expan abbr="a&etilde;rem">aerrem</expan> cadens, & percutiens, vt libet, <lb/>&c.<emph.end type="italics"/> non &longs;perare non potui aliquam aliam Experien<lb/>tiam, præter vnicam in Bilance factam, in quam glo<lb/>bus cadens, & percutiens, neque e&longs;t corpus graue <lb/>quodcumque, neque vt-libet cadit, percutitque. </s>

<s>Sed<lb/>nimirùm tu talem Fxperientiam, tamet&longs;i foret vnica, <lb/>tanti faciendam e&longs;&longs;e cen&longs;ui&longs;ti, vt e&longs;&longs;et in&longs;tar omnium, <lb/>ac veritatem &longs;ic demon&longs;traret, vt facit ver non vna <lb/>hirundo. </s>

<s>Et, &longs;i talem quidem ip&longs;am inueni&longs;&longs;em, qua<lb/>lem &longs;perandam feceras, <emph type="italics"/>facilem, claram, indubitatam,<emph.end type="italics"/> ac, <lb/>verbo vno vt dicam, <emph type="italics"/>veram:<emph.end type="italics"/> abfui&longs;&longs;em profectò, vt <lb/>aliam te importunè rogitarem; fui&longs;&longs;et illa enim abun<lb/>dè, & &longs;atis. </s>

<s>Nunc autem, cùm eam longè &longs;ecus &longs;e ha<lb/>bere compererim, & tu ip&longs;e non au&longs;is ampliùs, qua<lb/>lem priùs diuendere, &longs;icuti mox videndum e&longs;t; quis <lb/>non aliam mecum abs te expetii&longs;&longs;et? </s><pb pagenum="143"/>

<s><emph type="italics"/>Quare quæ deinceps numeris xx. </s>

<s>adiicis, <lb/>fru&longs;trà &longs;unt: cùm ex iis etiam vltrò datis, nihil aduer&longs;us in&longs;i<lb/>nuatam à nobis Experientiam, aut omninò contra nos (ob <lb/>Exemplorum, quibus vteris, dißimilitudinem) concludas.<emph.end type="italics"/></s>

<s><emph type="italics"/>Fru&longs;trà &longs;unt,<emph.end type="italics"/> in quis; &longs;ed nimirùm, quia quod repo<lb/>neres, non fuit, & prætextu Exemplorum, quæ articulis <lb/>XXI, & XXII. habentur, di&longs;&longs;imulare vi&longs;um e&longs;t, quæ op<lb/>po&longs;ui XX. circa varia Experimenta. </s>

<s>Siquidem illa in eo <lb/>recen&longs;ui, quæ tu videbaris potui&longs;&longs;e præ&longs;ertim intelli<lb/>gere, cùm diceres <emph type="italics"/>rem Experientiâ facilè con&longs;tare in graui <lb/>quocumque;<emph.end type="italics"/> ac o&longs;tendi ip&longs;a non e&longs;&longs;e, qualia tu dicebas, <lb/><emph type="italics"/>facilia, clara, indubitata;<emph.end type="italics"/> teque ideò &longs;ollicitaui, vt decla<lb/>rares quemadmodum con&longs;taret tibi grauia ex altitu<lb/>dine dupla decidentia impetus e&longs;&longs;e duplò maioris, tri<lb/>plò ex tripla, &c. </s>

<s>Tu verò, cùm quid re&longs;ponderes (aut <lb/>dic &longs;altem, quomodo po&longs;&longs;im id interpretari) non &longs;up<lb/>peteret, factum &longs;atis e&longs;&longs;e puta&longs;ti, &longs;i ea diceres <emph type="italics"/>e&longs;&longs;e fru&longs;trà.<emph.end type="italics"/><lb/>Sed fru&longs;trà fuerint, quatenus ex te fru&longs;trà requi&longs;iui quæ <lb/>laterent te; at non fuere fru&longs;trà, vt o&longs;tenderem, te non <lb/>debui&longs;&longs;e id, quod in te minimè e&longs;&longs;et, o&longs;tentare. </s>

<s>Certè <lb/>enim iam non potui&longs;ti illud, quod mox, prætexere, <lb/><emph type="italics"/>non e&longs;&longs;e tibi operæ, tempori&longs;que faciendam iacturam;<emph.end type="italics"/> cùm <lb/>excitatæ difficultates <expan abbr="manife&longs;t&utilde;">manife&longs;tum</expan> fecerint, quàm vtiliter <lb/>operam, tempu&longs;que in iis impendi&longs;&longs;es. </s>

<s>Quanquam & <lb/>nulla vnquam pote&longs;tin rebus huiu&longs;cemodi diligentia <lb/>e&longs;&longs;e &longs;uperflua; ip&longs;eque te&longs;tor fui&longs;&longs;e te, quod &longs;pectat ad <lb/>me, ampliùs præ&longs;titurum paucis quibu&longs;dam ver&longs;ibus <lb/>explicantibus vnicum, de quo con&longs;taret, Experimen<lb/>tum; quàm opere toto, toti&longs;que ratiociniis; ac in eo <lb/>&longs;um &longs;emper, vt &longs;i vel deinceps proferre po&longs;&longs;is vnicum, <pb pagenum="144"/>manus vltrò dem, & totum quicquid con&longs;crip&longs;ero, <lb/>deuoueam, flammi&longs;que addicam. </s>

<s>Quippe fiu&longs;trà &longs;int <lb/>mille ratiocinia, &longs;i vel vnicum refragetur Experimen<lb/>tum; vt fru&longs;tra &longs;omniemus monteis aureos, qui abeant <lb/>&longs;tatim vel minima expergefactione in fumum. </s>

<s>Quod <lb/>ad ea &longs;pectat, quæ habeo &longs;equentibus articulis, tu <lb/>Exempla dicis, vt po&longs;&longs;is di&longs;&longs;imilitudinem cau&longs;&longs;ari; cùm <lb/>Experimenta &longs;int, quæ ad rem attineant, ac &longs;upparia <lb/>&longs;altem &longs;int iis, quibus controuer&longs;ia dirimenda videa<lb/>tur. </s>

<s>Nam, ne <expan abbr="hæreã">hæream</expan> in &longs;ingulis, & <expan abbr="dicã">dicam</expan> &longs;altem quidpiam <lb/>de Primo; <expan abbr="Not&utilde;">Notum</expan> e&longs;t, &longs;i va&longs;e cylindrico oppleto, integra <lb/>momento &longs;ubducatur ba&longs;is, totum aquæ contentæ cy<lb/>lindrum &longs;tatim effluxurum, eo modo, quo &longs;tatim elabe<lb/>retur cylindrus marmoreus, aut quiuis alius &longs;olidus, &longs;i <lb/>eodem va&longs;e contineretur. </s>

<s>Vt autem in cylindro mar<lb/>moreo cadente non velociùs de&longs;cendit pars &longs;uprema, <lb/>quàm infima, aut intermedia quælibet, quòd omnes <lb/>ex æquo ferantur deor&longs;um, & par conficiant &longs;patium, <lb/>pariterque accelerentur; ita concipimus in aqueo non <lb/>velociùs de&longs;cendere partem &longs;upremam, quàm infi<lb/>mam, aut quamlibet mediam, &longs;ed parem e&longs;&longs;e omnium <lb/>de&longs;cen&longs;um, omniumque accelerationem; atque id<lb/>circò perinde e&longs;&longs;e &longs;upremæ parti aquæ, &longs;iue aqua &longs;ub<lb/>&longs;it, &longs;iue nulla &longs;it: quatenus quæ &longs;ube&longs;t, tantum præce<lb/>dendo aufugit, quantum ip&longs;a pote&longs;t con&longs;equendo in<lb/>&longs;tare: ac fieri proinde, vt &longs;uprema aqua ad ba&longs;in dela<lb/>bens, tanto de&longs;cendat tempore, quanto &longs;i ex eadem <lb/>altitudine per aërem delaberetur. </s>

<s>Iam, cùm exiguum <lb/>folùm foramen ad ip&longs;am ba&longs;in aperitur, idem propor-<pb pagenum="145"/>tione contingit. </s>

<s>Nam &longs;i&longs;olus quidem e&longs;&longs;et cylindiulus <lb/>aquæ re&longs;pondens ip&longs;i foramini, manife&longs;tum e&longs;t ip&longs;um <lb/>perinde effluxurum, ac totum cylindrum ba&longs;i tota <lb/>aperta. </s>

<s>Quoniam verò talis cylindrulus copio&longs;iore <lb/>aqua ambitur, non ideò quidem minùs effluit, &longs;ed <lb/>efficitur, vt dum pars &longs;uprema antecedenteis con&longs;equi<lb/>tur, circum&longs;tantes aquæ &longs;upremæ partes in ip&longs;ius lo<lb/>cum propter fluxilitatem &longs;ubeant, ac pari modo, con<lb/>tinente<gap/>que &longs;equantur, de&longs;cendant, ac effluant; aliis <lb/>nimirum, alii&longs;que inde&longs;inenter &longs;ub&longs;titutis, ab ip&longs;a v&longs;que <lb/>&longs;uperficie, quæ idcircò &longs;emper complanata appareat, <lb/>quov&longs;que &longs;ub effluxus finem excauetur, dum quæ &longs;u<lb/>pere&longs;t aqua parcior e&longs;t, quàm vt perinde facilè, abun<lb/>deque confluere po&longs;&longs;it. </s>

<s>Itáque etiam foramine aper<lb/>to, aqua &longs;umma in locum ba&longs;eos, ip&longs;umve foramen <lb/>tanta velocitate cadit, quanta per aërem caderet; ac <lb/>licet proinde de eiusimpetu ex effluxu non &longs;ecus iudi<lb/>care, quàm ex ip&longs;o ca&longs;u; vt pote cùm effluendo cadat, <lb/>& cadendo effluat; ac pari &longs;emper tempore ex &longs;ummo <lb/>ad imum perueniat. </s>

<s>Vide igitur an Exemplum di&longs;&longs;i<lb/>mile &longs;it, & non potiùs Experimentum (&longs;uppar mini<lb/>mùm) illiu&longs;met rei, de qua agitur: & quia quæritur, an <lb/>impetus exprimatur duplex ex altitudine dupla, an ex <lb/>quadrupla, i&longs;tud verò experimentum (&longs;eu exemplum <lb/>mavis) duplum probat ex altitudine quadrupla, non <lb/>dupla; agno&longs;ce quo iure dicas quæ habentur memo<lb/>ratis articulis <emph type="italics"/>fru&longs;tra e&longs;&longs;e, ac iis etiam vltrò datis, nihil me <lb/>aduer&longs;us in&longs;inuatam à te experientiam, aut omninò contra <lb/>te, ob exemplorum, quibus vtor, dißimilitudinem concludere.<emph.end type="italics"/></s><pb pagenum="146"/>

<s><emph type="center"/>IN ARTICVLOS XXIII. XXIV. XXV. XXVI. XXVII. <lb/>XXVIII. </s>

<s>De Experimento in Bilance facto, ac <lb/>aliud reuerâ probante, quàm velocitates <lb/>e&longs;&longs;e &longs;icut &longs;patia.<emph.end type="center"/></s>

<s><emph type="italics"/>At numero xxiii, & quatuor &longs;equentibus Controuer&longs;iæ <lb/>caput attingis, cùm Experientiam de globo per aërem deciden<lb/>te examinas. </s>

<s>Jngenuè enim fatendum e&longs;t, in mentem mibi <lb/>nunquam incidi&longs;&longs;e, vt inquirerem, an globus ex vnius dia<lb/>metri altitudine decidens, po&longs;&longs;et vltra æquilibrium, & pondus <lb/>&longs;ibi æquale ampliùs aliquid attollere.<emph.end type="italics"/></s>

<s>Commendanda &longs;anè ingenua confe&longs;&longs;io (quan<lb/>quam addendum fui&longs;&longs;e videtur, <emph type="italics"/>non incidi&longs;&longs;e tibi in <lb/>mentem, vt inquireres,<emph.end type="italics"/> non modò, <emph type="italics"/>an globus ex vnius dia<lb/>metri altitudine decidens, po&longs;&longs;et vltra æquilibrium, & pondus <lb/>&longs;ibi æquale, ampliùs aliquid attollere:<emph.end type="italics"/> &longs;ed etiam, <emph type="italics"/>an globus <lb/>idem æquilibrium, & pondus &longs;ibi æquale ex dimidio, quadran<lb/>te, octante, & penè dicam ex vncia altitudinis &longs;uæ diametr<gap/><lb/>attolleret;<emph.end type="italics"/> cùm præci&longs;io &longs;it inter plus, & minus, & ip&longs;e <lb/>in vtramque partem aberrâris tantopere) Commen<lb/>dandumid, inquam; &longs;ed cùm i&longs;tud &longs;it, vt præclarè ais, <lb/><emph type="italics"/>Controuer&longs;iæ caput,<emph.end type="italics"/> quatenus hoc vnum Experimentum <lb/>fuit, quo res controuer&longs;a determinaretur, <expan abbr="cõprobare-turque">comprobare<lb/>turque</expan> à te: patere me duo quædam &longs;ubmirari. </s>

<s>Vnum, <lb/>cur adeò &longs;olemniter prouoca&longs;&longs;es me <emph type="italics"/>ad facileis, claras, <lb/>indubitatas Experientias,<emph.end type="italics"/> quæ controuer&longs;iæ caput face<lb/>rent, ac Demon&longs;trationem tuam, &longs;cientiamque totam <lb/>con&longs;tabilirent: cùm ecce habens vnicam, videri iis <lb/>po&longs;&longs;es, qui rerum amantes verbis non capiuntur, ita <lb/>o&longs;citanter illam peregi&longs;&longs;e, vt nihil e&longs;&longs;et minùs, quàm <pb pagenum="147"/>quod diceretur. </s>

<s>Profectò ni&longs;i v&longs;us fui&longs;&longs;es voce <emph type="italics"/>Præ<lb/>ci&longs;ionis,<emph.end type="italics"/> alii&longs;que con&longs;imilibus, videri dumtaxat potui&longs;<lb/>&longs;es opinione præoccupatus, ac præ illius a more, volui&longs;<lb/>&longs;e non opinionem experientiæ, &longs;ed experientiam <lb/>opinioni accom modare: Nunc autem non video, cur <lb/>tot paginis, tantoque apparatu in&longs;titeris (etiam tot <lb/>cautiones adhibendas iis, qui rem experiri &longs;crupulo<lb/>&longs;iùs vellent, præ&longs;cribens) vt te expertum crederemus, <lb/><emph type="italics"/>naturam illud in globo peculiare ac proprium e&longs;&longs;e volui&longs;&longs;e, <lb/>vt eius diameter præci&longs;a e&longs;&longs;et men&longs;ura illius altitudinis, ex <lb/>qua, &c.<emph.end type="italics"/> ac iterùm, <emph type="italics"/>hanc e&longs;&longs;e inter globos, & alias figu<lb/>ras differentiam, quòd in globis diameter altitudines præcis è <lb/>definiat, vnde pondus, &c.<emph.end type="italics"/></s><s> Alterum, cur huiu&longs;imodi Ex<lb/>perimento deprehen&longs;o fal&longs;o; hoc e&longs;t, cùm verùm iam <lb/>non &longs;it, vt contenderas, <emph type="italics"/>con&longs;tare Experientiâ corpus graue <lb/>quodcumque ex qualibet altitudine per aërem cadens, & <lb/>percutiens vt libet, perpetuò ex altitudine dupla dupla præcisè <lb/>ampliùs, & ex tripla, quadruplave di&longs;tantia, triplò, qua<lb/>druplove fortiùs percutere;<emph.end type="italics"/> cur, inquam, pergas etiam<lb/>num eam Ratiocinationem habere, imò & acriter <lb/>tueri pro Phy&longs;ica Demon&longs;tratione, quam non alij <lb/>fundamento, quàm huic vnico Experimento &longs;uper<lb/>ex&longs;truxeris? </s>

<s>Hoc &longs;anè e&longs;t, quod mihi videtur faten<lb/>dum &longs;imùl ingenuè fui&longs;&longs;e, ac parcendum &longs;imùl labo<lb/>ri, quo æque te exerceres, ac me, quemque declinare <lb/>potucras, &longs;i neque meam Re&longs;pon&longs;ionem, neque tuas <lb/>Vindicias e&longs;&longs;e cuulgandas cen&longs;ui&longs;&longs;es; cùm alioquin <lb/>iam de&longs;titutus omni argumento, quo Demon&longs;tra<lb/>tionem &longs;uffulcias, ludere videaris omnem operam, dum <lb/>operosè adeò in ea propugnanda de&longs;udas. </s><pb pagenum="148"/>

<s><emph type="italics"/>In quo tu quidem f&oelig;licior fui&longs;ti; &longs;ed vereor non pa<lb/>rùm, ne accuratior illa tua experientia neutiquam tuæ parti <lb/>&longs;uffragetur; quamuis dicas com nodè ad<emph.end type="italics"/> G<emph type="italics"/>alilei mentem <lb/>accidi&longs;&longs;e, vt globus non-ni&longs;i ex quatuor diametrorum altitu<lb/>dine decidens attollere potuerit duplum eius ponderis, quod ex <lb/>vnius diametri eleuatione &longs;ummum extulerat; &longs;icut nec tri<lb/>plum, ni&longs;i ex altitudine diametrorum nouem, &c. </s>

<s>Ego enim <lb/>tuo exemplo inductus, cùm idem tentare item voluerim; ne<lb/>que globum ex vnius diametri altitudine, &longs;uum pondus toties <lb/>multiplicatum attollere comperi; neque ad duplicatum, tri<lb/>plicatumque pondus eleuandum, ad tantam altitudinem attolli <lb/>debui&longs;&longs;e. </s>

<s>V&longs;us &longs;um quidem bilance obuia, & fortaßis non ita <lb/>exacta, & globo Porphyretico vnciæ<emph.end type="italics"/> 1, <emph type="italics"/>drachm<emph.end type="italics"/> 2 <emph type="italics"/>&longs;atis exactè. <lb/></s>

<s>Reperi autem hunc globum repetita aliquoties operatione ex <lb/>vnius diametri altitudine eleuare &longs;olùm vncias<emph.end type="italics"/> 5, <emph type="italics"/>dr.<emph.end type="italics"/> 2 <emph type="italics"/>(ne&longs;cio <lb/>an vitio bilancis acciderit, vt maius pondus non extulerit) at <lb/>idem globus duplum illius ponderis, ex diametris tribus, tri<lb/>plum ex quinque, quadruplum ex &longs;eptem, quintuplum ex <lb/>nouem &longs;ustulit; interruptus autem nihil vlteriùs tentare po<lb/>tui. </s>

<s>Ex his autem adhûc vides (quod totius controuer&longs;iæ ca<lb/>put e&longs;t) æqualibus spatiis æqualia acquiri velocitatis aug<lb/>menta. </s>

<s>Hanc ego tamen operationem tibi tanquam exactam <lb/>non propono, quia necdum mihi per otium licuit eam adhi<lb/>bere diligentiam, quamres huius momenti pro &longs;uo merito po<lb/>&longs;tulat: &longs;ed vt te quoque ad exactam illius rei experientiam <lb/>inuitem; ex qua tota de motu accelerato controuer&longs;ia diri<lb/>menda videatur.<emph.end type="italics"/></s>

<s>Po&longs;trema hæc verba, quàm e&longs;&longs;ent te digna; ni&longs;i <lb/>aliunde Demon&longs;trationem, quod mox obiiciebam, ita <lb/>propugnares, ac&longs;i foret iam controuer&longs;ia à te dirempta<gap/><pb pagenum="149"/>Et quod inuitas quidem me ad experiundum iterùm; <lb/>&longs;cito me iterum expertum, ac adhibitos mihi fui&longs;&longs;e ad<lb/>iutores in&longs;igni peritia, & in experiundo &longs;edulitate, ac <lb/>diligentia claros Petrum Petitum, & Danielem <lb/>Auberium Maurerium; ac nihil tamen vnquam mihi, <lb/>quale tu narras, contigi&longs;&longs;e. </s>

<s>Nam v&longs;urpatis globis <lb/>duobus altero plumbeo vnius vnciæ, altero ligneo <lb/>drachmæ vnius cum triente, fuit &longs;emper eadem proxi<lb/>mè ratio, quam in Re&longs;pon&longs;ione iam de&longs;crip&longs;i, exhibita; <lb/>& cùm aberratum ab ea &longs;en&longs;ibiliùs e&longs;t, ecce quid <expan abbr="adh&utilde;c">adhunc</expan> <lb/><expan abbr="præ&longs;tit&utilde;">præ&longs;titum</expan> fuerit iis numeris, quos ip&longs;e habes. </s>

<s>Plumbeus, <lb/>cùm ex diametro vna extuli&longs;&longs;et vncias 7, dr. </s>

<s>1: extu<lb/>lit deinceps ex tribus 11, 3: ex quinque 14, 2: ex &longs;eptem <lb/>16, 3: ex nouem 17, 6: cùm iuxta tuam ob&longs;eruationem <lb/>efferre debui&longs;&longs;et ex tribus 14, 2: ex quinque 21, 3: ex <lb/>&longs;eptem 28, 4: ex nouem 35. 5. Ligneus, <expan abbr="c&utilde;">cum</expan> ex diametro <lb/>vna extuli&longs;&longs;et drachmas quindecim, extulit deinceps <lb/>ex tribus 24, ex quinque 30, ex &longs;eptem 36, ex <lb/>nouem 41: Cùm debui&longs;&longs;et per te efferre ex tribus 30, <lb/>ex quinque 45, ex &longs;eptem 60: ex nouem 75. Immane <lb/>quanto di&longs;crimine! Et non cau&longs;&longs;or quidem proptereà <lb/>cuam fidem; &longs;ed e&longs;t cur demirer profitentem te <emph type="italics"/>veram, <lb/>ac certam &longs;cientiam<emph.end type="italics"/> in hac Experientia, vt <emph type="italics"/>clara, facili, <lb/>indubia<emph.end type="italics"/> fundatam, &longs;ic iam hærere, qua&longs;i priùs expertus <lb/>nihil fueris; ac non au&longs;is hanc operationem, tanquam <lb/>certam proponere, partim Bilancis incu&longs;ans vitium, <lb/>quæ exacta fortè non fuerit, partim quampiam occu<lb/>pationem, quæ te ob&longs;eruantem interruperit. </s>

<s>Profe<lb/>ctò enim Tu, &longs;i quis alius, certus e&longs;&longs;e huius rei debui&longs;ti; <lb/>vt qui non modò fueris profe&longs;&longs;us te certam de ip&longs;a <pb pagenum="150"/>&longs;cientiam tradere; &longs;ed etiam iam &longs;cientiæ, &longs;eu Demon<lb/>&longs;trationis, qua feceris certam, Vindicias con&longs;cribas. <lb/></s>

<s>Non moror item, quòd po&longs;tquàm mihi f&oelig;licitati cui<lb/>piam verti&longs;ti, <emph type="italics"/>incidi&longs;&longs;e mihi in mentem vt quidpiam, quod <lb/>tu non inq<gap/>i&longs;i &longs;&longs;es, inquirerem<emph.end type="italics"/> (vtcumque ea videri po&longs;&longs;it <lb/>non tam fui&longs;&longs;e f&oelig;licitas, quàm non-nihil maior circa <lb/>rem non raram, neque inex&longs;pectatam atter<gap/>tio) non <lb/>moror, inquam, quòd temperâris aduer&longs;atiuâ, <emph type="italics"/>&longs;ed ve<lb/>reor:<emph.end type="italics"/> quippe cùm fauente mihi Experientia &longs;pon&longs;orem <lb/>me dem, non e&longs;&longs;e quamobrem de me, deque Galileo <lb/>verearis, quatenus dixi <emph type="italics"/>pondus duplum non eleuari ante <lb/>ca&longs;um ex altitudine quadrupla, neque triplum ante ca&longs;um ex <lb/>nonupla, &c.<emph.end type="italics"/> &longs;ed e&longs;&longs;e quamobrem verearis de te, qui <lb/>præ&longs;tare perinde te, refragante Experientiâ, &longs;pon&longs;orem <lb/>non po&longs;&longs;is. </s>

<s>Non in&longs;to demùm quanto oporteat te tuæ &longs;on<lb/>tentiæ amore teneri, qui etiam quæ&longs;ieris ex qualicum<lb/>que illo progre&longs;&longs;u remedium, quò iubere po&longs;&longs;es <lb/>viderem, <emph type="italics"/>ex his adhûc (quod totius controuer&longs;iæ caput <lb/>foret) æqualibus spatiis æqualia acquiri velocitatis augmen<lb/>ta:<emph.end type="italics"/> cùm, vt præteream me longè &longs;ecus inter experiun<lb/>dum vidi&longs;&longs;e, vti ex facta gemina comparatione clarum <lb/>e&longs;t; tu, mendo&longs;o etiam progre&longs;&longs;u, tanquam vero &longs;up<lb/>po&longs;ito, id videre me iubeas, quod ne ip&longs;e quidem aut <lb/>videas, aut videre po&longs;&longs;is. </s>

<s>Siquidem, vt videres, opor<lb/>teret quemadmodum velocitas acqui&longs;ita ex &longs;patio, al<lb/>titudineve diametri vnius, exprimitur eleuatione pon<lb/>deris vnciarum 5, dr. </s>

<s>2: ita acqui&longs;itam ex &longs;patio duplo, <lb/>&longs;iue ex altitudine diametrorum duntaxat duarum, <lb/>exprimi eleuatione dupli ponderis, vnciarum videlicet <pb pagenum="151"/>10, dr. </s>

<s>4; & ex triplo, &longs;iue ex altitudine diam etrorum <lb/>trium, eleuatione tripli, &longs;eu <expan abbr="vnciat&utilde;">vnciatum</expan> 15, dr. </s>

<s>6, cùm tu ta<lb/>men videas eleuari duplum, &longs;iue vncias 10, dr. </s>

<s>4, non <lb/>ex &longs;patio duplo, &longs;ed ex triplo, ex quo eleuari oporteret <lb/>non duplum, &longs;ed triplum, &longs;euvncias 15, dr. </s>

<s>6. Idip&longs;um <lb/>dico de cæteris ad v&longs;que altitudinem diam etrorum <lb/>nouem, ex qua attolli oporteret ponderis nonuplum, <lb/>&longs;eu vncias 47, dr. </s>

<s>2, non, vt ais, quintuplum &longs;olùm, &longs;eu <lb/>vncias 26, dr. </s>

<s>2. An placuit tibi progre&longs;&longs;us ille per nume<lb/>ros impareis, vnum, tria, quinque, &longs;eptem, nouem, quo<lb/>rum &longs;untinter &longs;e interualla æqualia? </s>

<s>Atqui oporteret <lb/>hoc ca&longs;u ex diametro vna nihil attolli ponderis, ac &longs;u<lb/>peratis deinde duabus diametris, attolli pondus &longs;im<lb/>plum, &longs;iue vncias 5, dr. </s>

<s>2, & &longs;uperatis adhûc duabus du<lb/>plum, & adhûc duabus triplum, &c: cùm tu velis ta<lb/>men ex altitudine nulla, qua&longs;i cyphra, ad altitudinem <lb/>v&longs;que integræ diametri, qua&longs;i vnius, attolli pondus &longs;im<lb/>plum, &longs;eu vncias 5, dr. </s>

<s>2, adeò proinde, vt &longs;i per &longs;patia <lb/>æqualia <expan abbr="m&etilde;&longs;urata">men&longs;urata</expan> diametris procedere velis, nece&longs;&longs;e &longs;it, <lb/>vt po&longs;t primam diametrum, cui velocitatem attollen<lb/>tem &longs;implum attribuis, accipias &longs;ecundam, cui attol<lb/>lentem duplum attribuas, &c. </s>

<s>Dicerem id fortè placui&longs;&longs;e, <lb/>quòd exi&longs;timâris videri vtcumque congruere cum eo, <lb/>quod defendispo&longs;teà, primum primæ partis dimidium, <lb/>qua&longs;i pro nihilo haberi, ac numerandum motum dun<lb/>taxat ab initio v&longs;que &longs;ecundi dimidii, & pergendum <lb/>per <expan abbr="&longs;ecundã">&longs;ecundam</expan>, tertiam, & cæteras parteis, quarum quæli<lb/>bet duo dimidia contineat. </s>

<s>Verum, vt taceam notum <lb/>e&longs;&longs;e, quàm parùm cohærenter id fieret, nihil e&longs;t cur <lb/>tempus in coniectando teram, cùm etiam pigeat terere <pb pagenum="152"/>in iis, quæ dicuntur apertè. </s>

<s><emph type="italics"/>Sed memineris totius &longs;ummi ponderis ex vnius diametri <lb/>altitudine eleuati, non e&longs;&longs;e in &longs;equentibus operationibus acci<lb/>piendum duplum, triplum, quadruplum, &c. </s>

<s>&longs;ed &longs;olius exce&longs;<lb/>&longs;us vltra æquilibrium a&longs;&longs;umendum e&longs;&longs;e duplum, triplum, qua<lb/>druplum, &c. </s>

<s>quærimus enim accelerationis, ac velocitatis <lb/>effectum, ad quem non pertinet æquilibrium.<emph.end type="italics"/></s>

<s>Nequicquam profectò &longs;ollicitus es. </s>

<s>Vtcumque enim <lb/>exi&longs;timâris id e&longs;&longs;e <expan abbr="nece&longs;&longs;ari&utilde;">nece&longs;&longs;arium</expan>, donec ea tibi in&longs;edit opi<lb/>nio, vt ex totidem diametris totidem præcisè eleuaren<lb/>tur pondera, præter æquilibrium, globo paria: nunc ta<lb/>men, cùm videas nihil e&longs;&longs;e nece&longs;&longs;e ad&longs;tringi, neque ad <lb/>diametrum, neque ad pondus (imò neque ad figuram <lb/>globi, &longs;i modò corpus eiu&longs;modi &longs;it, quod lancem ex <lb/>æquo circa medium afficiat) &longs;ed liberum e&longs;&longs;e quamli<lb/>bet altitudinem pro prima a&longs;&longs;umere, & quodlibet pon<lb/>dus, quod &longs;ummum ex ea attolletur pro pondere pri<lb/>mo: con&longs;tat tale pondus, quodcum que illud &longs;it, & <lb/>æquilibrio quidem comprehen&longs;o, germanam e&longs;&longs;e men<lb/>&longs;uram eius impetus, qui exprimitur ex ca&longs;u à tali altitu<lb/>dine; cùm &longs;i aliquid addatur tali ponderi, impetus &longs;it <lb/>minor, &longs;i detrahatur aliquid, etiam ex æquilibrio, &longs;it <lb/>maior. </s>

<s>Quanquam & &longs;i per&longs;tes putare detrahendum <lb/>e&longs;&longs;e <expan abbr="æquilibri&utilde;">æquilibrium</expan>, nihil erit quamobrem repugnem, aut <lb/>quamobrem ip&longs;e proptereà lucratus aliquid videaris, <lb/>cùm eo detracto tam ex primo, quàm cæteris ponderi<lb/>bus, quæ pondera &longs;uperfutura, &longs;unt pari progre&longs;&longs;ione <lb/>&longs;int con&longs;equutura. </s>

<s>Nam in exemplo quidem tuo, v g. <lb/></s>

<s>&longs;eu numeros 5.2, 10.4, 15.6, 21, 26.2, detracto æqui<lb/>librio, &longs;eu comprehen&longs;o habeas (quod tibi forta&longs;&longs;is <pb pagenum="153"/>exprimendum fuit) eadem continuò erit progre&longs;&longs;io <lb/>quinarii numeri cum quadrante, &longs;eu dr. </s>

<s>2; vt putà, &longs;eu <lb/>dicas 4.2, 9.4, 14.6, 20, 25.2: &longs;eu 6.2, 11.4, 16.6, 22, 27.2. <lb/>Sed res e&longs;t per &longs;e &longs;atis manife&longs;ta. </s>

<s><emph type="italics"/>Nunc autem, Vir per&longs;picacißime, cùm in ea tota re <lb/>diligentiam tuam, ac &longs;olertiam vehementer probem, & exa<lb/>ctiorem adhûc à te ex&longs;pectem; perinde probare non po&longs;&longs;um <lb/>quæ &longs;equuntur reliqua: & primùm quod ais numero xxviii. <lb/></s>

<s>fore, vt &longs;i penes globorum diametros men&longs;urandæ e&longs;&longs;ent eo<lb/>rum velocitates, demißi ex eadem altitudine globi duo eiu&longs;<lb/>dem materiæ, &longs;ed mole inæquales, pari celeritate non de&longs;cen<lb/>derent. </s>

<s>Ponis autem exempli gratiâ duos globos, quorum <lb/>vnus &longs;it diametro decies maiore, quàm alter, & minorem <lb/>hunc dicis decuplò velociùs altero moueri. </s>

<s>Sed &longs;agacitas tua <lb/>hoc loco non aduertit primùm, à maiore globo vnius diametri <lb/>de&longs;cen&longs;u tantum velocitatis acquiri, quantum à minore globo <lb/>decem diametrorum de&longs;cen&longs;u acquiritur: nihilque omninò re<lb/>ferre, &longs;i è duabus velocitatibus inter &longs;e æqualibus altera plu<lb/>reis in parteis &longs;ubdiuidatur, quæ &longs;imùl iunctæ alteram exæ<lb/>quent; &longs;icut nec ratio acceleratæ velocitatis per quodlibet <lb/>spatium variabitur, &longs;i partes eiu&longs;dem &longs;patij æquales ab vno <lb/>minores de&longs;ignentur, ab altero maiores. </s>

<s>Deinde, illud etiam <lb/>non aduertit, vt &longs;i penes spatii parteis æqualeis in quacumque <lb/>ratione acceptas, accelerationis velocitas men&longs;uretur, futurum <lb/>omninò &longs;it, vt perinde eorumdem globorum diametris ea<lb/>dem quoque accelerationis velocitas men&longs;uretur; præ&longs;ertim &longs;i <lb/>diametri (vt in propo&longs;ito exemplo) &longs;upponantur commen&longs;u<lb/>rabiles; quod & ex ip&longs;a rei natura, & ex proximè adducto <lb/>eius exemplo, qui &longs;patium quodlibet, per quod fieret de&longs;cen&longs;us, <lb/>nunc maiores in parteis diuideret, nunc in minores, euidenter<emph.end type="italics"/><pb pagenum="154"/><emph type="italics"/>manife&longs;tum e&longs;t. </s>

<s>Non rectè igitur concludis globos eiu&longs;dem <lb/>naturæ, &longs;ed mole inæqualeis, inæquali velocitate de&longs;cen&longs;uros, <lb/>&longs;i penes eorum diametros expenderentur eorum velocitates.<emph.end type="italics"/></s>

<s>Quoniam igitur me tam parùm e&longs;&longs;e per&longs;picacem, <lb/>&longs;agacemque, arguis, vt quod dixi de duobus globis <lb/>non aduerterim; age di&longs;quiramus, tua-ne per&longs;picacia, <lb/>& &longs;agacitas aduerterit &longs;atis eam, quam in&longs;titui&longs;ti ani<lb/>maduer&longs;ionem. </s>

<s>Ego quidem &longs;oleo in rebus, quæ di<lb/>cuntur graues, grauitatem duplicem (duplexve pon<lb/>dus) di&longs;tinguere. </s>

<s>Vnam appello Simplicem, eam nem<lb/>pe, quæ conuenit rei etiam quie&longs;centi: vt putà qualem <lb/>habet lapis, dum immotus terram &longs;uppo&longs;itam pre<lb/>mit, aut claua immota &longs;uppo&longs;itum cuneum. </s>

<s>Alteram <lb/>Adiectitiam voco, eam putâ, quæ rei ex motu accele<lb/>rato aduenit, & de&longs;inente motu euane&longs;cit; qualem &longs;ci<lb/>licet habet lapis, prout ex alto decidit, aut claua, prout <lb/>tum decidit, tum robu&longs;ta quoque impingitur manu. <lb/></s>

<s>Cùm verò &longs;implex grauitas men&longs;ura adiectitiæ &longs;it, qua<lb/>tenus pro exce&longs;&longs;u grauitatis &longs;implicis, quo vnum cor<lb/>pus &longs;uperat aliud, exce&longs;&longs;us quoque e&longs;t adiectitiæ, &longs;i <lb/>vtrumque quidem ex eadem decidat altitudine: ideò <lb/>&longs;implici grauitate duorum corporum pondere inæqua<lb/>lium data, habeo adiectitiam vtriu&longs;que ex pari ca&longs;u <lb/>acqui&longs;itam, in eadem ratione, proportioneve, qua &longs;im<lb/>plicem: Adeò vt, &longs;i &longs;implex vnius &longs;it librarum decem, <lb/>& alterius centum; vbi adiectitia prioris fuerit centum, <lb/>po&longs;terioris futura &longs;it mille. </s>

<s>Et quia grauitas vtriu&longs;que <lb/>adiectitia ex effectu, &longs;eu percu&longs;&longs;ione in rem &longs;ubiectam <lb/>facta cogno&longs;citur: ideò rem attendo penes percu&longs;&longs;io<lb/>nem, quatenus ip&longs;a notior e&longs;t, faciléque intelligitur, <pb pagenum="155"/>vbi percu&longs;&longs;io facta per vnum corporum illorum nota <lb/>fuerit, notam quoque eam fore, quæ fict per alterum: <lb/>adeò vt &longs;i, exempli gratiâ, prius corpus in vnam bi<lb/>lancis lancem decidens eam percu&longs;&longs;ionem faciat, qua <lb/>altera cum pondere centum librarum attollatur, deci<lb/>dens po&longs;terius eam facturum &longs;it, qua attollatur cum <lb/>pondere librarum mille. </s>

<s>Iam, cùm tua verba fuerint, <lb/><emph type="italics"/>Tantam præcisè corporis e&longs;&longs;e velocitatem, quantus impetus, <lb/>quantàque ip&longs;a percußio fuerit: impetum enim omnem, & <lb/>percußionem ex velocitate e&longs;&longs;e, imò impetum ip&longs;um velocita<lb/>tem e&longs;&longs;e nullóque hæc ab inuicem di&longs;crimine dirimi: vt me<lb/>ritò proinde quaratione accre&longs;cit velocitas, eadem impetus, & <lb/>percußio augeantur:<emph.end type="italics"/> eapropter licet dicere velocitates <lb/>corporum illorum in fine motus ita &longs;e habere, vt &longs;i à <lb/>priore acqui&longs;iti &longs;int decem gradus velocitatis, quibus <lb/>pondus decem librarum adauctum &longs;it v&longs;que ad cen<lb/>tum, acqui&longs;iti etiam fuerint decem gradus à po&longs;teriore, <lb/>quibus pondus centum librarum adauctum fuerit v&longs;<lb/>que ad mille. </s>

<s>Et certè i&longs;ta graduum velocitatis æquali<lb/>tas in proportione partium grauitatis adie ctitiæ funda<lb/>ta, dici pote&longs;t cau&longs;&longs;a cur duo corpora pondere, &longs;iue <lb/>grauitate &longs;implici &longs;ummè inæqualia (vt &longs;i alterum pen<lb/>dat libras mille, alterum non ampliùs, quàm vnciam) <lb/>æquali cadant tempore; vnde & vici&longs;&longs;im arguantur <lb/>e&longs;&longs;e æqui-velocia. </s>

<s>Accedamus propiùs ad hypothe&longs;in. </s>

<s>O&longs;tendere <lb/>volui velocitatis gradus men&longs;urandos non e&longs;&longs;e, vt tu <lb/>a&longs;&longs;erebas, penes globorum diametros, quæ men&longs;ura<lb/>rent &longs;ingulos ca&longs;us. <emph type="italics"/>Sunto enim,<emph.end type="italics"/> inquam, <emph type="italics"/>globi, verbi <lb/>caußâ, duo ex eadem materia, quorum vnus &longs;it diametro<emph.end type="italics"/><pb pagenum="156"/><emph type="italics"/>decies maiore, quàm alius, & dimittatur vterque ex eadem<gap/><lb/>altitudine: tunc, quia minor decidet per diametros decuplò <lb/>plureis, quàm mator, fiet, vt attollat pondera &longs;ibi æqualia <lb/>decuplò multipliciora, quàm attollat maior ex &longs;ibi æqualibus: <lb/>Quare & &longs;equitur, vtper idem &longs;patium feratur decuplò ve<lb/>lociùs, ac decuplò citiùs, temporeve decies breuiore perue<lb/>niat ad lancem, quàm maior: hoc autem con&longs;tat quàm fal&longs;um <lb/>&longs;it; cùm, &c.<emph.end type="italics"/></s><s> Con&longs;idera iam, an quid dicerem, non ad<lb/>uerterim. </s>

<s>E&longs;to pondus maioris globi mille vnciarum, <lb/>& clatus globus vna &longs;ui diametro &longs;upra lancem, in eam <lb/>dimittatur; tum gradum velocitatis iuxta te acqui&longs;ie<lb/>rit, quo lancem percutiens alteram attollat cum pon<lb/>dere vnciarum mille, præter æquilibrium. </s>

<s>E&longs;to pon<lb/>dus minoris, vnius, & dimittatur &longs;imiliter globus ex <lb/>vna &longs;ui diametro, tum etiam gradum velocitatis vnum <lb/>iuxta te acqui&longs;ierit, quo lancem vnam percutiens alte<lb/>ram attollet cum pondere vnius vnciæ vltra æquili<lb/>brium. </s>

<s>Attollatur po&longs;teà, & dimittatur minor globus <lb/>ex &longs;ecunda &longs;ui diametro, tum velocitatis gradus acqui<lb/>&longs;ierit duos, quibus attollantur duæ vnciæ, ac pari modo <lb/>ex tertia diametro attollentur tres, ex quarta quatuor, <lb/>& &longs;ic deinceps, quov&longs;que ex decima, hoc e&longs;t ex altitu<lb/>dine, è qua dimi&longs;&longs;us fuerit maior globus, attollantur <lb/>decem. </s>

<s>Itaque ex duobus illis globis ex eadem altitu<lb/>dine dimi&longs;&longs;is, percutiet minor lancem impetu decuplò <lb/>maiore, proportione &longs;ui ponderis, quàm maior &longs;ui re&longs;<lb/>pectu percutiat (cùm ille &longs;cilicet attollat decuplum &longs;ui <lb/>ponderis, i&longs;te attollat &longs;olùm tantumdem). Igitur &, <lb/>cùm impetus, ac velocitas idem &longs;int, erit velocitas mi<lb/>noris maior decuplò per illud &longs;patium, quàm maioris, <pb pagenum="157"/>&longs;icque globus minor illud tempore decies breuiore, <lb/>quàm maior percurret. </s>

<s>Atque ego quidem &longs;ic ad rem <lb/>aduerti. </s>

<s>Ais iam tu, <emph type="italics"/>meam &longs;agacitatem non aduerti&longs;&longs;e, à <lb/>maiore globo vnius diametri de&longs;cen&longs;u tantum velocitatis ac<lb/>quiri, quantum à minore globo decem diametrorum de&longs;cen&longs;u <lb/>acquiritur.<emph.end type="italics"/></s><s> Verùm cùm ego aduerterim rem &longs;e reip&longs;a <lb/>ita habere: aduerti tamen &longs;imùl id aduer&longs;ari tuis de<lb/>cretis, vnde & tua &longs;agacitas aduerti&longs;&longs;e duntaxat vide<lb/>tur quid fieret, non verò quid ex propriis a&longs;&longs;ertionibus <lb/>&longs;equeretur. </s>

<s>Pergis <emph type="italics"/>nihil omninò referre, &longs;i ex duabus ve<lb/>locitatibus inter &longs;e æqualibus altera plureis in parteis &longs;ub<lb/>diuidatur. </s>

<s>quæ &longs;imùl iunctæ alteri exæquentur, &longs;icut nec ratio <lb/>acceleratæ velocitates per quodlibet &longs;patium variabitur, &longs;ipar<lb/>tes eiu&longs;dem spatii æquales ab vno minores de&longs;ignentur, ab <lb/>alio maiores:<emph.end type="italics"/> at nihil refert quidem, &longs;i velocitates æqua<lb/>les &longs;int, vt illæ reuerâ per illud &longs;patium &longs;unt: &longs;ed pluri<lb/>mùm refert, &longs;i inæquales &longs;int, vt tuis ex decretis e&longs;&longs;e de<lb/>ducuntur, Quod deinde &longs;ubdis, diuer&longs;um non e&longs;t. </s>

<s><emph type="center"/>IN ARTICVLOS XXIX. XXX. XXXI. XXXII. XXXIII.<emph.end type="center"/></s>

<s><emph type="center"/>De Tempore, quo R. P. colligit parteis &longs;patij <lb/>&longs;ingulas decur&longs;um non iri.<emph.end type="center"/></s>

<s><emph type="italics"/>Nihilo rectiùs numero xxx: etiam reprehendis, quòd <lb/>&longs;ine respectu ad tempus definitionem accelerati motus aut <lb/>inqui&longs;ierim, aut etiam con&longs;tituerim. </s>

<s>Et&longs;i enim priùs accele<lb/>rationem motus cum partibus spatij, quàm cum partibus <lb/>temporis æqualibus contulerim, cùm tamen vtrumque abun<lb/>dè, ac diligenter eadem Epi&longs;tola factum à me cerneres; &longs;atis <lb/>iu&longs;tam huius repreben&longs;ionis an&longs;am accipere inde non potui&longs;ti.<emph.end type="italics"/><pb pagenum="158"/><emph type="italics"/>Volui&longs;&longs;es fortaßis (quod &longs;ine dubio facere potui) vt motum <lb/>vniformiter acceleratum potius definirem e&longs;&longs;e eum,<emph.end type="italics"/> qui tem<lb/>poribus æqualibus velocitatis augmenta in continua <lb/>ratione dupla reciperet: <emph type="italics"/>&longs;ed cùm Galileus æqualia cele<lb/>ritatis incrementa partibus temporis æqnalibus tribueret, <lb/>procliue fuit, vt æqualia illa velocitatis augmenta statim &longs;pa<lb/>tij potiùs, quàm temporis partibus æqualibus attribuerentur. <lb/></s>

<s>Sed hæc leuiora &longs;unt.<emph.end type="italics"/></s>

<s>Dictum hucv&longs;que e&longs;t de tuæ Demon&longs;trationis A&longs;<lb/>&longs;umptione. </s>

<s>Probare deinceps volui&longs;ti con&longs;equutionem <lb/>Propo&longs;itionis; veruntamen duo qua&longs;i membra huiu&longs;ce <lb/>Probationis fuerunt. </s>

<s>Nam po&longs;tquàm ex tuo &longs;upe<lb/>riore Experimento collegi&longs;ti <emph type="italics"/>ex dupla di&longs;tantia celerita<lb/>tem acquiri duplam, ex tripla triplam, &c.<emph.end type="italics"/> agendum e&longs;&longs;e <lb/>deinceps cen&longs;ui&longs;ti de Tempore, quòd <emph type="italics"/>ad ip&longs;um quoque <lb/>celeritas motus respectum includat:<emph.end type="italics"/> ac &longs;ubinde adnixus es <lb/>declarare <emph type="italics"/>Primùm,<emph.end type="italics"/> non &longs;ic decurri parteis &longs;patij, vt &longs;e<lb/>cunda percurratur dimidio temporis, quo prima, tertia <lb/>triente, quarta quadrante, &c. </s>

<s>vtcumque id videatur <lb/>&longs;equi ex ratione illa incre&longs;centis &longs;patiorum in&longs;tar ce<lb/>leritatis: <emph type="italics"/>Secundò<emph.end type="italics"/> autem &longs;ic potiùs decurri, vt initio <lb/>&longs;umpto ab inferiore primæ partis dimidio, quod cer<lb/>to tempore percurratur, &longs;ecunda, quæ eius dimidij &longs;it <lb/>dupla, percurratur pari tempore: tertia verò triente <lb/>eiu&longs;dem temporis, tanquam re&longs;pondens infimo eiu&longs;<lb/>dem primæ partis trienti: quarta quadrante, vt re&longs;<lb/>pondens quadranti, atque ita de cæteris; Ex quibus <lb/>&longs;ubinde &longs;equatur, vt quemadmodum pars &longs;ecunda <lb/>æquali tempore percurritur, &longs;ic percurrantur duæ &longs;i<lb/>mùl &longs;equentes; &longs;ic quatuor &longs;imùl &longs;uccedentes; &longs;ic <pb pagenum="159"/>aliæ octo, &c. </s>

<s>Itaque dicendum e&longs;t prius de priore <lb/>capite. </s>

<s>Interim <expan abbr="aut&etilde;">autem</expan> (circa id, quod heic obiicis) Recte<lb/>ne, &longs;it, an perperam factum, quod admonuerim <emph type="italics"/>non de<lb/>bui&longs;&longs;e temporis mentionem in definitione accelerati motus <lb/>omitti;<emph.end type="italics"/> contextus meus, quem retexere nihil e&longs;t opus, <lb/>&longs;atis o&longs;tendit. </s>

<s>Quod autem deinceps <emph type="italics"/>Epistola eadem <lb/>acceleratum motum non minùs diligenter cum tempore, quàm <lb/>cum &longs;patio contuleris:<emph.end type="italics"/> idip&longs;um arguit non debui&longs;&longs;e mi<lb/>norem temporis rationem <emph type="italics"/>in eo definiendo<emph.end type="italics"/> haberi, quàm <lb/>&longs;patii (vt præteream potui&longs;&longs;e quoque haberi non<lb/>nihil maiorem, quatenus à me in&longs;inuatum e&longs;t) ac futu<lb/>ram deinceps fui&longs;&longs;e comparationem tam cum illo, <lb/>quàm cum i&longs;to cohærentiorem. </s>

<s>Quod &longs;ubiicis <emph type="italics"/>me <lb/>fortaßis volui&longs;&longs;e;<emph.end type="italics"/> idip&longs;um e&longs;t, quod potiùs veritatis amo<lb/>re volui&longs;&longs;em, &longs;i licui&longs;&longs;et quidem per te: &longs;ed nihil heic <lb/><expan abbr="præuertend&utilde;">præuertendum</expan> e&longs;t: non &longs;anè, <emph type="italics"/>quòd i&longs;ta &longs;unt leuia;<emph.end type="italics"/> quandò <lb/>in iis cardo controuer&longs;iæ vertitur: &longs;ed quòd &longs;it de ra<lb/>tione dupla temporibus æqualibus &longs;peciatim dicen<lb/>dum inferiùs. </s>

<s><emph type="italics"/>Grauius e&longs;t, optime<emph.end type="italics"/> G<emph type="italics"/>a&longs;&longs;ende, quòd numero xxxi. </s>

<s>xxxii. <lb/></s>

<s>xxxiii. </s>

<s>non &longs;olum contra expre&longs;&longs;am Epistolæ meæ &longs;ententiam, <lb/>&longs;ed contra euidentem quoque Demon&longs;trationis lucem velis à me <lb/>ea dici, quæ verbis expreßis nego, quæque fal&longs;a e&longs;&longs;e non tan<lb/>tum pronuncio, &longs;ed clarè etiam, atque euidenter demon&longs;tro: ex <lb/>ii&longs;que deinde, tanquam meis, ea mihi ab&longs;urda affingas, in <lb/>quæ nemo, quantumvis hebes impingat. </s>

<s>Demon&longs;trare certé <lb/>debueras ea, quæ à me <expan abbr="tanquã">tanquam</expan> fal&longs;a reiecta vide bas, ex consti<lb/>tutis à me principiis nihilominus &longs;equi, antequam eadem, vt <lb/>mea decreta impeteres: imò id &longs;olum faciendum tibi fuerat, <lb/>vt me caußæ præuaricatorem euinceres, qui ea ip&longs;a fal&longs;a<emph.end type="italics"/><pb pagenum="160"/><emph type="italics"/>demon&longs;trarem, quæ ex meis nihilominus principiis clara, eui<lb/>dentique ratione inferrentur. </s>

<s>Quid enim tibi opus fuit mul<lb/>tis paginis impugnare ea, quæ iam expugna&longs;&longs;em: & conqui&longs;i<lb/>tis vndique rationibus fal&longs;a o&longs;tendere, quæ fal&longs;a e&longs;&longs;e prior <lb/>agno&longs;cerem? </s>

<s>Et tamen nihil e&longs;t in tota tua Epi&longs;tola aliud, in <lb/>quo acrius, animo&longs;iu&longs;que depugnes.<emph.end type="italics"/></s>

<s>Quomodo quæ&longs;o, optimus, & non pe&longs;&longs;imus po<lb/>tiùs e&longs;&longs;em, &longs;i is quidem, quem tu me hoc articulo de<lb/>pingis, forem? </s>

<s>Verùm, quia num tibi quid affinxerim: <lb/>num quædam à te reiecta vt fal&longs;a, ex tuis principiis &longs;e<lb/>qui non o&longs;tenderim; num po&longs;tquam tu quædam ex<lb/>pugna&longs;ti vt fal&longs;a, ego non tam illa, quàm ex illis vt <lb/>tuis, cætera &longs;uperfluè impugnauerim; quia, inquam <lb/>num i&longs;ta &longs;e verè, fal&longs;óve habeant, cogno&longs;cendum e&longs;t <lb/>ex ijs, quæ à te &longs;ubiiciuntur; idcircò nihil e&longs;t, <lb/><figure id="fig38"></figure><lb/>quod ad i&longs;ta regeri generatim debeat. </s>

<s><emph type="italics"/>Atque in primis, eandem iterùm mihi Propo&longs;itio<lb/>nem affingis, quam iam &longs;upra numero<emph.end type="italics"/> 7. <emph type="italics"/>indicaui, <lb/>& in hunc locum examinandam reieci. </s>

<s>Vis enim, <lb/>& &longs;iue demon&longs;tratione,s&s&longs;ine vlla vel probabili ratione <lb/>ais, & qua&longs;i pro tuo iure &longs;upponis,<emph.end type="italics"/> graue de&longs;cen<lb/>dens per &longs;patium AB in parteis quotlibet <lb/>æqualeis diui&longs;um, percurrere partem &longs;ecundam <lb/>DE, in dimidio eius temporis, quo percurritur <lb/>prior pars AD, <emph type="italics"/>& quod idem est,<emph.end type="italics"/> partem DE per<lb/>curri velocitate dupla eius velocitatis, qua tran&longs;<lb/>curritur AD. </s>

<s>Quàm falsò repetas hanc Propo&longs;itionem tibi <lb/>à me affictam, feci abundè manife&longs;tum, cùm id <lb/>obiter non &longs;um prætergre&longs;&longs;us, quod tu citato <pb pagenum="161"/>loco, hoc e&longs;t, in articulum xii, attigeras obiter &longs;olùm. <lb/></s>

<s>Quippe tuis verbis recitatis, & deducta occa&longs;ione, ob <lb/>quam illa texueras, demon&longs;tratum e&longs;t tuam fui&longs;&longs;e, <lb/>quam iam inficiaris, expre&longs;&longs;am &longs;ententiam; heincque <lb/>adeò probatum manet me non modò probabili, &longs;ed <lb/>conuincenti etiam ratione (ni&longs;i te velis Paralogi&longs;tam, <lb/>quod ab&longs;it vt cen&longs;eam, ridiculo&longs;i&longs;&longs;imum haberi) ac <lb/>non meo iure, &longs;ed ex tuis verbis hanc &longs;uppo&longs;itionem, <lb/>qua&longs;i tuam &longs;upponere, G<emph type="italics"/>raue de&longs;cendens per spatium <lb/>AB in parteis quotlibet æqualeis diui&longs;um, percurrere partem <lb/>&longs;ecundam DE<emph.end type="italics"/> (quæ illeic fuit BC) <emph type="italics"/>in dimidio eius tem<lb/>poris, quo percurritur prior pars AD<emph.end type="italics"/> (quæ illeic AB) & <lb/>quod idem e&longs;t, <emph type="italics"/>partem DE percurri veiocitate dupla eius, <lb/>velocitatis, qua tran&longs;curritur AD.<emph.end type="italics"/></s><s> Sequitur. </s>

<s><emph type="italics"/>At Primum, quid amabò, caußæ est, cur cùm antè nume<lb/>ro tuæ Re&longs;pon&longs;ionis X. volueris velocitatem per totam AE <lb/>duplam e&longs;&longs;e velocitatis per primam partem AD, idque ex <lb/>meis quoque principiis nece&longs;&longs;arium e&longs;&longs;e a&longs;&longs;erueris: nunc, mutato <lb/>con&longs;ilio, velocitatem per &longs;olam partem DE velocitatis per <lb/>partem AD acqui&longs;itæ duplam e&longs;&longs;e contendas: & quidem, vt <lb/>ais, ex principiis item meis?<emph.end type="italics"/></s>

<s>Quid cau&longs;&longs;æ &longs;it, quæris? </s>

<s>Non &longs;anè mutatio con&longs;ilij <lb/>in me; &longs;ed quæ fal&longs;orum principiorum, incommodo<lb/>rumque ex iis deductorum variatio in te ob&longs;eruatur. <lb/></s>

<s>Nam quòd velis quidem velocitatem acqui&longs;itam in E <lb/>e&longs;&longs;e duplam velocitatis acqui&longs;itæ in D, vt &longs;patium AE, <lb/>&longs;patij AD duplum e&longs;t: contendo iam velocitatem, qua <lb/>percurritur DE, e&longs;&longs;e duplam eius, qua tran&longs;curritur AD, <lb/>&longs;eu, quæ acquiritur per AD: &, quòd tu contendas ab <lb/>A, v&longs;que ad E, augeri æquabiliter, idcircò &longs;um argu-<pb pagenum="162"/>mentatus articulo illo velocitatem per totam AE, du<lb/>plam e&longs;&longs;e velocitatis per totam AD. </s>

<s>Cùm hoc autem <lb/>&longs;uo iam loco demon&longs;tratum abundè &longs;it: ideò illud &longs;o<lb/>lùm, quod tu huius loci facis proprium, e&longs;t attenden<lb/>dum. </s>

<s>Quæ&longs;o itaque; cùm velis in D acqui &longs;itum e&longs;&longs;e <lb/>vnum velocitatis gradum, & duos in E, an velis gradum <lb/>acqui&longs;itum in D, manere per ip&longs;am DE, ac e&longs;&longs;e vnum <lb/>ex iis duobus, qui acqui&longs;iti reperiuntur in E; an nolis? <lb/></s>

<s>Si velis; igitur perip&longs;am DE &longs;unt duo gradus, vnus <lb/>nempe manens, & alius, qui interim acquiritur. </s>

<s>Si no<lb/>lis; igitur oportet duos gradus, qui &longs;unt in E, acqui&longs;i<lb/>tos e&longs;&longs;e per &longs;olam DE. An-non ergo vtrovis modo <lb/>nece&longs;&longs;e e&longs;t velocitatem per &longs;olam DE, duplam e&longs;&longs;e <lb/>eius, quæ acquiritur per AD? </s>

<s>Dilemma e&longs;t, neutrum<lb/>que e&longs;t membrum, circa quod liceat tergiuer&longs;ari. </s>

<s>Nam <lb/>circa &longs;ecundum quidem, dicere nihil potes: cùm id <lb/>&longs;it tamen reuerâ tuum; quatenus, vt &longs;uperiùs quoque <lb/>adnotatum e&longs;t, vis velocitatem acqui&longs;itam per totam <lb/>DE, e&longs;&longs;e duplam acqui&longs;itæ in D, & acqui&longs;itam in D <lb/>perire: nam alioquin in E velocitas iam e&longs;&longs;et tripla, &longs;i<lb/>ue in E tres gradus e&longs;&longs;ent: cùm e&longs;&longs;e tu velis &longs;olùm duos, <lb/>& acqui&longs;itos quidem per &longs;olam DE. </s>

<s>Circa primum <lb/>autem &longs;i forta&longs;&longs;is dicas manere quidem primum gra<lb/>dum, &longs;ed nihil agere; &longs;equetur &longs;olo &longs;ecundo gradu, qui <lb/>per DE acquiretur, agente, partem DE tempore ni<lb/>hilo breuiore tran&longs;curri, quàm ip&longs;am AD: cùm etiam <lb/>per te percurratur minùs, quam dimidio. </s>

<s>Et, &longs;i dicas <lb/>agere: Aut ob &longs;ui con&longs;tantiam duplò aget ampliùs, <lb/>quàm per AD, vt &longs;uperiùs deduximus; & tunc incom<lb/>modum &longs;equetur, quod &longs;uprà quoque o&longs;ten&longs;um e&longs;t; <pb pagenum="163"/>quatenus DE percurretur præcisè triente primi tem<lb/>poris; & &longs;ecundum tempus integrum non effluet, ni&longs;i <lb/>&longs;ub partem &longs;patij octauam, quod tu vis effluere cum <lb/>ip&longs;a &longs;ecunda: Aut certè tantumdem; & tunc, quia etiam <lb/>tantumdem aget, qui gradus acquiretur per ip&longs;am <lb/>DE: recurret idip&longs;um, quod tu refugis; nempe partem <lb/>DE percurri velocitate dupla illius, qua decur&longs;a fuerit <lb/>AD. </s>

<s><emph type="italics"/>Sed neutram Propo&longs;itionem probas, aut ex &longs;tatutis à me <lb/>principiis vlla ratione deducis: & vt priorem iam &longs;uprà fal<lb/>&longs;am euici; ita nunc i&longs;tam e&longs;&longs;e impoßibilem, hac ratione cui<lb/>denter demon&longs;tro.<emph.end type="italics"/></s>

<s>Imò de Priore quidem apertè probaui; neque tu <lb/>quicquam aliud, quàm, vt aiunt, principium petii&longs;ti: <lb/>& cùm te iam dicis euici&longs;&longs;e eam fal&longs;am; notum e&longs;t quæ<lb/>&longs;tionem non e&longs;&longs;e, an fal&longs;am euiceris, &longs;ed an euiceris <lb/>non-tuam, &longs;eu ex tuis principiis minimè deductam. </s>

<s>De <lb/>Po&longs;teriore etiam rem feci apertam; neque cùm ego <lb/>in&longs;titi nullum e&longs;&longs;e in mea argumentatione Paralo<lb/>gi&longs;mum, tu potui&longs;ti vllum o&longs;tendere: & cum iam &longs;u&longs;ci<lb/>pis demon&longs;trandum eam e&longs;&longs;e impo&longs;&longs;ibilem, minimè <lb/>attendis quæ&longs;tionem non e&longs;&longs;e, an impo&longs;&longs;ibilis &longs;it, &longs;ed <lb/>ex tuis ne deducta principiis. </s>

<s><emph type="italics"/>Ex &longs;tatutis à me principiis, nece&longs;&longs;e e&longs;t, vt graue quodcum<lb/>que per spatium quodlibet, putà AB de&longs;cendens, æqualibus <lb/>temporibus spatia continuò maiora, ac maiora decurrat in con<lb/>tinua ratione dupla.<emph.end type="italics"/></s>

<s><emph type="italics"/>Ex &longs;tatutis,<emph.end type="italics"/> inquis, <emph type="italics"/>principiis:<emph.end type="italics"/> imò hæc tibi con<lb/>clu&longs;io e&longs;t; quæ & fal&longs;a e&longs;t, & non probabitur deinceps <lb/>à te, ni&longs;i ex ip&longs;i&longs;inet principiis, quæ vt fal&longs;a &longs;unt, ita <pb pagenum="164"/>nunc per ip&longs;am à te circulo in&longs;igni probantur. </s>

<s>Sed <lb/>tuum e&longs;to principium; quid inde? </s>

<s><emph type="italics"/>At hoc dato, nece&longs;&longs;arium etiam e&longs;t, vt quanto tempore gra<lb/>ue de&longs;cendens percurrit &longs;ecundam partem DE, tantò præcisè <lb/>spatium duplò minus antè percurrerit; nempe SD, quod <lb/>&longs;upponitur dimidium &longs;uperioris spatij AD.<emph.end type="italics"/></s>

<s>An-non agno&longs;cis circulum? </s>

<s>Neque enim alia ratio<lb/>ne probas &longs;patia continuò percurri in ratione dupla, <lb/>quàm quia &longs;upponis tanquam principium, partem DE <lb/>percurri tanto tempore, quantò dimidium SD. </s>

<s>Sed <lb/>& hoc e&longs;to. </s>

<s><emph type="italics"/>Nece&longs;&longs;e e&longs;t igitur, vt partes SD, & DE æquali <lb/>tempore percurrantur.<emph.end type="italics"/></s>

<s>Imò impo&longs;&longs;ibile e&longs;t; tantum abe&longs;t, vt nece&longs;&longs;arium; <lb/>neque in te e&longs;t, vt nece&longs;&longs;itatem probes, ni&longs;i priùs o&longs;ten<lb/>deris velocitates e&longs;&longs;e vt &longs;patia, quod tantum abe&longs;t, vt <lb/>hactenus quidem præ&longs;titeris, quin potiùs præ&longs;tare co<lb/>natus, tuo in Bilance Experimento, ip&longs;o euentu fueris <lb/>delu&longs;us. </s>

<s>Quanquam e&longs;to & i&longs;tud quoque. </s>

<s><emph type="italics"/>At Tempus, quo percurritur SD pars inferior ip&longs;ius <lb/>AD, nece&longs;&longs;ariò breuius e&longs;t tempore, quo decurritur pars <lb/>&longs;uperior AS (alioquin motus per AD æquabilis e&longs;&longs;et, non <lb/>autem acceleratus, vt per &longs;e manife&longs;tum e&longs;t.)<emph.end type="italics"/></s>

<s>Admitto id quidem, &longs;ed independenter ex tuis <lb/>principiis. </s>

<s><emph type="italics"/>Pars igitur DE non percurritur in dimidio totius tem<lb/>poris, quo decurritur AD, &longs;ed in tempore aliquantò breuiore.<emph.end type="italics"/></s>

<s>Id quoque admitto; &longs;ed omninò ex aliis principiis, <lb/>quàm tuis. </s>

<s><emph type="italics"/>Et con&longs;equenter pars DE non tran&longs;curritur velocitate<emph.end type="italics"/><pb pagenum="165"/><emph type="italics"/>dupla eius velocitatis, qua percurritur AD, &longs;ed velocitate <lb/>maiore.<emph.end type="italics"/></s>

<s>Et hoc admitto denique; verùm aliis prorsùs, quàm <lb/>tuis principiis per&longs;ua&longs;us. </s>

<s><emph type="italics"/>Ad hanc Demon&longs;trationem quid profers?<emph.end type="italics"/></s>

<s>Hem! quid profero? </s>

<s>Videlicet Primò tefal&longs;a v&longs;ur<lb/>pare principia, neque alia lege concludere ex ip&longs;is ve<lb/>rum, quàm &longs;i quis ex eo, quod a&longs;&longs;umat <emph type="italics"/>arbores omneis <lb/>e&longs;&longs;e in cælo,<emph.end type="italics"/> & <emph type="italics"/>Lunam e&longs;&longs;e arborem,<emph.end type="italics"/> concludat <emph type="italics"/>Lunam <lb/>e&longs;&longs;e in cælo.<emph.end type="italics"/></s><s> Secundò, committere te, vt vulgo aiunt, cir<lb/>culum, incidereve in Diallelum; vti obiter in&longs;inuatum <lb/>e&longs;t, & tota ex &longs;erie tui operis con&longs;tat. </s>

<s>Tertiò, te noua <lb/>contradictione temetip&longs;um inuoluere, dum coactus vi <lb/>&longs;uperioris dilemmatis, dicere teneris velocitatem per <lb/>DE duplam e&longs;&longs;e velocitatis per AD, & nunc a&longs;&longs;umis, <lb/>aut te proba&longs;&longs;e contendis eandem velocitatem per <lb/>DE duplam e&longs;&longs;e velocitatis per SD, quod &longs;it &longs;olùm di<lb/>midium ip&longs;ius DE. </s>

<s>Quartò te rursùs eâ implicari, <lb/>quòd cùm huc v&longs;que volueris acqui&longs;itos e&longs;&longs;e ab A in <lb/>E duos gradus, qui &longs;imùl iuncti &longs;int duplum illius, qui <lb/>acqui&longs;itus e&longs;t ex A in D; velis iam eo&longs;dem duos gra<lb/>dus e&longs;&longs;e duplum illius, qui &longs;olummodò &longs;it acqui&longs;itus <lb/>ex S in D. </s>

<s>Quintò te idcircò omnia perturbare; qua<lb/>tenus quicquid hactenus dixi&longs;ti de &longs;patio in parteis <lb/>æqualeis diui&longs;o, & incipiendo quidem ab A, vt proba<lb/>res velocitates acqui&longs;itas e&longs;&longs;e vt &longs;patia; de &longs;patiis iam, <lb/>ac velocitatibus ita loqueris, vt &longs;i incipiendum &longs;it ab S, <lb/>neglecto pror&longs;us dimidio AS. Sextò, non re&longs;ponde<lb/>re te quæ&longs;tioni; quoniam quæ&longs;tio e&longs;t, non an veloci<lb/>tas per &longs;olam DE &longs;it dupla velocitatis per AD; &longs;ed an <pb pagenum="166"/>e&longs;&longs;e duplam &longs;equatur ex tuis principiis, veluti præmo<lb/>nitum e&longs;t. </s>

<s>Po&longs;tremò te vitiosè id o&longs;tendere, quatenus <lb/>a&longs;&longs;umis vnum ex tuis principiis, cum quo Propo&longs;itio <lb/>huiu&longs;modi non cohære&longs;cat: cùm id non &longs;ufficiat, ni&longs;i <lb/>o&longs;tendas; te aut non habere aliud principium, quàm <lb/>a&longs;&longs;umptum hoc: aut habere quidem, &longs;ed ex nullo ta<lb/>men ip&longs;orum illam con&longs;equi: aut habere iure eam de te <lb/>&longs;iduciam, vt impo&longs;&longs;ibile &longs;it te tibi contradicere, ac <lb/>non clarè per&longs;picere quid ex principio quolibet vel &longs;e<lb/>quatur, vel non &longs;equatur. </s>

<s><emph type="italics"/>Eam certe, vt legitimam admittis?<emph.end type="italics"/></s>

<s>Quin imò quàm varias ob cau&longs;&longs;as cen&longs;eam reiicien<lb/>dam, tanquam &longs;puriam, habes. </s>

<s><emph type="italics"/>At, quod à te inexspectatum fuit, addis (quod in pari <lb/>ca&longs;u etiam aliàs facis) inde vel maximè mea decreta reuelli, <lb/>quòd ex iis adeò pugnantia concludantur.<emph.end type="italics"/></s>

<s>Quamobrem verò id à me e&longs;&longs;e debuit inex&longs;pecta<lb/>tum; tibi præ&longs;ertim, viro &longs;apienti, cui nihil continge<lb/>re ex inopinato debet? </s>

<s>An quia putâras non debere <lb/>me tua decreta expendere, &longs;ed in tua verba, qua&longs;i man<lb/>cipium domino addictum iurare? </s>

<s>An quia volueras, <lb/>vt &longs;i quid fal&longs;um, aut repugnans occurreret, id non <lb/>tam lenirem, vt conatus &longs;um facere, quàm omninò di&longs;<lb/>&longs;imularem? </s>

<s>An quia contenderas, vt quicquid id fo<lb/>ret, nihil aliud, quam plauderem, & nihil con&longs;cientiam <lb/>reueritus, creditæ mihi veritati remitterem nuncium, vt <lb/>tibi adularer? </s>

<s>Horum nihil credo: &longs;ed tamen non &longs;a<lb/>tis per&longs;picio, quî id fecerim præter tuam &longs;pem; ni&longs;i <lb/>quòd i&longs;torum tuorum decretorum tanta per&longs;ua&longs;ione <lb/>certus fueris, vt quemadmodum eatenus incideras in <pb pagenum="167"/>creminem, qui quicquam repugnans in ijs deprehen<lb/>di&longs;&longs;et (&longs;ic enim po&longs;teà memoras) ita ego minimus <lb/>omnium, in quos po&longs;&longs;es incidere, impar pror&longs;us forem, <lb/>à quo quicquam tale deprehenderetur. </s>

<s><emph type="italics"/>Id, mi<emph.end type="italics"/> G<emph type="italics"/>a&longs;&longs;ende, &longs;i adducta demon&longs;tratione diceres, tuo <lb/>iure vtique diceres: at &longs;ine demonstratione, &longs;ine vlla veri&longs;imi<lb/>litudine id non &longs;emel tantum dicere, &longs;ed inculcare <gap/>, &longs;ed <lb/>in&longs;tare etiam acriùs, & tanquam de con&longs;tanti victoria trium<lb/>phare, vide an i&longs;tud &longs;it ingenitæ moderationis tuæ, atque etiam <lb/>dignitatis.<emph.end type="italics"/></s>

<s>Imò, mi Cazræe, Tuip&longs;e, quo iure in me &longs;ic in&longs;ultes, <lb/>Vide. </s>

<s>Iacturam fortè faciam vnius, aut alterius pagi<lb/>næ; &longs;ed nece&longs;&longs;itatem profectò imponis retexendi quid<lb/>piam ex ijs, ob quæ ita inueheris. </s>

<s>Conquereris, quòd, <lb/><emph type="italics"/>meo iure, & &longs;ine vlla demon&longs;tratione, aut veri&longs;imilitudine di<lb/>xerim, atque inculcârim tua decretainde maximè reuelli, quòd <lb/>adeò pugnantia exijs concludantur.<emph.end type="italics"/> (nam quòd alioquin <lb/>tanquam de con&longs;tanti victoria triumphârim, hoc e&longs;t, <lb/>ex&longs;ultabundus ge&longs;tierim, & qua&longs;i thra&longs;ofuerim gloria<lb/>tus; id vt à me alienum e&longs;t, ita Deo propitio, nu&longs;quam <lb/>deprehendes.) Itaque id-ne ab&longs;que iure, & &longs;ine vlla <lb/>demon&longs;tratione, aut veri&longs;imilitudine fecerim, perui<lb/>deamus. </s>

<s>Verba tua fuerant vt retuli, articulo XXXI. <lb/><emph type="italics"/>Cùm enim ex &longs;uperioribus iam euidenter co<gap/> in naturali <lb/>grauium de&longs;cen&longs;u &longs;emper ex dupla di&longs;tantia celeritatem haberi <lb/>duplam, & ex tripla di&longs;tantia triplam, atque ita deinceps ea<lb/>dem ratione celeritatem augeri; nihil procliuius e&longs;&longs;e potest, <lb/>quàm vt quis existimet accelerationem illam fieri per &longs;ubdi<lb/>ui&longs;ionem primi cuiu&longs;libet temporis in parteis &longs;emper minores, <lb/>pro multitudine, & ratione spatiorum æqualium, quæ motu<emph.end type="italics"/><pb pagenum="168"/><emph type="italics"/>decurruntur: ita videlicet, vt pars &longs;ecunda spatii ab&longs;oluatur <lb/>dimidia parte temporis, quo prima decur&longs;a e&longs;t: & tertia pars <lb/>&longs;patii tertia parte eiu&longs;dem primi temporis percurratur, & ita <lb/>de cæteris.<emph.end type="italics"/></s><s> Excepi ego, <emph type="italics"/>heic profectò rur&longs;us mirari tuam <lb/>&longs;agacitatem par e&longs;t, quatenùs eam non fugit error, qui ex po&longs;i<lb/>tione à te a&longs;&longs;erta con&longs;equitur, tamet&longs;i ip&longs;e non con&longs;equi, ex iis, <lb/>quæ &longs;equuntur, contendas.<emph.end type="italics"/></s><s> Duo heic fuerunt: <emph type="italics"/>Vnum,<emph.end type="italics"/> Er<lb/>rorem e&longs;&longs;e, quòd &longs;ecundum &longs;patium æquale percurra<lb/>tur dimidio illius temporis, quo primum; tertium trien<lb/>te, quartum quadrante, atque ita de reliquis: <emph type="italics"/>Alterum,<emph.end type="italics"/><lb/>huiu&longs;modi errorem con&longs;equi ex tua pofitione, quòd <lb/>celeritates &longs;e habeant vt &longs;patia, atque adeò, quod ex <lb/>duplo di&longs;tantiæ celeritas habeatur dupla, ex triplo tri<lb/>pla, &c. </s>

<s>Et <emph type="italics"/>de Priore<emph.end type="italics"/> quidem non fuit controuer&longs;ia, <lb/>cùm tu e&longs;&longs;e errorem & confe&longs;&longs;us fueris, & aliquot <lb/>etiam argumentis o&longs;tenderis. <emph type="italics"/>De Po&longs;teriore<emph.end type="italics"/> tota lis <lb/>fuit, an nempe huiu&longs;modi error tuis ex principiis, &longs;eu <lb/>ex po&longs;itione mox memorata &longs;equeretur, an-non. </s>

<s>Et, <lb/>&longs;i &longs;equeretur, an cùm deinceps & errorem o&longs;tenderes, <lb/>& ex eo admi&longs;&longs;o repugnantia deduceres, non reuerâ <lb/>o&longs;tenderes, ac deduceres aduer&longs;us teip&longs;um, vt cuius er<lb/>ror reuerâ e&longs;&longs;et, tanquam nece&longs;&longs;ariò deductus ex tuis <lb/>principiis. </s>

<s>Iam verò illum ex tuis principiis, &longs;eu propo&longs;itione <lb/>memorata &longs;equi, ex eo argumentatus &longs;um, quòd tem<lb/>pora e&longs;&longs;ent incre&longs;centium velocitatum &longs;ubmultiplicia: <lb/>adeò, vt quod &longs;patium æquale &longs;ecundum dupla velo<lb/>citate percurritur, dimidio temporis percurratur, quo <lb/>primum: & quod tertium tripla, triente; quod quar<lb/>tum quadrupla, quadrante, atque ita de cæteris. <pb pagenum="169"/>Subiunxi autem, <emph type="italics"/>atque ego quidem huc-v&longs;que nullum video <lb/>paralogi&longs;mum:<emph.end type="italics"/> ac tum &longs;um conatus ex errore &longs;uppo<lb/>&longs;ito deducere ab&longs;urditatem. </s>

<s>Quæ&longs;o igitur, an meo <lb/>iure, & &longs;ine vlla, ni&longs;i demon&longs;tratione, &longs;altem veri&longs;imili<lb/>tudine dixerim hunc errorem ex tuis principiis deduci? <lb/></s>

<s>Et cùm fuerim conte&longs;tatus in mea &longs;eu demon&longs;tratio<lb/>ne, &longs;eu veri&longs;imili ratione nullum &longs;ube&longs;&longs;e paralogi&longs;<lb/>mum; cur tu, &longs;i quempiam e&longs;&longs;e puta&longs;ti, verè &longs;ube&longs;&longs;e <lb/>non o&longs;tendi&longs;ti? </s>

<s>Nam quòd fueris ratiocinatus ex con<lb/>clu&longs;ione illa <expan abbr="quã">quam</expan> &longs;tatutum à te principium dixi&longs;ti, ve<lb/>locitatem per &longs;ecundam partem non e&longs;&longs;e duplam ve<lb/>locitatis per primam, id non arguit illud non &longs;equi ex <lb/>alio tuo principio, ex quo aliunde etiam potuerit per <lb/>media quæpiam alia mendo&longs;a illa conclu&longs;io trahi: ac <lb/>poti&longs;&longs;imùm, cum &longs;it adeò verum, quod dicitur vulgò, <lb/><emph type="italics"/>ex po&longs;ito vno ab&longs;urdo con&longs;equi po&longs;&longs;e innumera.<emph.end type="italics"/></s><s> Quam<lb/>obrem neque vllus exinde concludi pote&longs;t paralogi&longs;<lb/>mus; neque non con&longs;tat quàm variè tua ratiocinatio <lb/>peccet, quámque mea illa confiimetur ex confecto <lb/>dilemmate, quod repetere nihil e&longs;t nece&longs;&longs;e. </s>

<s>Quæ&longs;o <lb/>etiam, potueri&longs;-ne paulò antè exaggerere <emph type="italics"/>debui&longs;&longs;e me <lb/>primùm demon&longs;trare ea, quæ à te tanquam fal&longs;a reiecta vi<lb/>de bam, ex con&longs;titutis à te principiis nihilominus &longs;equi, ante<lb/>quam eadem, vt tua decreta impeterem,<emph.end type="italics"/> &c. </s>

<s>Scilicet res <lb/>præ&longs;tita fuerat, & ita quidem, vt te inuita&longs;&longs;em, ad de<lb/>tegendum paralogi&longs;mum, &longs;i quem &longs;ube&longs;&longs;e exi&longs;timares. <lb/></s>

<s>Mi&longs;&longs;um autem facio, vt non modo hoc præterm &longs;eris, <lb/>&longs;ed di&longs;&longs;imulâris etiam incommodum ex hac po&longs;itione <lb/>deductum de Progre&longs;&longs;ione illa &longs;patiorum plu&longs;quam <lb/>tripla eodem articulo &longs;upputata; ni&longs;i quod ad calcem <pb pagenum="170"/>eius obiter memini&longs;ti, non tanquam incommodi, &longs;ed <lb/>tanquam veræ progre&longs;&longs;ionis, quam vano labore re<lb/>qui&longs;ierim. </s>

<s>Ad duosarticulos &longs;equenteis, nempe XXXII, & XXXIII, <lb/>poti&longs;&longs;imùm &longs;pectat, quod rursùs es ante conque&longs;tus <lb/><emph type="italics"/>me non &longs;olùm contra expre&longs;&longs;am Epi&longs;tolæ tuæ &longs;ententiam, &longs;ed <lb/>contra euidentem quoque demon&longs;trationis lucem velle à te ea <lb/>dici, quæ verbis expreßis negas, quæque fal&longs;a e&longs;&longs;e non tantum <lb/>pronuncias, &longs;ed clare etiam, atque euidenter demon&longs;tras.<emph.end type="italics"/></s><s> At <lb/>quomodo quæ&longs;o dicere id potes; cùm ex iam dictis <lb/>quæ&longs;tio &longs;it duplex; <emph type="italics"/>vna,<emph.end type="italics"/> an &longs;it error, percurri &longs;ecundum <lb/>&longs;patium dimidio temporis, quo primum, tertium trien<lb/>re, &c. <emph type="italics"/>altera,<emph.end type="italics"/> an is error &longs;equatur ex tuis principiis. <lb/></s>

<s>Tu verò &longs;ic me impetas, qua&longs;i litem tibi mouerim de <lb/>prima, non autem &longs;olùm de &longs;ecunda; & cùm deberes <lb/>ip&longs;e tueri errorem non &longs;equi ex tuis principiis, qua &longs;ola <lb/>de re agitur; o&longs;tendas &longs;olùm errorem e&longs;&longs;e; qua de re nu&ltail; <lb/>la e&longs;t controuer&longs;ia? </s>

<s>Heinc mihi initium articuli XXXII. <lb/>fuit, <emph type="italics"/>Demon&longs;tras ip&longs;e alia ratione (&longs;ed nimirùm aduer&longs;um te) <lb/>non fieri accelerationem pro &longs;ubdiui&longs;ione i&longs;ta temporis:<emph.end type="italics"/> ac tum <lb/>recitata membratim tua demon&longs;tratione, a&longs;&longs;en&longs;i vbi<lb/>que te verè errorem, incommodumque concludere; ac <lb/>monui &longs;olùm con&longs;tanter, te concludere aduer&longs;us te<lb/>ip&longs;um, quatenus error, incommodumque ex tuis prin<lb/>cipiis con&longs;equeretur. </s>

<s>An dicere igitur potes, <emph type="italics"/>me con<lb/>tra expre&longs;&longs;am &longs;ententiam, & demon&longs;trationem tuam velle <lb/>te ea dicere, quæ verbis expreßis pronuncias, &c.<emph.end type="italics"/> cùm non <lb/>modò noluerim, verùm ne cogitârim quidem. </s>

<s>Sic <lb/>cùm articulo XXXIII. o&longs;tendi&longs;&longs;es rur&longs;us tuo modo, ex <lb/>comparatione &longs;ecundæ partis cum inferiore primæ di-<pb pagenum="171"/>midio con&longs;equi aliud In<lb/>commodum: non repugnaui ego &longs;imiliter, quin tuo modo <lb/>o&longs;tendi&longs;&longs;es; imò & expre&longs;sè admi&longs;i incommodum, <lb/>qua&longs;i à te o&longs;ten&longs;um; & excepi &longs;olùm <emph type="italics"/>nihil e&longs;&longs;e, quod ma<lb/>gis principij fal&longs;itatem proderet, quàm tot repugnantium, at<lb/>que ab&longs;urdorum capitum deductio.<emph.end type="italics"/></s><s> An ergo etiam illeic <lb/>negaui te dicere quæ diceres, aut demon&longs;trare, quæ de<lb/>mon&longs;trares: & non potiùs &longs;emper in eo &longs;olùm fui, quòd <lb/>cognitus error à te in &longs;eip&longs;o, & in con&longs;equente multi<lb/>plici incommodo; non foret tamen per&longs;pectus in <lb/>cau&longs;&longs;a, &longs;eu in principio antecedente: eo modo, quo po<lb/>te&longs;t deformitas pueri agno&longs;ci, & probro haberi ab eo, <lb/>qui pote&longs;t non agno&longs;cere e&longs;&longs;e &longs;e illius <expan abbr="parent&etilde;">parentem</expan>; & fami<lb/>liare illud e&longs;t, <emph type="italics"/>mutato nomine, de te fabula narratur?<emph.end type="italics"/> <expan abbr="Ver&utilde;">Verum</expan> <lb/>hæc &longs;atis, vt inde con&longs;ter, tua-ne fuerit iu&longs;ta quercla. </s>

<s><emph type="italics"/>Vt porrò ex tuis etiam, &<emph.end type="italics"/> G<emph type="italics"/>alilei principiis rem euincam, <lb/>& eapropemodum omnia, quæ tam acriter nobis obiectas, & <lb/>tanquam ab&longs;urda tantopere in&longs;ectaris, tibi nobi&longs;cum e&longs;&longs;e <lb/>communia demon&longs;trem. </s>

<s>Concipe in triangulo AB<emph.end type="italics"/>C, <emph type="italics"/>& <lb/>in eius latere AC parteis æqualeis non iam<emph.end type="italics"/><lb/><figure id="fig39"></figure><lb/><emph type="italics"/>&longs;patij, &longs;ed temporis<emph.end type="italics"/> AD, DE, EF, <emph type="italics"/>&c. <lb/></s>

<s>& in<emph.end type="italics"/> D <emph type="italics"/>acqui&longs;itum quem volueris gra<lb/>dum velocitatis, expre&longs;&longs;um linea<emph.end type="italics"/> DG; <emph type="italics"/>erit <lb/>ex tuis, &<emph.end type="italics"/> G<emph type="italics"/>alilei principiis acqui&longs;itus in<emph.end type="italics"/><lb/>E <emph type="italics"/>gradus &longs;ecundus expre&longs;&longs;us linea<emph.end type="italics"/> EH, <emph type="italics"/>&longs;ic<lb/>que velocitas in<emph.end type="italics"/> E, <emph type="italics"/>dupla erit velocitatis in <lb/>D.<emph.end type="italics"/></s>

<s>Quamobrem igitur aggre&longs;&longs;us ar<lb/>gumentari ad hominem, & demon<lb/>&longs;trare tanta volens aduer&longs;us Galileum, <lb/>ac me, in ip&longs;o limineaberras? </s>

<s>Scilicet neque Galilei, <pb pagenum="172"/>neque mea &longs;ententia e&longs;t, <emph type="italics"/>acqui&longs;itum in E gradum &longs;ecun<lb/>dum exprimi lineâ EH,<emph.end type="italics"/> &longs;ed huius lineæ dimidio &longs;o<lb/>lum: &longs;iquidem tota linea EH non &longs;ecundum modò <lb/>gradum exprimit, acqui&longs;itum abv&longs;que D, verùm etiam <lb/>primum acqui&longs;itam ab v&longs;que A, ip&longs;umque iunctum <lb/>cum &longs;ecundo. </s>

<s><emph type="italics"/>Conclude&longs; ne igitur velocitatem tempore<emph.end type="italics"/> DE <emph type="italics"/>acqui&longs;i<lb/>tam duplam e&longs;&longs;e velocitatis acqui&longs;itæ toto tempore AD?<emph.end type="italics"/></s>

<s>Non; &longs;ed acqui&longs;itam toto tempore AE: ita vt tem<lb/>pore AD acquiratur vnus velocitatis gradus, & illo <lb/>per&longs;euerante, æquiualentéque duobus, quantum ad <lb/>&longs;patia &longs;uperanda tempore æquali attinet, acquiratur <lb/>interim alius &longs;uccedente tempore DE, qui cum eo <lb/>iunctus fiat aggregatum, quod &longs;it ip&longs;ius duplum, vt <lb/>deductum &longs;uperiùs e&longs;t. </s>

<s><emph type="italics"/>Hoc certè, &longs;i conce&longs;&longs;eris, cùm tempora<emph.end type="italics"/> AD, <emph type="italics"/>&<emph.end type="italics"/> DE <lb/><emph type="italics"/>ponantur æqualia, nece&longs;&longs;e omnino fuerit, vt etiam spatia <lb/>æqualibus illis temporibus emen&longs;a inter &longs;e &longs;int, vt velocita<lb/>tes: acproinde vt spatium &longs;ecundo tempore<emph.end type="italics"/> DE <emph type="italics"/>decur&longs;um &longs;pa<lb/>tii tempore<emph.end type="italics"/> AD <emph type="italics"/>tran&longs;mißi præcisè &longs;it duplum: non autem (vt <lb/>&longs;tatuit<emph.end type="italics"/> G<emph type="italics"/>alileus) triplum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Si conce&longs;&longs;ero?<emph.end type="italics"/> inquis, atqui vides vt iam negârim, nec <lb/>me negaturum ignora&longs;&longs;e potes: cùm ab initio v&longs;que <lb/>controuer&longs;iæ, & à primis illis Re&longs;pon&longs;ionis articulis <lb/>non alia ratione exhibuerim opinionem intelligen<lb/>dam; adeò proinde, vt &longs;i ip&longs;e pro&longs;equi velles vlterius, <lb/>argumentando ad hominem, contentus e&longs;&longs;e non de<lb/>bueris &longs;ola hac interrogatione, & conce&longs;&longs;ionem &longs;up<lb/>ponere, quam iure à me non obtineres: &longs;ed &longs;uppo&longs;ita <lb/>negatione, vrgere in me aliquid, quod appo&longs;itum ad <pb pagenum="173"/>rem foret. </s>

<s>An verò po&longs;&longs;es iam vrgere dilemm<gap/>e eo<lb/>dem, quo ego in te v&longs;us &longs;um? </s>

<s>Vt po&longs;&longs;is, ob&longs;tat pri<lb/>mùm, quòd ego &longs;ecundum membrum manife&longs;tò re&longs;<lb/>puam, cui tamen inhærere te ex ijs, quæ heic habes, in<lb/>telligi pote&longs;t: quódque circa primum videas admitte<lb/>re me, & manere primum gradum toto tempore DE; <lb/>& manendo non e&longs;&longs;e otio&longs;um, &longs;ed agere aliquid; & <lb/>agere duplum illius, qui interim acquiritur; & ex dupla <lb/>vnius, & &longs;implici alteriùs actione &longs;uperari tria &longs;patia: <lb/>ac tu non po&longs;&longs;is ex admi&longs;&longs;o à me triplo &longs;patio per tem<lb/>pus DE percurrendo, deducere incommodum vllum, <lb/>vt ego deduxi ex triente temporis, quo tu debes admit<lb/>tere DE pro &longs;patio &longs;umptum percurri. </s>

<s>Ob&longs;tat &longs;e<lb/>cundò, quòd vt facias, mutare duntaxat terminos <lb/>oporteat: hoc e&longs;t, vbi ego tempus tu &longs;patium; vbi <lb/>ego &longs;patium tu tempus debeas dicere, vt factitatum <lb/>&longs;uperiùs e&longs;t, cùm retorquere conatus es, quod ego <lb/>obieceram, vt defenderem nullum fui&longs;&longs;e in Galileo <lb/>Paralogi&longs;mum. </s>

<s>Scilicet confu&longs;io inde &longs;equitur, è <lb/>qua extricari non liceat, neque rem iam ten<lb/>to, vt tempori parcam; tamet&longs;i &longs;altem videretur circa <lb/>ea, quæ &longs;equuntur, tentanda. </s>

<s>Adnoto ergo potius, <lb/>quod heic infers <emph type="italics"/>fore velocitates, vt &longs;patia, & &longs;patium tem<lb/>pore<emph.end type="italics"/> DE <emph type="italics"/>decur &longs;um fore duplum, non triplum:<emph.end type="italics"/> negari tibi <lb/>con&longs;equutionem; eò quòd a&longs;&longs;umas, vt rem conce&longs;&longs;am <lb/>duos gradus velocitatis, qui reperiuntur in tempore <lb/>DE, acquiri ambo per illud tempus: cùm tamen ego <lb/>velim vnum tantum acquiri, & alium e&longs;&longs;e permanen<lb/>tem, præ&longs;tantemque duplum illius, qui acquiritur: <lb/>adeò vt, coniuncta vtriu&longs;que actione acquiratur &longs;patij <pb pagenum="174"/><emph type="italics"/>non duplum, &longs;ed triplum.<emph.end type="italics"/></s>

<s>At &longs;i <emph type="italics"/>hac ratione conuictus velocitatem toto tempore<emph.end type="italics"/> DE <lb/><emph type="italics"/>acqui&longs;itam, alterius toto tempore<emph.end type="italics"/> AD <emph type="italics"/>acqui&longs;itæ duplam e&longs;&longs;e <lb/>negaueris; maioremque agnoueris, quod in tuis, & Galilei <lb/>decretis admittere cogeris: cur tam acriter reprehendis in <lb/>nostris?<emph.end type="italics"/></s>

<s><emph type="italics"/>Conuictus?<emph.end type="italics"/> & quomodo tandem? <emph type="italics"/>Si duplam ne<lb/>gem, &longs;i ma orem agno&longs;cam?<emph.end type="italics"/> Ego verò acqui&longs;itam to<lb/>to tempore DE neque duplam, neque maiorem, &longs;ed <lb/>omninò æqualem illi, quæ acquiritur toto tempore <lb/>AD agno&longs;co. </s>

<s>Indeque e&longs;t illa definitio motus æqua<lb/>biliter accelerati, quod, <emph type="italics"/>temporibus æqualibus æqualiæ <lb/>acquirat velocitatis incrementa:<emph.end type="italics"/> & hoc &longs;olum e&longs;t, quod <lb/>in meis, & Galilei decretis admittere cogor: ac iure <lb/>idcircò reprehendo in tuis, quód cogaris admittere ad<lb/>uer&longs;us propriam definitionem, <emph type="italics"/>æqualibus spatiis æqua<lb/>lia momenta velocitatis non acquiri.<emph.end type="italics"/></s>

<s><emph type="italics"/>Placet ne verò etiam, vt de velocitate tempore<emph.end type="italics"/> DE <emph type="italics"/>ac<lb/>qui&longs;ita perpendamus, cuiu&longs;nam alterius velocitatis &longs;it <lb/>æqualis?<emph.end type="italics"/></s>

<s>Placet; quandò res cordi e&longs;t, & tantopere tibi pla<lb/>cet tuum illud de deducendo infra initium initio, ab <lb/>ip&longs;o putà S, <gap/>nuentum. </s>

<s><emph type="italics"/>Temporibus<emph.end type="italics"/> AD, <emph type="italics"/>&<emph.end type="italics"/> DE <emph type="italics"/>bifariam diui&longs;is in<emph.end type="italics"/> S, <emph type="italics"/>&<emph.end type="italics"/> K, <lb/><emph type="italics"/>erit adhùc ex tuis, &<emph.end type="italics"/> G<emph type="italics"/>alilei decretis velocitas acqui&longs;ita in<emph.end type="italics"/><lb/>D <emph type="italics"/>dupla velocitatis in<emph.end type="italics"/> S: <emph type="italics"/>&longs;icut velocitas acqui&longs;ita in<emph.end type="italics"/> E <emph type="italics"/>dupla <lb/>est velocitatis acqui&longs;itæ in<emph.end type="italics"/> D, <emph type="italics"/>& velocitates omnes, ac &longs;ingulæ <lb/>inter<emph.end type="italics"/> D, <emph type="italics"/>&<emph.end type="italics"/> E <emph type="italics"/>de&longs;ignabiles, duplæ quoque erunt velocitatis <lb/>alterius inter<emph.end type="italics"/> S, <emph type="italics"/>&<emph.end type="italics"/> D <emph type="italics"/>aßignabilis: vt velocitas<emph.end type="italics"/> KL, <emph type="italics"/>me<lb/>dia inter<emph.end type="italics"/> D <emph type="italics"/>&<emph.end type="italics"/> E, <emph type="italics"/>dupla erit velocitatis in<emph.end type="italics"/> VX <emph type="italics"/>mediæ<emph.end type="italics"/><pb pagenum="175"/><emph type="italics"/>inter<emph.end type="italics"/> S, <emph type="italics"/>&<emph.end type="italics"/> D, <emph type="italics"/>& ita de cæteris.<emph.end type="italics"/></s>

<s>Concedo; hæc enim reuerâ in opinionem, quam <lb/>&longs;equor, quadrant, &longs;ecus ac in tuam, quæ tantoperè <lb/>auer&longs;atur progredi adhuc, promouendo comparatio<lb/>nem vltra S ver&longs;us A, ne initium magis ver&longs;us initium <lb/>promoueatur. </s>

<s>Concedo, inquam, quatenus hæ omnes <lb/>velocitates ab A incipiunt, & eandem inter &longs;e ratio<lb/>nem, quam ip&longs;a tempora ob&longs;eruant. </s>

<s><emph type="italics"/>Ex quo nece&longs;&longs;ariò con&longs;equens e&longs;t, vt tota velocitas acqui&longs;i<lb/>ta toto tempore<emph.end type="italics"/> DE, <emph type="italics"/>præcisè, & exactè dupla &longs;it velocitatis <lb/>acqui&longs;itæ toto tempore<emph.end type="italics"/> SD. </s>

<s>Tamet&longs;i punctum, à quo incipiunt velocitates, iam <lb/>varies: concedo nihilominus, & neque id modò, &longs;ed <lb/>etiam velocitatem acqui&longs;itam tempore DE duplam <lb/>e&longs;&longs;e acqui&longs;itæ tempore AS, & tempore DK, & tem<lb/>pore KE. </s>

<s>Nempe acqui&longs;ita tempore DE non e&longs;t tota <lb/>EH, vt falsò &longs;upponis, &longs;ed eius dimidium, quod pro<lb/>inde duplum e&longs;t non totius DG, quam falsò totam <lb/>acqui&longs;itam &longs;upponis ab S, in D, &longs;ed dimidij eius dun<lb/>taxat. </s>

<s>Hoc autem cùm æquale &longs;it acqui&longs;itæ ab A in S, <lb/>à D in K, à K in E: ideò acqui&longs;ita à D in E, pari modo <lb/>e&longs;t earum omnium dupla. </s>

<s><emph type="italics"/>Non autem totius acqui&longs;itæ tempore<emph.end type="italics"/> AD. </s>