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version 1.5, 2002/06/28 13:03:38

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]><archimedes> <info> <author>Gassendi, Pierre</author> <title>De proportione qua gravia decidentia accelerantur</title> <date>1646</date> <place>Paris</place> <editor></editor> <publisher></publisher> <translator></translator> <lang>la</lang> <chunk unit="page*">page</chunk><locator>0000000028</locator> </info> <text> <front> </front> <body> <chap> <pb/>

]><archimedes> <info> <author>Gassendi, Pierre</author> <title>De proportione qua gravia decidentia accelerantur</title> <date>1646</date>

<place>Paris</place> <editor></editor> <publisher></publisher> <translator></translator> <lang>la</lang> <chunk unit="page*">page</chunk><locator>0000000028</locator> </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>

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

<s>c. 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>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>

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

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

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

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

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

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

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

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

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<s>AD ART. XXIX. XXX. XXXI. XXXII. XXXIII. <lb/>De Tempore, quo R.P. colligit parteis &longs;patij <lb/>&longs;ingulas decur&longs;um non iri. </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/>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>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>

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

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<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/>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/>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>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>

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

<s>c. 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>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>

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<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/>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>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>

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<s>ART. XXI. XXII. XXIII. XXIV. XXV. <lb/>Non e&longs;&longs;e Atomorum minùs, quàm Ari&longs;toteleæ <lb/>Materiæ tolerabilem in Religione po&longs;itionem. </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>

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<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/>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>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/>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>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>

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<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/>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>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. 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>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>

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<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/>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>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/>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>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>

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<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/>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/>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>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>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>

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

<s>c. 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>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>

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

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<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/>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/>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/>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>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>

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

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<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/>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>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"/> 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/>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/>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 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/>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"/> 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>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"/> 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>

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<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/>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>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>

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

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<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/>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>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"/> 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/>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>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>

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<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>c. 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>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>

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<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"/> 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/>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>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>

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<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"/> Hactenus nihil e&longs;t, quod non probem. <lb/>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"/> 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>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"/> 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>

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<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/>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>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>

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

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<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>c. &longs;extantis minuti, ac &longs;it <lb/>illius men&longs;ura certa, exempli gratiâ, congius. </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/>Non &longs;anè, &longs;ed omninò ad <expan abbr="quadruplã">quadruplam</expan>. </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>

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

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

<s>c. 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>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>c. 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>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>

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

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

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

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

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<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/>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>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>

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<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/>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>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/>&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>&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>c. 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>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>

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

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

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

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<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"/> 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"/> 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/>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>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>

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

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<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/>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>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>

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<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. 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>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>

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

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

<s>c. 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>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>

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<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/>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>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>

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<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/>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>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>

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<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/>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>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>

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<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/>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>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>

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<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/>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>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>

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<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/>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>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"/> 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>

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

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<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/>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>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>

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<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/>Omninò dimidio. </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/>breuiore, quàm &longs;it dimidium temporis, quo decur&longs;um. <lb/>fuerit AE. Quanto-nam ergo? </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>c. &longs;ex, <lb/>tempus, quo decurretur EG, futurum &longs;it minutorum <lb/>duorum. </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/>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>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>

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<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/>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>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"/> 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>

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

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<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>c. 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>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? 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>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>

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<s>Hæc porrò e&longs;t<emph.end type="italics"/> G<emph type="italics"/>alilei ratio.<emph.end type="italics"/> 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/>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>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>

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<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/>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>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>

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<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/>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/>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>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>

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<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/>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>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>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"/> 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>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/>Nam, vt mutares terminos, de quibus, vt ais, contro. <lb/>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"/> 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>

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<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"/> Quæ&longs;o ergo te, quid tibi affinxi? <lb/>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>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>

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<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/>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>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>

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<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/>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>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>

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<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/>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 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>

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<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/>&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>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/>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>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>

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<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/>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>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>

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<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/>Sed hæc leuiora &longs;unt.<emph.end type="italics"/></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>

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<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/>xxxiii. </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>

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<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/>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"/> Sequitur. </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"/> 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/>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>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/>Si velis; igitur perip&longs;am DE &longs;unt duo gradus, vnus <lb/>nempe manens, & alius, qui interim acquiritur. </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>

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<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/>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>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"/> 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/>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>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"/> 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>

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<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/>& 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>& 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>

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<s><emph type="italics"/>Vides igitur in tua quoque, &<emph.end type="italics"/> G<emph type="italics"/>alilei &longs;ententia perinde, <lb/>atque eadem ratione, qua in no&longs;tra, velocitatem &longs;ecunda parte<emph.end type="italics"/><lb/>DE <emph type="italics"/>acqui&longs;itam non totius velocitatis acqui&longs;itæ in prima parte<emph.end type="italics"/><lb/>AD <emph type="italics"/>duplam e&longs;&longs;e, &longs;ed velocitatis acqui&longs;itæ in vltima eius me<lb/>dietate<emph.end type="italics"/> SD. </s><pb pagenum="176"/>

<s>Nego, <emph type="italics"/>videre me perinde, atque eadem ratione.<emph.end type="italics"/> Nam <lb/>in mea quidem, & Galilei &longs;ententia &longs;umendo has <lb/>parteis DE, AD, SD pro partibus <lb/><figure id="fig40"></figure><lb/>temporis, res e&longs;t nece&longs;&longs;aria; at in tua, <lb/>&longs;umendo ea&longs;dem pro partibus &longs;patij, <lb/>o&longs;ten&longs;um iam e&longs;t velocitatem per DE <lb/>debere e&longs;&longs;e duplam velocitatis per AD. <lb/>Et o&longs;tendetur paulò pò&longs;t non probari <lb/>duplam velocitatis per SD, ni&longs;i ip&longs;um<lb/>met petendo principium. </s>

<s>Et o&longs;tendetur paulò pò&longs;t non probari <lb/>duplam velocitatis per SD, ni&longs;i ip&longs;um<lb/>met petendo principium. </s>

<s><emph type="italics"/>Eadem quoque ratione cogéris fateri ve<lb/>locitatem tertio tempore<emph.end type="italics"/> EF <emph type="italics"/>acqui&longs;itam ve<lb/>locitatis primo tempore acqui&longs;itæ triplam &longs;o<lb/>lùm non e&longs;&longs;e, &longs;ed triplo maiorem.<emph.end type="italics"/></s>

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<s>tangis: futurum &longs;cilicet, <lb/>vt tempore quocumque dato putà vno horæ minuto primo; quo <lb/>decur&longs;a &longs;upponatur de&longs;ignati &longs;patii pars quæcumque prima, vt<emph.end type="italics"/><lb/>AD, <emph type="italics"/>tempus aliud de&longs;ignato illi æquale attingt antè non po&longs;<lb/>&longs;it, quàm ab eodem mobili decur&longs;um fuerit &longs;patium infinitum: <lb/>Cùm enim ab&longs;urdum hoc aliunde non concludas, ni&longs;i ex fal&longs;a <lb/>hypothe&longs;i, quòd &longs;patij pars &longs;ecunda dimidio primi temporis,<emph.end type="italics"/><pb pagenum="180"/><emph type="italics"/>& con&longs;equenter tertia & quartapars, tertia, & quarta parte <lb/>primi eiu&longs;dem temporis decurrantur: iamque ex tuis etiam <lb/>principiis, ea &longs;uppo&longs;itio fal&longs;a, & impoßibilis o&longs;ten&longs;a &longs;it: <lb/>euer&longs;o malè iacto fundamento, tota &longs;uperex&longs;tructa moles <lb/>corruit.<emph.end type="italics"/></s>

<s>Conclu&longs;i ego illud ab&longs;urdum ex hypothe&longs;i fal&longs;a <lb/>quidem, &longs;ed non vt fal&longs;a, verùm vt tua; & tu o&longs;tendens <lb/>fal&longs;am &longs;eu ex tuis, &longs;eu ex meis principiis, lucratus nihil <lb/>es, lucraturus &longs;olùm, &longs;i o&longs;tendere non-tùam potui&longs;&longs;es. <lb/>Itaque & &longs;emper monui, & <expan abbr="iter&utilde;">iterum</expan> moneo moneboque <lb/>iterùm, nihil e&longs;&longs;e opus, vt e&longs;&longs;e probes fal&longs;um, <emph type="italics"/>Partem <lb/>&longs;ecundam spatii percurri dimidio temporis, quo primam:<emph.end type="italics"/> &longs;ed <lb/>opus e&longs;&longs;e, vt o&longs;tendas id non e&longs;&longs;e tuum, hoc e&longs;t non ex<lb/>pre&longs;sè a&longs;&longs;umptum à te vt verum, nece&longs;&longs;ariumque prin<lb/>cipium, quo Paralogi&longs;mi Galileum argueres; & non <lb/>nece&longs;&longs;ariò con&longs;equi ex eo, quod defendis velocitates <lb/>&longs;e habere vt &longs;patia. </s>

<s>Itaque & &longs;emper monui, & <expan abbr="iter&utilde;">iterum</expan> moneo moneboque <lb/>iterùm, nihil e&longs;&longs;e opus, vt e&longs;&longs;e probes fal&longs;um, <emph type="italics"/>Partem <lb/>&longs;ecundam spatii percurri dimidio temporis, quo primam:<emph.end type="italics"/> &longs;ed <lb/>opus e&longs;&longs;e, vt o&longs;tendas id non e&longs;&longs;e tuum, hoc e&longs;t non ex<lb/>pre&longs;sè a&longs;&longs;umptum à te vt verum, nece&longs;&longs;ariumque prin<lb/>cipium, quo Paralogi&longs;mi Galileum argueres; & non <lb/>nece&longs;&longs;ariò con&longs;equi ex eo, quod defendis velocitates <lb/>&longs;e habere vt &longs;patia. </s>

<s>Nempe hoc po&longs;terius <emph type="italics"/>fundamentum<emph.end type="italics"/><lb/>e&longs;t, quòd vt <emph type="italics"/>male iactum euertendum &longs;it,<emph.end type="italics"/> &longs;i contendas qui<lb/>dem, vt tam illud <emph type="italics"/>ab&longs;urdum,<emph.end type="italics"/> quàm <emph type="italics"/>tota &longs;uperex&longs;tructa mo<lb/>les corruat.<emph.end type="italics"/> Quod interim putas ab&longs;urdum euer&longs;um, <lb/>non tantùm quatenus obiectum e&longs;t tibi articulo XII. <lb/>&longs;ed etiam quatenus obiicitur po&longs;teà articulo xlii. </s>

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<s>xxxvi. </s>

<s>xxxvii. <lb/>ac xxxviii. </s>

<s>xxxvii. <lb/></s>

<s>ac xxxviii. </s>

<s>pro&longs;equeris, vt eam propo&longs;itionem refellas, qua <lb/>contendo velocitatem tota &longs;ecunda parte<emph.end type="italics"/> DE <emph type="italics"/>acqui&longs;itam <lb/>præcisè duplam e&longs;&longs;e totius velocitatis per inferiorem primæ<emph.end type="italics"/><pb pagenum="182"/><emph type="italics"/>partis medietatem<emph.end type="italics"/> SD <emph type="italics"/>acqui&longs;itæ: & &longs;imiliter velocitatem <lb/>per tertiam, & quartam partem, &c. </s>

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<s>Cùm ergo non modò probatum non &longs;it, &longs;ed fal<lb/>&longs;um quoque & impo&longs;&longs;ibile ip&longs;a Experientia &longs;uffra<lb/>gante o&longs;ten&longs;um, <emph type="italics"/>velocitatem tota &longs;ecunda parte<emph.end type="italics"/> DE <lb/><emph type="italics"/>acqui&longs;itam pr&ecedil;cisè duplam e&longs;&longs;e totius velocitatis per inferio<lb/>rem primæ partis medietatem<emph.end type="italics"/> SD, <emph type="italics"/>acqui&longs;itæ, &longs;imiliterque, &c.<emph.end type="italics"/><lb/>Quæ&longs;o quî adhûc valeas talem &longs;ententiam defendere, <pb pagenum="185"/>querique, quòd nullum non mouerim lapidem <emph type="italics"/>ad euer<lb/>tendum hanc veritatem?<emph.end type="italics"/> Atque ego quidem, quòd ex<lb/>inde inferres, <emph type="italics"/>Tempus, quo percurritur DE, e&longs;&longs;e præcisè <lb/>æquale tempori, quo percurritur SD,<emph.end type="italics"/> ob duplam nempe <lb/>velocitatem, &longs;icuti &longs;patium duplum e&longs;t, huiu&longs;cemodi <lb/>lapides, & articulis quidem XXXV. ac XXXVI. moui, I. <lb/>fore, vt &longs;uppo&longs;ito tempore, quo percurritur SD, <lb/>minutorum v. </s>

<s>c. duorum, idem &longs;patium SD, <lb/>percurreretur &longs;imùl minuto vno cum triente, &longs;iue &longs;e<lb/>cundis 80: ac rur&longs;us &longs;ecundis 53, ac iterum 18, iterumque <lb/>6, &c. </s>

<s>duorum, idem &longs;patium SD, <lb/>percurreretur &longs;imùl minuto vno cum triente, &longs;iue &longs;e<lb/>cundis 80: ac rur&longs;us &longs;ecundis 53, ac iterum 18, iterumque <lb/>6, &c. </s>

<s>Cùm aliunde &longs;tatui&longs;&longs;es tempus per SD, bre<lb/>uius e&longs;&longs;e tempore per AS, fore tamen ip&longs;i æquale. </s>

<s>III. <lb/>Tempus per DE non æquale fore, &longs;ed &longs;e&longs;quialterum <lb/>temporis per SD. IV. Futurum, vt aut concluderes ni<lb/>hil, aut vtereris paralogi&longs;mo, quo Galileum v&longs;um cau&longs;<lb/>&longs;areris. </s>

<s>Tempus per DE non æquale fore, &longs;ed &longs;e&longs;quialterum <lb/>temporis per SD. IV. Futurum, vt aut concluderes ni<lb/>hil, aut vtereris paralogi&longs;mo, quo Galileum v&longs;um cau&longs;<lb/>&longs;areris. </s>

<s>V. Fore, vt quæuis magnitudo, etiam &longs;emi<lb/>diameter Mundi, tantulo tempore, quantulo SD li<lb/>neola percurreretur. </s>

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<s>Nempe ex quinque argumentis, quæ &longs;unt mox an<lb/>tè indigitata, <expan abbr="terti&utilde;">tertium</expan> delegi&longs;ti, de quo (&longs;i liceat tua pace <lb/>dicere) vitilitigares. </s>

<s>Quippe <expan abbr="error&etilde;">errorem</expan> calami, quo po&longs;tre<lb/>mo loco &longs;crip&longs;i AE pro DE, pro errore mentis habui&longs;ti. <lb/>Qua&longs;i verò habere oculos oporteat, & <expan abbr="nõ">non</expan> videre <expan abbr="plan&utilde;">planum</expan> <lb/>&longs;en&longs;um, quo &longs;cribere volui <emph type="italics"/>vt AS ad SD, ita AD ad DE?<emph.end type="italics"/><lb/>Aut qua&longs;i in huiu&longs;inodi tanta literarum farragine, im<lb/>portunaque inculcatione, non vnam pro alia irrepere <lb/><expan abbr="human&utilde;">humanum</expan> &longs;it? </s>

<s>Quippe <expan abbr="error&etilde;">errorem</expan> calami, quo po&longs;tre<lb/>mo loco &longs;crip&longs;i AE pro DE, pro errore mentis habui&longs;ti. <lb/></s>

<s>Et cùm volueris ip&longs;e po&longs;teà videri huma<lb/>nior, dum legens IC, adnota&longs;ti <emph type="italics"/>dicere me volui&longs;&longs;e HC<emph.end type="italics"/><lb/>(quanqùam dicere nolui HC, &longs;ed ND, tribus inte<lb/>gris ver&longs;ibus, ad illud v&longs;que, <emph type="italics"/>vt tu concludis,<emph.end type="italics"/> qui in &longs;eheda <lb/>fuere, ob idem initium, ca&longs;u prætermi&longs;&longs;is) cùm, <expan abbr="inquã">inquam</expan>, <lb/>illeic humanior fueris, cur heic quoque e&longs;&longs;e nolui&longs;ti? <lb/>Debui&longs;ti ergo potiùs re&longs;titutâ literâ D, o&longs;tendere me <lb/>impropriè loquutum, qua&longs;i ignorantem diui&longs;ionem <lb/>rationis e&longs;&longs;e <emph type="italics"/>&longs;umptionem exce&longs;&longs;us, quo antecedens &longs;uperat <lb/>con&longs;equens, ad ip&longs;ummet con&longs;equens:<emph.end type="italics"/> hoc e&longs;t, <emph type="italics"/>e&longs;&longs;e compa<lb/>rationem differentiæ terminorum cum ip&longs;orum alterutro.<emph.end type="italics"/> Sed <lb/>ita nimirùm agere fuit cordi, vt dicere po&longs;&longs;es, quamuis <lb/>vt par e&longs;t, di&longs;ponerentur termini, nihil me hac ratione <lb/>conclu&longs;urum, ni&longs;i prius &longs;upponerem <emph type="italics"/>velocitatem per to<lb/>tam<emph.end type="italics"/> AE <emph type="italics"/>duplam e&longs;&longs;e velocitatis acqui&longs;itæ per<emph.end type="italics"/> DE, <emph type="italics"/>quod ta<lb/>men fal&longs;um non ignorarem.<emph.end type="italics"/> Ego verò fal&longs;um <expan abbr="quid&etilde;">quidem</expan> e&longs;&longs;e, <lb/>&longs;ed & tuum e&longs;&longs;e non ignoro: ac ne ex &longs;uperiùs dedu<lb/>ctis argumentum repetam, paucis o&longs;tendo nihil e&longs;&longs;e <lb/>hac &longs;uppo&longs;itione, aut omninò vlla tergiuer&longs;atione <lb/>opus. </s>

<s>Qua&longs;i verò habere oculos oporteat, & <expan abbr="nõ">non</expan> videre <expan abbr="plan&utilde;">planum</expan> <lb/>&longs;en&longs;um, quo &longs;cribere volui <emph type="italics"/>vt AS ad SD, ita AD ad DE?<emph.end type="italics"/><lb/>Aut qua&longs;i in huiu&longs;inodi tanta literarum farragine, im<lb/>portunaque inculcatione, non vnam pro alia irrepere <lb/><expan abbr="human&utilde;">humanum</expan> &longs;it? </s>

<s>Debui&longs;ti ergo potiùs re&longs;titutâ literâ D, o&longs;tendere me <lb/>impropriè loquutum, qua&longs;i ignorantem diui&longs;ionem <lb/>rationis e&longs;&longs;e <emph type="italics"/>&longs;umptionem exce&longs;&longs;us, quo antecedens &longs;uperat <lb/>con&longs;equens, ad ip&longs;ummet con&longs;equens:<emph.end type="italics"/> hoc e&longs;t, <emph type="italics"/>e&longs;&longs;e compa<lb/>rationem differentiæ terminorum cum ip&longs;orum alterutro.<emph.end type="italics"/> Sed <lb/>ita nimirùm agere fuit cordi, vt dicere po&longs;&longs;es, quamuis <lb/>vt par e&longs;t, di&longs;ponerentur termini, nihil me hac ratione <lb/>conclu&longs;urum, ni&longs;i prius &longs;upponerem <emph type="italics"/>velocitatem per to<lb/>tam<emph.end type="italics"/> AE <emph type="italics"/>duplam e&longs;&longs;e velocitatis acqui&longs;itæ per<emph.end type="italics"/> DE, <emph type="italics"/>quod ta<lb/>men fal&longs;um non ignorarem.<emph.end type="italics"/> Ego verò fal&longs;um <expan abbr="quid&etilde;">quidem</expan> e&longs;&longs;e, <lb/>&longs;ed & tuum e&longs;&longs;e non ignoro: ac ne ex &longs;uperiùs dedu<lb/>ctis argumentum repetam, paucis o&longs;tendo nihil e&longs;&longs;e <lb/>hac &longs;uppo&longs;itione, aut omninò vlla tergiuer&longs;atione <lb/>opus. </s>

<s>Ex verbis paulò antè ex tua di&longs;&longs;ertatione reci<lb/>tatis, negare non potes, quin hoc totum tuum &longs;it: <pb pagenum="187"/><emph type="italics"/>vt<emph.end type="italics"/> AE, <emph type="italics"/>ad<emph.end type="italics"/> AD, <emph type="italics"/>ita<emph.end type="italics"/> AD <emph type="italics"/>ad<emph.end type="italics"/> AS. Quamobrem, aut <lb/>neges oportet ratiocinia Geometrica, aut fatearis le<lb/>gitimè diuidendo ita concludi, <emph type="italics"/>vt<emph.end type="italics"/> AS, <emph type="italics"/>ad<emph.end type="italics"/> SD; <emph type="italics"/>ita<emph.end type="italics"/> AD <lb/><emph type="italics"/>ad<emph.end type="italics"/> DE. </s>

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<s>Sed ne putes tamen, &longs;i <lb/>pars &longs;uperior<emph.end type="italics"/> AS <emph type="italics"/>mente, & cogitatione diui&longs;ibilis intelligatur <lb/>infinitas in parteis, con&longs;equens proptereà e&longs;&longs;e, vt per illas par<lb/>teis omneis mente confictas acceleratio varietur: motus enim, <lb/>eiu&longs;que acceleratio effectus Phy&longs;icus est, qui proptereà (vt in <lb/>cæteris rebus Phy&longs;icis accidit) per parteis &longs;en&longs;ibileis, ea&longs;que <lb/>pro ratione ponderis, & re&longs;i&longs;tentiæ medij, maiores, aut mino<lb/>res metiendus videatur. </s>

<s>Accedit, quòd tecum, & cum<emph.end type="italics"/> G<emph type="italics"/>a<lb/>lileo non &longs;entio corpus graue de&longs;cendens &longs;tatim à quiete, atque <lb/>in omnibus, ac &longs;ingulis indiui&longs;ibilibus momentis accelerare <lb/>motum.<emph.end type="italics"/> C<emph type="italics"/>uius rei cau&longs;&longs;a e&longs;t, quòd acceleratio omnis à &longs;olo <lb/>medio e&longs;t; vnde de&longs;cen&longs;us in vacuo &longs;ui &longs;emper &longs;imilis, atque <lb/>vniformis ex&longs;i&longs;teret: &longs;icut tunc quoque tota cau&longs;&longs;a de&longs;cen&longs;us, <lb/>nempe grauitas, &longs;emper eadem, ac &longs;ui &longs;imilis per&longs;eueraret. <lb/>Igitur, cùm graue quodcumque per aërem, aut aliud medium <lb/>de&longs;cendit, talis de&longs;cen&longs;us à &longs;olagrauitate inchoatur, etiam me<lb/>dio plus, aut minùs re&longs;i&longs;tente, prout ip&longs;um grauius, aut leuius <lb/>e&longs;t, & faciliùs, aut difficiliùs diuiditur: nec priùs acceleratur <lb/>motus de&longs;cendentis corporis, quàm à medij accurrentis, &longs;éque <lb/>à tergo claudentis motu, eóque iam notabili, medii re&longs;i&longs;tentia <lb/>&longs;upereretur, & grauitatis ni&longs;us, natiuaque velocitas Phy&longs;icè <lb/>augeatur: ad quod &longs;ine dubio requiritur pars temporis, ac spa<lb/>tii non Mathematicè minima, &longs;ed Phy&longs;icè notabilis, quæ cùm <lb/>pro grauium diuer&longs;itate, & varia re&longs;i&longs;tentia mediorum modò.<emph.end type="italics"/><pb pagenum="193"/><emph type="italics"/>maior &longs;it, modò minor: heinc e&longs;t, cur accelerationis ratio à <lb/>primo spatii percurrendi puncto minùs tutò inchoetur. </s>

<s>Igitur, cùm graue quodcumque per aërem, aut aliud medium <lb/>de&longs;cendit, talis de&longs;cen&longs;us à &longs;olagrauitate inchoatur, etiam me<lb/>dio plus, aut minùs re&longs;i&longs;tente, prout ip&longs;um grauius, aut leuius <lb/>e&longs;t, & faciliùs, aut difficiliùs diuiditur: nec priùs acceleratur <lb/>motus de&longs;cendentis corporis, quàm à medij accurrentis, &longs;éque <lb/>à tergo claudentis motu, eóque iam notabili, medii re&longs;i&longs;tentia <lb/>&longs;upereretur, & grauitatis ni&longs;us, natiuaque velocitas Phy&longs;icè <lb/>augeatur: ad quod &longs;ine dubio requiritur pars temporis, ac spa<lb/>tii non Mathematicè minima, &longs;ed Phy&longs;icè notabilis, quæ cùm <lb/>pro grauium diuer&longs;itate, & varia re&longs;i&longs;tentia mediorum modò.<emph.end type="italics"/><pb pagenum="193"/><emph type="italics"/>maior &longs;it, modò minor: heinc e&longs;t, cur accelerationis ratio à <lb/>primo spatii percurrendi puncto minùs tutò inchoetur. </s>

<s>Hæc <lb/>porrò, &longs;i cum tuis, ac<emph.end type="italics"/> G<emph type="italics"/>alilei decretis minùs fortè conueniant; <lb/>principiis certè Phy&longs;icis aptè congruunt. </s>

<s>Sed reliqua breuiùs <lb/>percurramus.<emph.end type="italics"/></s>

<s>Peruentum iam e&longs;t ad Ph&longs;iycæ tuæ Demon&longs;tratio<lb/>nis Conclu&longs;ionem: quæ quoniam e&longs;t eadem cum ip&longs;o <lb/>con&longs;equente Propo&longs;itionis, idcircò elicienda fuit vi <lb/>con&longs;equutionis qua illud dependet ab antecedente. <lb/>Quod porrò notas quæ&longs;ii&longs;&longs;e me; quanto, amabò, iure <lb/>quæ&longs;iuii: cùm <expan abbr="&longs;tupend&utilde;">&longs;tupendum</expan> &longs;it te ab v&longs;que initio defini&longs;&longs;e <lb/>motum æquabiliter acceleratum, qui æqualibus &longs;patiis <lb/>æqualia celeritatis augmenta acquireret; ac &longs;patia illa <lb/>æqualia &longs;emper & habui&longs;&longs;e, & &longs;ic expre&longs;&longs;i&longs;&longs;e per lineas <lb/>in parteis æqualeis diui&longs;as, vt e&longs;&longs;et in iis vna prima, vna <lb/>&longs;ecunda, &c. </s>

<s>Quod porrò notas quæ&longs;ii&longs;&longs;e me; quanto, amabò, iure <lb/>quæ&longs;iuii: cùm <expan abbr="&longs;tupend&utilde;">&longs;tupendum</expan> &longs;it te ab v&longs;que initio defini&longs;&longs;e <lb/>motum æquabiliter acceleratum, qui æqualibus &longs;patiis <lb/>æqualia celeritatis augmenta acquireret; ac &longs;patia illa <lb/>æqualia &longs;emper & habui&longs;&longs;e, & &longs;ic expre&longs;&longs;i&longs;&longs;e per lineas <lb/>in parteis æqualeis diui&longs;as, vt e&longs;&longs;et in iis vna prima, vna <lb/>&longs;ecunda, &c. </s>

<s>nunc autem rem &longs;ic perturbare, vt pars <lb/>prima vna æqualium non &longs;it; vt primum primæ dimi<lb/>dium pro nihilo &longs;it, vt reliquum pro tota &longs;it: vt motus <lb/>æquabiliter acceleratus non incipiat, cùm incipit; vt <lb/>incipiat, po&longs;tquam incepit, & alia id genus, quæ ob<lb/>iecta &longs;unt, quæque repetere iam piget? </s>

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<s>Neque enim in <lb/>compingendo v. </s>

<s>g. animalculo acari no&longs;trum &longs;en&longs;um <lb/>con&longs;ulit, qui ip&longs;um habet qua&longs;i punctum, &longs;iue rem vi&longs;u <lb/>minimam; &longs;ed &longs;eip&longs;am potiùs, prout illud texit ex <lb/>innumeris myriadibus partium infra omnem &longs;en&longs;us <lb/>acutiem ex&longs;i&longs;tentium, & nece&longs;&longs;ariarum tamen, vt rem <lb/>faciat per&longs;e mobilem, ac vegetationis, &longs;en&longs;us, appeti<lb/>tus capacem. </s>

<s>animalculo acari no&longs;trum &longs;en&longs;um <lb/>con&longs;ulit, qui ip&longs;um habet qua&longs;i punctum, &longs;iue rem vi&longs;u <lb/>minimam; &longs;ed &longs;eip&longs;am potiùs, prout illud texit ex <lb/>innumeris myriadibus partium infra omnem &longs;en&longs;us <lb/>acutiem ex&longs;i&longs;tentium, & nece&longs;&longs;ariarum tamen, vt rem <lb/>faciat per&longs;e mobilem, ac vegetationis, &longs;en&longs;us, appeti<lb/>tus capacem. </s>

<s>Vt præteream &longs;en&longs;um haberi regulam <lb/>plu&longs;quàm Le&longs;biam, propter diuer&longs;itatem &longs;en&longs;uum acu-<pb pagenum="195"/>tiorum, hebetiorumque, & adiumentorum, quibus <lb/>po&longs;&longs;unt &longs;ubtiliora omnibus rebus antè perceptis per<lb/>cipere; & &longs;ine &longs;pe tamen, vt vnquam naturæ &longs;ubtilita<lb/>tem a&longs;&longs;equantur. </s>

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<s>Cùm non po&longs;&longs;is: vide quàm fru&longs;trà <lb/>eò confugeris, vt <emph type="italics"/>&longs;tandum alicubi &longs;it, quòd diui&longs;io e&longs;&longs;e infi<lb/>nita non poßit.<emph.end type="italics"/></s>

<s>Hanc iterùm difficultatem qua&longs;i præ&longs;entiens, præ<lb/>uenien&longs;que, <emph type="italics"/>quid ni,<emph.end type="italics"/> inquis, <emph type="italics"/>iam primùm in ea parte con<lb/>&longs;i&longs;tamus, ex qua totius motus accelerati ratio perfectè intelli<lb/>gatur?<emph.end type="italics"/> Dicere ergo vis, non e&longs;&longs;e ex&longs;pectandum, ad <lb/>hoc vt con&longs;i&longs;tamus, quov&longs;que ad eam diui&longs;ionem per<lb/>uenerimus, ex qua partes AS, & SD &longs;int duo puncta <lb/>Phy&longs;ica, &longs;eu duæ Phy&longs;icè indiui&longs;ibiles partes: &longs;ed in illa <lb/>&longs;tandum, in qua tam AS, quàm SD con&longs;tent adhùc ex <lb/>tot Phy&longs;icis partibus, <emph type="italics"/>vt ex ijs ratio accelerati motus per<lb/>fectè intelligatur.<emph.end type="italics"/> At imprimis, &longs;i ita &longs;it, fru&longs;trà ergo <lb/>dicis alicubi &longs;tandum, <emph type="italics"/>quòd diui&longs;io e&longs;&longs;e infinita non poßit:<emph.end type="italics"/><lb/>cùm etiam diui&longs;ione ex&longs;i&longs;tente non infinita, progredi <lb/>adhûc vlteriùs liceat: atque idcircò vigent adhûc in<lb/>commoda omnia, quæ obiecta &longs;unt: quandò pote&longs;t <pb pagenum="196"/>adhûc pars AS, &longs;ubdiuidi in plura, pluraque dimidia. <lb/>Deinde, cùm in dimidio SD, tot requiris parteis, vt <lb/><emph type="italics"/>ex ip&longs;is ratio accelerati motus perfectè intelligatur:<emph.end type="italics"/> quot<lb/>nam quæ&longs;o &longs;unt, quas requiris? </s>

<s>Deinde, cùm in dimidio SD, tot requiris parteis, vt <lb/><emph type="italics"/>ex ip&longs;is ratio accelerati motus perfectè intelligatur:<emph.end type="italics"/> quot<lb/>nam quæ&longs;o &longs;unt, quas requiris? </s>

<s>An aliquot pauculas, <lb/>v. </s>

<s>c. &longs;ex, quas nempe recen&longs;es, dum rationem motus <lb/>accelerati explicas per trientem, quadrantem, per quin<lb/>tam, perque &longs;extam parteis tantum? </s>

<s>&longs;ex, quas nempe recen&longs;es, dum rationem motus <lb/>accelerati explicas per trientem, quadrantem, per quin<lb/>tam, perque &longs;extam parteis tantum? </s>

<s>Sanè vel ne&longs;ciens <lb/>tot requiris, vt innumerabiles &longs;int; & tum ab&longs;is longi&longs;<lb/>&longs;imè ab eo, vt cau&longs;&longs;eris &longs;tandum, quòd <emph type="italics"/>diui&longs;io e&longs;&longs;e infinita <lb/>non poßit,<emph.end type="italics"/> qua&longs;i vel in fine, vel certe non longè à fine <lb/>con&longs;i&longs;tendum &longs;it: tum etiam ab eo, vt ex cognitis par<lb/>tibus <emph type="italics"/>ratio motus intelligatur.<emph.end type="italics"/> Rem vt experiamur, ac<lb/>cipiamus, ecce, ca&longs;um globi ferrei (quod tuum po&longs;teà <lb/>exemplum e&longs;t) ex cælo Lunæ in centrum terræ: atque <lb/>in ip&longs;o talem partem, <emph type="italics"/>in qua iam primum,<emph.end type="italics"/> vt ais, <emph type="italics"/>con&longs;i&longs;ta<lb/>mus.<emph.end type="italics"/> Cùm tuo ex decreto, men&longs;ura durationis om<lb/>nium partium i&longs;ti primæ æqualium &longs;it æqualis duratio <lb/>totidem minutiorum partium &longs;igillatim acceptarum <lb/>in inferiore eius dimidio: ergo inferius eius dimidium <lb/>diui&longs;ibile e&longs;t in tot parteis, non Mathematicas, men<lb/>teve confictas, &longs;ed Phy&longs;icas, &longs;iue in ip&longs;a rerum natura <lb/>ex&longs;i&longs;tenteis, quot partes &longs;unt à cælo Lunæ, v&longs;que in <lb/>centrum terræ, ip&longs;i AD æquales. </s>

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<s>Videlicet <emph type="italics"/>cau&longs;<lb/>&longs;am accelerationis<emph.end type="italics"/> decernis <emph type="italics"/>e&longs;&longs;e &longs;olum medium, v. </s>

<s>c. aërem: <lb/>neque enim prius accelerari motum à grauitate inchoatum, <lb/>quàm à medii accurrentis, &longs;eque à tergo claudentis motu, eó<lb/>que iam notabili re&longs;i&longs;tentia &longs;uperetur.<emph.end type="italics"/> Quo loco rursùs <lb/>æquiuocatio in nomine <emph type="italics"/>notabilis.<emph.end type="italics"/> Nam <emph type="italics"/>notabilem<emph.end type="italics"/> intel<lb/>ligis aut naturæ, aut nobis. </s>

<s>aërem: <lb/>neque enim prius accelerari motum à grauitate inchoatum, <lb/>quàm à medii accurrentis, &longs;eque à tergo claudentis motu, eó<lb/>que iam notabili re&longs;i&longs;tentia &longs;uperetur.<emph.end type="italics"/> Quo loco rursùs <lb/>æquiuocatio in nomine <emph type="italics"/>notabilis.<emph.end type="italics"/> Nam <emph type="italics"/>notabilem<emph.end type="italics"/> intel<lb/>ligis aut naturæ, aut nobis. </s>

<s>Et nobis quidem <emph type="italics"/>notabilem<emph.end type="italics"/><pb pagenum="198"/>non debes intelligere: cùm natura no&longs;træ <emph type="italics"/>notationi<emph.end type="italics"/> non <lb/>alligetur; & priu&longs;quam no&longs;tra per&longs;picacia <emph type="italics"/>notare<emph.end type="italics"/> quic<lb/>quam valeat, natura iam tran&longs;ierit per innumerabi<lb/>leis parteis. </s>

<s>Si ergo naturæ; quæro quot partes in mo<lb/>tu nece&longs;&longs;ariæ &longs;int, vt natura progre&longs;&longs;a e&longs;&longs;e <emph type="italics"/>notabiliter<emph.end type="italics"/><lb/>reputetur? </s>

<s>An-non &longs;altem myrias deberet e&longs;&longs;e &longs;atis? <lb/>An-non &longs;altem decem, centum, & mille myriades? </s>

<s>An-non &longs;altem myrias deberet e&longs;&longs;e &longs;atis? <lb/></s>

<s>An-non &longs;altem decem, centum, & mille myriades? </s>

<s>An<lb/>non &longs;altem <expan abbr="myriad&utilde;myrias">myriadummyrias</expan>; a<gap/> &longs;altem decem, <expan abbr="cent&utilde;">centum</expan>, <lb/>mille myriades myriadum? </s>

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<s>Si dicas &longs;e non claudere; <lb/>igitur &longs;patium illud à tergo vacuum remanet; quod <lb/>non es &longs;anè admi&longs;&longs;urus. </s>

<s>Si &longs;e claudere, ergo cum &longs;e <lb/>claudendo agat (neque enim alia ratione putas hanc <lb/>cau&longs;&longs;am agere) ab ea v&longs;que parte agit aliquid: ergo ab <lb/>initio v&longs;que grauitatem iuuat: ergo & motum accele<lb/>rat: ergo ex&longs;pectandæ non &longs;unt tam innumerabiles <lb/>partes, vt motus notabilis &longs;it, & acceleratio incipiat. <lb/>Quod <emph type="italics"/>cau&longs;&longs;am hanc<emph.end type="italics"/> verò dicis <emph type="italics"/>nece&longs;&longs;ariam, vt re&longs;i&longs;tentia <lb/>&longs;uperetur:<emph.end type="italics"/> vides quàm non &longs;it nece&longs;&longs;arium, cùm graui<lb/>tate &longs;ola agente &longs;uperatam iam facias, priu&longs;quàm aër <lb/>aliquid agat, &longs;iue mobili iam promoto per totum &longs;upe<lb/>rius dimidium &longs;uperueniat, ac &longs;e&longs;e claudat. </s>

<s>Quod <emph type="italics"/>cau&longs;&longs;am hanc<emph.end type="italics"/> verò dicis <emph type="italics"/>nece&longs;&longs;ariam, vt re&longs;i&longs;tentia <lb/>&longs;uperetur:<emph.end type="italics"/> vides quàm non &longs;it nece&longs;&longs;arium, cùm graui<lb/>tate &longs;ola agente &longs;uperatam iam facias, priu&longs;quàm aër <lb/>aliquid agat, &longs;iue mobili iam promoto per totum &longs;upe<lb/>rius dimidium &longs;uperueniat, ac &longs;e&longs;e claudat. </s>

<s>Vtcum<lb/>que autem e&longs;&longs;e debeat <emph type="italics"/>notabilis<emph.end type="italics"/> pars; &longs;ic cine probas <lb/>platicè &longs;ubtilem determinationem in primæ partis me-<pb pagenum="199"/>dio? </s>

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<s>Imò, vnde tutiùs inchoetur, quàm <lb/>vnde e&longs;t periculi nihil? </s>

<s>Nam tibi quidem meritò ef<lb/>ficiuntur omnia &longs;u&longs;pecta, cùm viâ regiâ &longs;emel relictâ, <lb/>non valeas ecce, ni&longs;i per dumos, &longs;alebra&longs;que incedere; <lb/>at verò illis, qui viam tenent, &longs;imile nihil timendum e&longs;t. <lb/>Sed nempe platicè a&longs;&longs;umenti, platicè perinde conclu<lb/>dendum fuit. </s>

<s>Sed nempe platicè a&longs;&longs;umenti, platicè perinde conclu<lb/>dendum fuit. </s>

<s>Sperandum quippe fuerat, vt conclu<lb/>deres, cur ante primæ partis medium, &longs;eu alicubi per <lb/>totum prius dimidium, acceleratio non inchoaretur; at <lb/>tu intereà de medio, totove priore dimidio nihil: &longs;ed <lb/>&longs;olùm, <emph type="italics"/>accelerationem à primo puncto non tutò inchoari.<emph.end type="italics"/><lb/>Quod autem addis, <emph type="italics"/>&longs;i i&longs;ta cum meis, &<emph.end type="italics"/> G<emph type="italics"/>alilei decretis <lb/>non fortè conueniant, principiis certè Phy&longs;icis aptè congruere;<emph.end type="italics"/><lb/>cedò &longs;olùm, Quibus? </s>

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<s>Quid tu ad i&longs;ta <lb/>igitur? </s>

<s>Dicis me, <emph type="italics"/>non &longs;olùm re&longs;pectum partium ad parteis <lb/>temporis exigere, quas neque ego, neque alius qui&longs;quam aßi<lb/>gnare poßit: &longs;ed tempora etiam illis ad&longs;cribere, quæ nullo <lb/>modo ip&longs;is conuenire non ignorem.<emph.end type="italics"/> Verumtamen, quæ<lb/>&longs;tio non e&longs;t de eo, quod ego, aut alius præ&longs;tare po&longs;&longs;i<lb/>mus, aut non po&longs;&longs;imus, in a&longs;&longs;ignandis temporibus, quæ <lb/>partibus quibu&longs;que conueniant: quanquam Galileum <lb/>quidem imitatus, &longs;umpto quocumque tempore primæ <lb/>parti debito, a&longs;&longs;ignaui tempus, quod exigitur ad &longs;ecun<lb/>dam, & quod ad vtrumque primæ partis dimidium, <lb/>paratus idem prorsùs præ&longs;tare circa quælibet tempora, <lb/>quarumcum que voles partium cætetarum, iuxta gene<lb/>rale &longs;cilicet Effatum, quod articulo <expan abbr="Re&longs;põ&longs;ionis">Re&longs;pon&longs;ionis</expan> XXXVI. <lb/>retuli, & in quod nihil fuit, quod à te obiiceretur. <lb/>Non item e&longs;t quæ&longs;tio, an tempora quæ partibus ad&longs;cri<lb/>bo, ip&longs;is nullo modo conuenire ignorem, an &longs;ciam (&longs;cio <lb/>enim e&longs;&longs;e longè alià, prout ex citato moxloco intelligi <lb/>pote&longs;t) &longs;ed an ea ad&longs;cribam iuxta tua principia. </s>

<s>Non item e&longs;t quæ&longs;tio, an tempora quæ partibus ad&longs;cri<lb/>bo, ip&longs;is nullo modo conuenire ignorem, an &longs;ciam (&longs;cio <lb/>enim e&longs;&longs;e longè alià, prout ex citato moxloco intelligi <lb/>pote&longs;t) &longs;ed an ea ad&longs;cribam iuxta tua principia. </s>

<s>Quo<lb/>nam verò modo id non fieri probas? <emph type="italics"/>Vis enim,<emph.end type="italics"/> inquis, <lb/><emph type="italics"/>primi &longs;patij partem dimidiam dimidia parte eius tem<lb/>poris percurri, quo totam primam partem, & tertiam <lb/>tertia, quartam quarta,<emph.end type="italics"/> &c. </s>

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<s>Deinde quatenus nihil e&longs;&longs;e <lb/>videtur po&longs;&longs;e ab&longs;urdius, quàm primum primæ partis <lb/>dimidium nullo po&longs;&longs;e habere loco in progre&longs;&longs;ione <pb pagenum="207"/>Geometrica, & eius tamen comparatione eam <expan abbr="pro-gre&longs;&longs;ion&etilde;">pro<lb/>gre&longs;&longs;ionem</expan> &longs;tabilire; <expan abbr="quã">quam</expan> ex fragmentis po&longs;terioris dimi<lb/>dij durationem quærere innumerabilium partium con<lb/>&longs;equent<gap/><expan abbr="&utilde;">um</expan>: quàm cogi ad <expan abbr="commini&longs;cend&utilde;">commini&longs;cendum</expan>, quæ in ip&longs;a te<lb/>tam malè cohæreant, vt quod commentum &longs;emel pla<lb/>cuerit, cohætere po&longs;&longs;e videatur. </s>

<s>Tandem, quatenus <lb/>etiam iuxta progre&longs;&longs;ionem in ratione dupla, quam &longs;o<lb/>lam vis e&longs;&longs;e continuam, repugnes tibi nece&longs;&longs;e e&longs;t, cùm <lb/>indefinite aiens <emph type="italics"/>æqualibus temporibus spatia decurri ma<lb/>iora &longs;emper, ac maiora in ratione dupla,<emph.end type="italics"/> nece&longs;&longs;e &longs;it eandem <lb/>rationem euertas, quotie&longs;cumque a&longs;&longs;ump&longs;eris tempo<lb/>ra a&longs;&longs;umptis maiora, & ip&longs;a tamen inter &longs;e æqualia. <lb/>Quippe cùm in tuo, v. </s>

<s>c. de ca&longs;u ex Luna exem<lb/>plo a&longs;&longs;ump&longs;eris primo tempore decurri pedes 100, &longs;e<lb/>cundo 200, tertio 400, quarto 800, quinto 1600, <lb/>&longs;exto 3200, &c. </s>

<s>Quippe cùm in tuo, v. </s>

<s>de ca&longs;u ex Luna exem<lb/>plo a&longs;&longs;ump&longs;eris primo tempore decurri pedes 100, &longs;e<lb/>cundo 200, tertio 400, quarto 800, quinto 1600, <lb/>&longs;exto 3200, &c. </s>

<s>con&longs;tat&longs;i deinceps duo tempora pri<lb/>ma pro vno a&longs;&longs;umas, duo &longs;equentia pro alio, duo <lb/>item &longs;equentia pro alio: aut &longs;i tria quidem prima pro <lb/>vno, tria &longs;uccedentia pro alio, &c. </s>

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<s>Dicerem heic de Incommodo, <lb/>in quod te recidi&longs;&longs;e con&longs;equenter obieci, <emph type="italics"/>de nunquam <lb/>ab&longs;oluendo tempore &longs;ecundo,<emph.end type="italics"/> aut <emph type="italics"/>percurrendis &longs;altem &longs;patijs <lb/>infinitis,<emph.end type="italics"/> &longs;i progre&longs;&longs;io &longs;patiorum fieret temporibus &ecedil;qua-<pb pagenum="208"/>libus in ratione continuò dupla. </s>

<s>Sed cùm tu nihil am<lb/>pliùs habeas, quàm quod te obiter attigi&longs;&longs;e memora<lb/>tum &longs;uperiùs e&longs;t; ideò nihil e&longs;t addendum ad ea, quæ in. <lb/>Re&longs;pon&longs;ione leguntur. </s>

<s>Sed cùm tu nihil am<lb/>pliùs habeas, quàm quod te obiter attigi&longs;&longs;e memora<lb/>tum &longs;uperiùs e&longs;t; ideò nihil e&longs;t addendum ad ea, quæ in. <lb/></s>

<s>Re&longs;pon&longs;ione leguntur. </s>

<s><emph type="center"/>IN ARTICVLOS XLIII, & XLIV. </s>

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<s>Secundò, vi&longs;um mihi <lb/>e&longs;t a&longs;&longs;umi po&longs;&longs;e aërem, qui infernè pre&longs;&longs;us, re&longs;ilien&longs;<lb/>que ad latera, in locum po&longs;terum &longs;uccederet, &longs;uperné<lb/>que in&longs;taret, pro cau&longs;&longs;a impellente; & magneticam Ter<lb/>ræ vim, quæ hamulorum, catenularumque in&longs;tar, in<lb/>fernè pelliceret, pro cau&longs;&longs;a trahente. </s>

<s>Tertiò vi&longs;um e&longs;t <lb/>aërem non po&longs;&longs;e inchoare motum, quatenus &longs;i nulla <lb/>e&longs;&longs;et Terra, & &longs;olus aër in vniuer&longs;o, & ip&longs;e quidem in<lb/>finitè fu&longs;us, vnaque lapis intra ip&longs;um, tunc lapis in <lb/>hanc potiùs partem, quàm in aliam non moueretur: <lb/>quare & motum lapidis videri debere ab attractione <lb/>incipere, ac tum po&longs;&longs;e ab aëre &longs;uccedente adiutari. <lb/>Quartò, cùm fui&longs;&longs;em ratiocinatus motum &longs;emel im<lb/>pre&longs;&longs;um futurum perpetuum, & æquabilem, ni&longs;i e&longs;&longs;et <lb/>cau&longs;&longs;a, quæ illum aut retundendo minueret, aut vrgen<lb/>do acceleraret; conclu&longs;i motum lapidis accelerari, quòd <lb/>&longs;tatim à prima attractione, & qua&longs;i po&longs;t primum <expan abbr="ict&utilde;">ictum</expan>, <lb/>&longs;uccederent continuò ictus alij, qui impre&longs;&longs;ione facta, <lb/>manenteque facerent motum celeriorem. </s>

<s>Quartò, cùm fui&longs;&longs;em ratiocinatus motum &longs;emel im<lb/>pre&longs;&longs;um futurum perpetuum, & æquabilem, ni&longs;i e&longs;&longs;et <lb/>cau&longs;&longs;a, quæ illum aut retundendo minueret, aut vrgen<lb/>do acceleraret; conclu&longs;i motum lapidis accelerari, quòd <lb/>&longs;tatim à prima attractione, & qua&longs;i po&longs;t primum <expan abbr="ict&utilde;">ictum</expan>, <lb/>&longs;uccederent continuò ictus alij, qui impre&longs;&longs;ione facta, <lb/>manenteque facerent motum celeriorem. </s>

<s>Quintò vi<lb/>&longs;um e&longs;t neque attractionem &longs;olam, neque impul&longs;io<lb/>nem &longs;olam, neque vllam aliam &longs;implicem cau&longs;&longs;am &longs;uf<lb/>ficere ad memoratam progre&longs;&longs;ionem: quia cùm hoc <lb/>modo ictus continenter facti progre&longs;&longs;uri e&longs;&longs;ent &longs;ecun<lb/>dum vnitatum &longs;eriem, con&longs;entaneum videbatur, vt & <lb/>velocitatis gradus acquirerentur, & &longs;patia quoque per<lb/>currerentur &longs;ecundum eandem &longs;eriem: &longs;icque in fine <lb/>cuiu&longs;que momenti &longs;patia aggregata non forent vt <lb/>quadrata temporum, vnum, quatuor, nouem, &longs;ex de<lb/>cim, & quadrata cætera; &longs;ed vt vnum tria, &longs;ex, decem, <lb/>& con&longs;equentia aggregata. </s>

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<s>Pari etiam <lb/>ex &longs;patiis &longs;eptem quarto momento &longs;uperatis, quin que <lb/>retuli ad gradus quinque, quos habui iam acqui&longs;itos, <lb/>ac manenteis, & duo ad duos, qui acquirerentur in<lb/>tereà: non attendens ip&longs;os e&longs;&longs;e treis duntaxat, quorum <lb/>tamen &longs;ingulis deberentur duo &longs;patia; vnde & per illos <lb/>&longs;uperarentur &longs;ex, ac ideò e&longs;&longs;e &longs;olùm nece&longs;&longs;e, vt tum ite<lb/>rùm acquireretur vnicus, quo &longs;eptimum &longs;uperaretur; <lb/>atque ita de cæteris. </s>

<s>Itaque, quam primùm animum <lb/>aduerti, di&longs;plicuit rem &longs;ic expo&longs;ui&longs;&longs;e, vt velocitates ita <lb/>&longs;e habere viderentur, quemadmodum &longs;patia, & non <lb/>modò &longs;patiorum, &longs;ed etiam velocitatum aggregata <lb/>perinde &longs;e habere, vt quadrata temporum: quod mi<lb/>hi quidem vi&longs;um e&longs;t ip&longs;i naturæ repugnare; &longs;ecundum <lb/>quam potiùs doberent velocitates e&longs;&longs;e quemadmo-<pb pagenum="213"/>dum tempora, & aggregata &longs;patiorum &longs;ola &longs;e habere <lb/>vt temporum (aut velocitatum proinde) quadrata. <lb/>Quare & retento eodem Schemate, &longs;ic omnia con<lb/>gruere mihi vi&longs;a &longs;unt, vt partes illæ cturum æquales ro<lb/>præ&longs;entarent &longs;emper æqualeis parteis temporis: lineæ <lb/>verò parallelæ ex vno crute in aliud ductæ, & &longs;tatim <lb/>à prima in parteis æqualeis diui&longs;æ, gradus æqualeis ve<lb/>locitatis; intercepta autem illa, æqualiaque triangula, <lb/>æqualeis parteis &longs;patii; ac denique ex triangulis impari <lb/>numero &longs;ub vnoquoque <expan abbr="mom&etilde;to">momento</expan> contentis, a&longs;&longs;umpta <lb/>bina, & quadrangulos con&longs;tituentia triangula, repræ<lb/>&longs;entarent &longs;patia per gradus manenteis decur&longs;a; & quod <lb/>impar &longs;upere&longs;&longs;et, repræ&longs;entaret &longs;patium gradu interim <lb/>acqui&longs;ito decur&longs;um. </s>

<s>Quare & retento eodem Schemate, &longs;ic omnia con<lb/>gruere mihi vi&longs;a &longs;unt, vt partes illæ cturum æquales ro<lb/>præ&longs;entarent &longs;emper æqualeis parteis temporis: lineæ <lb/>verò parallelæ ex vno crute in aliud ductæ, & &longs;tatim <lb/>à prima in parteis æqualeis diui&longs;æ, gradus æqualeis ve<lb/>locitatis; intercepta autem illa, æqualiaque triangula, <lb/>æqualeis parteis &longs;patii; ac denique ex triangulis impari <lb/>numero &longs;ub vnoquoque <expan abbr="mom&etilde;to">momento</expan> contentis, a&longs;&longs;umpta <lb/>bina, & quadrangulos con&longs;tituentia triangula, repræ<lb/>&longs;entarent &longs;patia per gradus manenteis decur&longs;a; & quod <lb/>impar &longs;upere&longs;&longs;et, repræ&longs;entaret &longs;patium gradu interim <lb/>acqui&longs;ito decur&longs;um. </s>

<s>Atque hoc quidem modo &longs;en<lb/>tentiam expre&longs;&longs;i partim in Re&longs;pon&longs;ione, partim etiam <lb/>&longs;uperiùs circa explicandum Controuer&longs;iæ &longs;tatum. </s>

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<s>De Grauitate verò, quod &longs;it qualitas in&longs;ita, & ab <lb/>attractione di&longs;tincta, cuius effectus &longs;it motus deorsùm, <lb/>& ille quidem aëre, alióve quovis medio &longs;eclu&longs;o, &longs;em<lb/>per idem, &longs;imili&longs;ve &longs;ui, aut æquabilis, videtur mihi dici <lb/>non po&longs;&longs;e. </s>

<s>Ac vt illa quidem præteream, quæ mox <lb/>&longs;unt de aëre, & nomine aëris vniuersè de medio dicta; <lb/>dicamus igitur de vacuo, in quo ais <expan abbr="graui&utilde;">grauium</expan> de&longs;cen&longs;um <pb pagenum="218"/>futurum æquabilem, ob grauitatem &longs;emper eandem. <lb/>Nihil autem e&longs;t nece&longs;&longs;e admoneam, quod &longs;atis in Epi<lb/>&longs;tolis antè memoratis expre&longs;&longs;i: lapidi nempe, ex&longs;i&longs;tenti <lb/>in vacuo, perinde e&longs;&longs;e penitùs, ac &longs;i Mundus prorsùs <lb/>non foret: quippe ni&longs;i perinde foret, habere igitur de<lb/>beret colligationem quampiam cum Mundo, aliqua<lb/>ve parte ip&longs;ius, &longs;iue per contactum corporeum, &longs;iue per <lb/>defluxum, atque tran&longs;mi&longs;&longs;ionem aut aliquorum cor<lb/>pu&longs;culorum, aut qualitatum, accidentiumve, non &longs;ine <lb/>&longs;ubiecto corporeo, fulcien eque prætermeantium: <lb/>quo ca&longs;u non e&longs;&longs;et lapis in vacuo, &longs;ed in &longs;patio cor<lb/>poribus, &longs;ub&longs;tantiave corporea pleno. </s>

<s>Nihil autem e&longs;t nece&longs;&longs;e admoneam, quod &longs;atis in Epi<lb/>&longs;tolis antè memoratis expre&longs;&longs;i: lapidi nempe, ex&longs;i&longs;tenti <lb/>in vacuo, perinde e&longs;&longs;e penitùs, ac &longs;i Mundus prorsùs <lb/>non foret: quippe ni&longs;i perinde foret, habere igitur de<lb/>beret colligationem quampiam cum Mundo, aliqua<lb/>ve parte ip&longs;ius, &longs;iue per contactum corporeum, &longs;iue per <lb/>defluxum, atque tran&longs;mi&longs;&longs;ionem aut aliquorum cor<lb/>pu&longs;culorum, aut qualitatum, accidentiumve, non &longs;ine <lb/>&longs;ubiecto corporeo, fulcien eque prætermeantium: <lb/>quo ca&longs;u non e&longs;&longs;et lapis in vacuo, &longs;ed in &longs;patio cor<lb/>poribus, &longs;ub&longs;tantiave corporea pleno. </s>

<s>Quamobrem <lb/>nihil penitùs cum ip&longs;o Mundo communicans, perinde <lb/>&longs;e habere debet, ac &longs;i Mundus foret redactus in ni<lb/>hilum, aut procul in immen&longs;itatem imaginariorum <lb/>&longs;patiorum tran&longs;latus. </s>

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<s>Si euane&longs;cit, <lb/>ergo debet pari ratione euane&longs;cere, qui &longs;ecundo mo<lb/>mento, & con&longs;equente quolibet ab aëre imprimitur; <lb/>neque enim potior e&longs;t ratio de vna cau&longs;&longs;a, quàm de <lb/>alia (imò neque vlla ratio de vtravis e&longs;t; cùm & dici <lb/>non valeat quid perire impetum faciat, &, &longs;i quid di<lb/>catur, probaturum &longs;it, quicquid vnico ictu à nobis per<lb/>cellitur, eo &longs;olo momento, quo percellitur, moueri, ne<lb/>que vel tan tillum per&longs;euerare po&longs;&longs;e in motu, tanquam <lb/>impetu illicò pereunte) quare & aëre nequicquam <lb/>pellente per&longs;euerabit nihilominus con&longs;titutus à te <lb/>æquabilis motus. </s>

<s>Sin manet: ergo impetus primi mo<lb/>menti additusimpetui &longs;ecundi, & quilibet anteceden<lb/>tes additi con&longs;equentibus motum efficient celeriorem. <lb/>Itaque motus à grauitate &longs;ola non &longs;ic elicietur, vt &longs;it <lb/>&longs;emper &longs;ui &longs;imilis, atque vniformis; neque grauitas <lb/>&longs;emper eadem, &longs;imili&longs;que &longs;ui, & inalterata (hoc e&longs;t, quæ <lb/>à me &longs;implex dicta e&longs;t, &longs;ine appellata adiectitia) per<lb/>&longs;euerabit. </s>

<s>Sin manet: ergo impetus primi mo<lb/>menti additusimpetui &longs;ecundi, & quilibet anteceden<lb/>tes additi con&longs;equentibus motum efficient celeriorem. <lb/></s>

<s>Itaque motus à grauitate &longs;ola non &longs;ic elicietur, vt &longs;it <lb/>&longs;emper &longs;ui &longs;imilis, atque vniformis; neque grauitas <lb/>&longs;emper eadem, &longs;imili&longs;que &longs;ui, & inalterata (hoc e&longs;t, quæ <lb/>à me &longs;implex dicta e&longs;t, &longs;ine appellata adiectitia) per<lb/>&longs;euerabit. </s>

<s><emph type="center"/>IN RESPONSIONIS CONCLVSIONEM.<emph.end type="center"/></s>

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<s>Veritatem autem eo loco habeo, <lb/>vt Eius amore, qui &longs;eip&longs;um e&longs;&longs;e Veritatem dixit, &longs;an<lb/>cti&longs;&longs;imum reputem, ip&longs;am, quantum agno&longs;citur, nulli <lb/>rei non præhabere, & à conditione per&longs;ona (aliunde <lb/>licet cari&longs;&longs;imæ, ac venerabili&longs;&longs;imæ, quæ eius po&longs;&longs;e&longs;&longs;io<lb/>nem &longs;ibi vendicet) qua&longs;i &longs;epo&longs;itam &longs;pectare. </s>

<s>Ac <lb/>tu quidem nunquam volui&longs;ti, opinor, vt quia plurimi <lb/>tuam virtutem, amicitiamque facerem: eapropter, &longs;i <lb/>quidquam tibi videretur, qua&longs;i tabulas vnà ob&longs;igna<lb/>rem; & in tuam iurans &longs;ententiam, quicquid diceres, <lb/>indubium haberem; tuaque permotus authoritate, non <lb/>hærerem, quin veritas planè, prorsúmque à te &longs;taret. <lb/>Quare iniurium haud-quaquam fuit, habere te vnum <lb/>ex iis viris doctis, qui quapiam in re falli po&longs;&longs;int, & <lb/>cùm habeant &longs;e homines, alienum non putent à &longs;e, vt <lb/>errare po&longs;&longs;e, &longs;ic po&longs;&longs;e ab aliis &longs;ecus &longs;entientibus mone<lb/>ri. </s>

<s>Quare iniurium haud-quaquam fuit, habere te vnum <lb/>ex iis viris doctis, qui quapiam in re falli po&longs;&longs;int, & <lb/>cùm habeant &longs;e homines, alienum non putent à &longs;e, vt <lb/>errare po&longs;&longs;e, &longs;ic po&longs;&longs;e ab aliis &longs;ecus &longs;entientibus mone<lb/>ri. </s>

<s>Ego itaque, non quòd &longs;im profe&longs;&longs;us e&longs;&longs;e eum m<gap/><lb/>qui docere te veritatem aliquam po&longs;&longs;em, &longs;ed quòd te <lb/>veritatem &longs;equi tuâ doctrinâ non e&longs;&longs;em per&longs;ua&longs;us, <pb pagenum="222"/>propo&longs;ui tibi candidè quas &longs;ubdubitandi rationes ha<lb/>berem. </s>

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<s>At cùm <lb/>id non fuerit aliunde, quàm ex iis tenebris deductum; <lb/>quomodo rem mihi aperuit, quæ coram allata à me <lb/>luce euanuit? </s>

<s>Spem factam ais, vt huius lucis à me al<lb/>latæ beneficio veritatem quæ&longs;itam certiùs inueniamus. <lb/>Et quomodo ergo tu &longs;ic eam habui&longs;ti, vt à me quæ&longs;i<lb/>tam mihi ab errore vindicatam iam exhibueris? </s>

<s>Spem factam ais, vt huius lucis à me al<lb/>latæ beneficio veritatem quæ&longs;itam certiùs inueniamus. <lb/></s>

<s>Et quomodo ergo tu &longs;ic eam habui&longs;ti, vt à me quæ&longs;i<lb/>tam mihi ab errore vindicatam iam exhibueris? </s>

<s>An <lb/>forte, quia iuxta lucem à me allatam es ratiocinatus? <lb/>Non &longs;anè: quin potiùs con&longs;titi&longs;ti &longs;emper in illis ii&longs;dem <lb/>tenebris, hoc e&longs;t hæ&longs;i&longs;ti &longs;emper principiis ex tua illa <lb/>fal&longs;a Experientia ductis. </s>

<s>An <lb/>forte, quia iuxta lucem à me allatam es ratiocinatus? <lb/></s>

<s>Non &longs;anè: quin potiùs con&longs;titi&longs;ti &longs;emper in illis ii&longs;dem <lb/>tenebris, hoc e&longs;t hæ&longs;i&longs;ti &longs;emper principiis ex tua illa <lb/>fal&longs;a Experientia ductis. </s>

<s>Ac laudabili&longs;&longs;imum quidem, <lb/>quod profiteris te veritatem, vbicumque inuenta fue<lb/>rit, perquàm grate, & cum plau&longs;u, &longs;uauitateque ample<lb/>xaturum: &longs;ed cùm &longs;it quidem quæ&longs;tio de ea, quam <lb/>profiteris &longs;imul te mihi aperui&longs;&longs;e, exhibui&longs;&longs;eque: quo<lb/>modo, amabò, vis i&longs;ta excipiam? </s>

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<s>Cùm tu igitur duas illas <emph type="italics"/>de Motu impre&longs;&longs;o à Motore <lb/>tran&longs;lato<emph.end type="italics"/> à me con&longs;criptas Epi&longs;tolas reuocaueris in exa<lb/>men; po&longs;tquàm exhibui&longs;ti in&longs;ignia &longs;ingularis bene<lb/>uolentiæ, & comitatis te&longs;timonia: tum explicare ag<lb/>gre&longs;&longs;us es, quæ improba&longs;ti circa Priorem. </s>

<s>Imprimis <lb/>verò, quòd comprobârim illud Galilei decretum, <lb/><emph type="italics"/>Motum corporum decidentium &longs;ic accelerari, vt &longs;uperatæ<emph.end type="italics"/><pb pagenum="229"/><emph type="italics"/>æqualibus temporibus spatia incre&longs;cant, &longs;icut numeri ab vni<lb/>tate impares,<emph.end type="italics"/> dicis me, <emph type="italics"/>Si illud quidem decretum in examen <lb/>adduxi&longs;&longs;em, per&longs;pecturum fui&longs;&longs;e & fal&longs;um, & Paralogi&longs;mo <lb/>euidente confirmatum.<emph.end type="italics"/> Ego verò neque inficior hallu<lb/>cinari potui&longs;&longs;e me; neque me habeo adeò &longs;olertem, vt <lb/>Paralogi&longs;mum à te in&longs;inuatum etiamnùm pervideam. <lb/>Peruelle proinde ip&longs;um o&longs;tendi&longs;&longs;es, atque adeò &longs;ubin<lb/>dica&longs;&longs;es, qua ergo alia proportione accelerationem de<lb/>cidentium fieri, aut experiundo notaueris, aut deduxe<lb/>ris demon&longs;trando. </s>

<s>Peruelle proinde ip&longs;um o&longs;tendi&longs;&longs;es, atque adeò &longs;ubin<lb/>dica&longs;&longs;es, qua ergo alia proportione accelerationem de<lb/>cidentium fieri, aut experiundo notaueris, aut deduxe<lb/>ris demon&longs;trando. </s>

<s>Certè non &longs;atis intelligo quam<lb/>obrem cen&longs;ueris, <emph type="italics"/>&longs;iue hæc proportio, &longs;iue alia &longs;it, eam nihil <lb/>referre ad meum in&longs;titutum:<emph.end type="italics"/> quippe &longs;i alia fuerit, quàm <lb/>quæ &longs;uppo&longs;ita à me e&longs;t, fru&longs;trà e&longs;t tota ratiocinatio. <lb/>Quod ad experientiam porrò attinet, ob&longs;eruationes à <lb/>Galileo recitatas prætereo: ad meas quod &longs;pectat, quot<lb/>quot mihi licuit, & quantum licuit peragere, illam pro<lb/>portionem &longs;emper exhibuerunt. </s>

<s>Quod ad experientiam porrò attinet, ob&longs;eruationes à <lb/>Galileo recitatas prætereo: ad meas quod &longs;pectat, quot<lb/>quot mihi licuit, & quantum licuit peragere, illam pro<lb/>portionem &longs;emper exhibuerunt. </s>

<s>Poti&longs;&longs;imæ fuere, cùm <lb/>rem præ&longs;titi, adnotatis &longs;patiis, tam in prolixiore &longs;ex<lb/>decim orgyis pariete, quàm in tubo vitreo inclinato <lb/>prolixiore duabus; ac &longs;ociis &longs;imul adhibitis, quorum <lb/>&longs;inguli ad &longs;ingula &longs;patia, eorumque notas attenderent, <lb/>vt tam decidente globo <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> parietem, quàm dela<lb/>bente per tubum, dicere po&longs;&longs;ent, ecquo momento ex <lb/>numeratis (& alta voce pronunciatis) æqualibus, glo<lb/>bus pertran&longs;iret vnamquamque notam. </s>

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<s>Et quia proinde vis propria manus, & tran&longs;la<lb/>titia nauis &longs;ibi non repugnant, &longs;ed &longs;e&longs;e veluti inten<lb/>dunt, vnam que totalem, fortioremque, quàm &longs;i &longs;igilla<lb/>tim e&longs;&longs;ent, con&longs;tituunt: heinc fieri videtur, vt &longs;e &longs;e non <lb/>de&longs;truant, &longs;ed vna euadant, quæ tantum &longs;it alterutrâ <lb/>fortior, quantum altera fortis e&longs;t. </s>

<s>Quare & cùm lapis <lb/>non tendat directè &longs;ur&longs;um, vt &longs;i à &longs;ola manu proiicere<lb/>tur: neque directe &longs;ecundùm horizontem, vt &longs;i vehere<lb/>tur, agereturve à &longs;olanaui; verùm feratur motu mi&longs;to, <lb/>obliquóve, & de&longs;cribat per aërem, qua&longs;i arcum (&longs;iue <lb/>potiùs lineam, quam dicunt parabolicam) cuius chorda, <lb/>&longs;eu ba&longs;is &longs;ecundum horizontem e&longs;&longs;e intelligatur; & &longs;a<lb/>gitta, &longs;eu axis &longs;ecundum perpendiculum (prout medium <lb/>e&longs;t inter a&longs;cen&longs;um, & de&longs;cen&longs;um) Exinde e&longs;t, cur lapis <lb/>neque minùs altùm, quàm &longs;i à &longs;ola manu proiiceretur, <lb/>perueniat: neque minus ptorsùm, quàm &longs;i à &longs;ola agere<lb/>tur naui, quatenus prolixitas lineæ e&longs;t quidem maior, <lb/>quàm &longs;implex a&longs;cen&longs;us, de&longs;cen&longs;u&longs;que ad perpendicu<lb/>lum; &longs;ed ad hoc vim &longs;uppletimpre&longs;&longs;io à naui: & pro<lb/>lixior quoque, quàm &longs;implex &longs;ecundum horizontem <lb/>progre&longs;&longs;io; &longs;ed ad hoc vim &longs;upplet impre&longs;&longs;io à manu. <lb/>Idem verò dicendum e&longs;t de &longs;emi parabolica linea: vt <lb/>dum lapis è carche&longs;io non proiectus, &longs;ed dimi&longs;&longs;us, ad <lb/>pternam perinde cadit, vt &longs;i nauis quie&longs;ceret: &longs;iqui<lb/>dem ip&longs;i grauitati lapidem adacturæ &longs;ecundùm perpen<lb/>diculum, accedit vis nauis, qua manus dimittens inte<lb/>rim transfertur, quæque tantumdem impetus addit, <pb pagenum="232"/>quantum e&longs;t nece&longs;&longs;e ad prolixitatem &longs;emiparaboles, <lb/>quàm perpendiculi, maiorem. </s>

<s>Idem verò dicendum e&longs;t de &longs;emi parabolica linea: vt <lb/>dum lapis è carche&longs;io non proiectus, &longs;ed dimi&longs;&longs;us, ad <lb/>pternam perinde cadit, vt &longs;i nauis quie&longs;ceret: &longs;iqui<lb/>dem ip&longs;i grauitati lapidem adacturæ &longs;ecundùm perpen<lb/>diculum, accedit vis nauis, qua manus dimittens inte<lb/>rim transfertur, quæque tantumdem impetus addit, <pb pagenum="232"/>quantum e&longs;t nece&longs;&longs;e ad prolixitatem &longs;emiparaboles, <lb/>quàm perpendiculi, maiorem. </s>

<s>Heinc mirabilis quidem <lb/>e&longs;t ea, quam obiicis, <emph type="italics"/>&longs;emiparabolarum plurium decuplò <lb/>etiam, aut centuplò contractiorum, apertiorumque æqui tem<lb/>poranea de&longs;criptio:<emph.end type="italics"/> &longs;ed videtur tamen apertè deduci ex <lb/>minore, & maiore vi, quæ alteri, vt per axem, perpendi<lb/>culumve duntaxat acturæ, &longs;uperadditur. </s>

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<s>Quòd <emph type="italics"/>experimenta de&longs;ideras alia,<emph.end type="italics"/> facillimum im<lb/>primis e&longs;t, quod vel tuo iu&longs;&longs;u peragi ab Equite pote&longs;t. <lb/>Si is enim pluribus lapillis ad manum a&longs;&longs;umptis, & <lb/>manu ita proten&longs;a, vt &longs;it in perpendiculo, quod pedem <lb/>proximè præter-radat, lapillum vnum primò dïmittat <lb/>quie&longs;cente equo; tum alium equo pedetentim, & pa&longs;&longs;u <pb pagenum="233"/>&longs;olito incedente; & rur&longs;us alium gradiente concitatiùs; <lb/>ac po&longs;teà alium moderatè currente; denique & alium <lb/>præteruolante tum ocyùs, tum ocy&longs;&longs;imè: eueniet &longs;anè, <lb/>vt lapilli omnes præter-radant &longs;emper eandem pedis <lb/>partem, omne&longs;que appareant ip&longs;i equiti ad perpendi<lb/>culum cadere: & quia tamen omnes eiu&longs;modi ca&longs;us, <lb/>præter illum, qui qua&longs;i axis equo quie&longs;cente factus fue<lb/>rit, &longs;emiparabolicæ erunt lineæ, eæque &longs;emper tantò <lb/>apertiores, quantò tran&longs;latio fuerit velocior: fiet, vt &longs;i <lb/>ip&longs;e è regione fueris, illa&longs;que adnotaueris, de&longs;ideraturus <lb/>non &longs;is luculentiora <expan abbr="experim&etilde;ta">experimenta</expan>. </s>

<s>Quòd <emph type="italics"/>experimenta de&longs;ideras alia,<emph.end type="italics"/> facillimum im<lb/>primis e&longs;t, quod vel tuo iu&longs;&longs;u peragi ab Equite pote&longs;t. <lb/></s>

<s>Si is enim pluribus lapillis ad manum a&longs;&longs;umptis, & <lb/>manu ita proten&longs;a, vt &longs;it in perpendiculo, quod pedem <lb/>proximè præter-radat, lapillum vnum primò dïmittat <lb/>quie&longs;cente equo; tum alium equo pedetentim, & pa&longs;&longs;u <pb pagenum="233"/>&longs;olito incedente; & rur&longs;us alium gradiente concitatiùs; <lb/>ac po&longs;teà alium moderatè currente; denique & alium <lb/>præteruolante tum ocyùs, tum ocy&longs;&longs;imè: eueniet &longs;anè, <lb/>vt lapilli omnes præter-radant &longs;emper eandem pedis <lb/>partem, omne&longs;que appareant ip&longs;i equiti ad perpendi<lb/>culum cadere: & quia tamen omnes eiu&longs;modi ca&longs;us, <lb/>præter illum, qui qua&longs;i axis equo quie&longs;cente factus fue<lb/>rit, &longs;emiparabolicæ erunt lineæ, eæque &longs;emper tantò <lb/>apertiores, quantò tran&longs;latio fuerit velocior: fiet, vt &longs;i <lb/>ip&longs;e è regione fueris, illa&longs;que adnotaueris, de&longs;ideraturus <lb/>non &longs;is luculentiora <expan abbr="experim&etilde;ta">experimenta</expan>. </s>

<s>Poteris verò ip&longs;e quo<lb/>que &longs;imile quidpiam experiri, &longs;i pilam manu &longs;u&longs;tentâ<lb/>ris, ac dimi&longs;eris, dum per aulam, aut pergulam nunc len<lb/>to pa&longs;&longs;u, nunc concitato, nunc etiam currendo incedes. <lb/>Nam vt pila tibi &longs;emper apparebit ad perpendiculum <lb/>cadere: ita agno&longs;ces ab ea de&longs;cribi &longs;emiparabolen nunc <lb/>contractam, nunc apertam, nunc apertiorem. </s>

<s>Nam vt pila tibi &longs;emper apparebit ad perpendiculum <lb/>cadere: ita agno&longs;ces ab ea de&longs;cribi &longs;emiparabolen nunc <lb/>contractam, nunc apertam, nunc apertiorem. </s>

<s>Quod <lb/>con&longs;equenter verò depo&longs;cis <emph type="italics"/><expan abbr="experiment&utilde;">experimentum</expan> in globo &longs;ursùm, <lb/>& &longs;ecundum mali nunc quie&longs;centis, nunc moti longitudinem <lb/>areu-bali&longs;ta emi&longs;&longs;o:<emph.end type="italics"/> id tanta facis vrbanitate, vt volenti&longs;<lb/>fimus recipiam me, cum fauente Numine in Prouin<lb/>ciam rediero, & ad mare acce&longs;&longs;ero, rem in tui gratiam <lb/>præ&longs;titurum. </s>

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<s>Vides aliunde me illeic <lb/>loci nihil aliud requirere, quàm commodam quan<lb/>dam v&longs;urpationem nominum, qua &longs;i quis aliam attu<lb/>lerit commodiorem, &longs;im complexurus. </s>

<s>Et quia is mo<lb/>tus mihi e&longs;t vi&longs;us dici po&longs;&longs;e <emph type="italics"/>naturalis,<emph.end type="italics"/> qui aut &longs;ponte fit, <lb/>aut &longs;ine repugnantia; is <emph type="italics"/>violentus,<emph.end type="italics"/> qui præter naturam, <lb/>aut cum aliqua repugnantia: heinc e&longs;t, cur <emph type="italics"/>Ince&longs;&longs;um na<lb/>turalem<emph.end type="italics"/> dixerim, quatenus nempe &longs;ponte fit; & <emph type="italics"/>Salta<lb/>tionem violentam,<emph.end type="italics"/> quatenus quadam cum repugnantia. <lb/>Non quod Ince&longs;&longs;us quoque non fiat cum repugnantia <lb/>aliqua, propter ip&longs;um pondus membrorum: aut Salta<lb/>tio non fiat &longs;ponte, &longs;iue ab eodem principio interno, <lb/>hoc e&longs;t anima: &longs;ed quòd neque Ince&longs;&longs;us fiat cum &longs;en&longs;i<lb/>bili adeò repugnantia, tantoque connixu ad eam &longs;u<lb/>perandam, vt Saltatio; neque Saltatio &longs;it perinde &longs;pon<lb/>tanea, incogitatáque, ac ip&longs;e Ince&longs;&longs;us; vt proinde cum <lb/>vterque motus aliqua ratione naturalis &longs;it, aliqua ra<lb/>tione violentus; Ince&longs;&longs;us tamen magis naturalis &longs;it, & <lb/>Saltatio magis violenta; cùm & id probetur ex eo, <lb/>quòd Ince&longs;&longs;us &longs;it incomparabiliter æquabilior, durabi<lb/>lior, minu&longs;que fatigans, quàm ip&longs;a Saltatio. </s>

<s>Non quod Ince&longs;&longs;us quoque non fiat cum repugnantia <lb/>aliqua, propter ip&longs;um pondus membrorum: aut Salta<lb/>tio non fiat &longs;ponte, &longs;iue ab eodem principio interno, <lb/>hoc e&longs;t anima: &longs;ed quòd neque Ince&longs;&longs;us fiat cum &longs;en&longs;i<lb/>bili adeò repugnantia, tantoque connixu ad eam &longs;u<lb/>perandam, vt Saltatio; neque Saltatio &longs;it perinde &longs;pon<lb/>tanea, incogitatáque, ac ip&longs;e Ince&longs;&longs;us; vt proinde cum <lb/>vterque motus aliqua ratione naturalis &longs;it, aliqua ra<lb/>tione violentus; Ince&longs;&longs;us tamen magis naturalis &longs;it, & <lb/>Saltatio magis violenta; cùm & id probetur ex eo, <lb/>quòd Ince&longs;&longs;us &longs;it incomparabiliter æquabilior, durabi<lb/>lior, minu&longs;que fatigans, quàm ip&longs;a Saltatio. </s>

<s>Neque <lb/>verò &longs;i ad eos ip&longs;os, quos tu in&longs;inüas, eruditos prouo<lb/>care lubuerit, non potero memet tueri Principis eo<lb/>rum authoritate, qui etiam in ijs, quæ à &longs;e mouentur, <lb/>cuiu&longs;modi &longs;unt animalia, motus alios <foreign lang="greek">fu/s<gap/></foreign> <emph type="italics"/>naturá,<emph.end type="italics"/><lb/>alios <foreign lang="greek">w<gap/>a\ fu/sin</foreign> <emph type="italics"/>præter naturam,<emph.end type="italics"/> pro varietate Po&longs;i<lb/>tionum, modorumque, fieri agno&longs;cit. </s>

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<s>Idem porrò dicendum e&longs;t circa id, quod miraris <lb/><emph type="italics"/>de volutione globi &longs;upra planum.<emph.end type="italics"/> Neque enim dixi il<lb/>lam e&longs;&longs;e ab&longs;olutè naturalem, qua&longs;i nullo modo ab alio <lb/>&longs;it: &longs;ed &longs;olùm comparatione motus, quo globus per <lb/>aërem tran&longs;adigitur, quique &longs;it præ&longs;ertim dicendus <lb/>violentus. </s>

<s>Scilicet globus, quà globus e&longs;t, &longs;eu ex figuræ <lb/>&longs;uæ natura, ad volutionem e&longs;t comparatus, imò com<lb/>parati&longs;&longs;imus; volutionem, inquam, quæ peragitur non <lb/>modò in loco, &longs;eu &longs;upra axem &longs;u&longs;tentantem, vt Ari&longs;to<lb/>teles admittit: &longs;ed maximè etiam per locum, &longs;eu &longs;u<lb/>pra planum horizontale, quod & &longs;u&longs;tentat, & nihil <lb/>re&longs;i&longs;tit; cùm aliunde tamen ex eodem Ari&longs;totele, nul<lb/>lum &longs;it corpus globo ineptius ad motum <foreign lang="greek">ei)s <gap/> w<gap/>e\n</foreign><lb/><emph type="italics"/>antror&longs;um,<emph.end type="italics"/> & qualis e&longs;t eorum, quæ per &longs;e mouentur. <lb/>Heinc proinde &longs;it, vt de globo &longs;upra planum con&longs;titu<lb/>to liceat dicere, illum ad motum &longs;upra planum, &longs;eu ad <lb/>volutionem ita propendere, vt minimo pul&longs;u, ac ve<lb/>luti nutu talem motum &longs;ubeat, ip&longs;oque ita afficiatur, <lb/>vt depo&longs;iturus illum nunquam &longs;it, ni&longs;i planum defece<lb/>rit, aut facta aliunde fuerit re&longs;i&longs;tentia. </s>

<s>Heinc proinde &longs;it, vt de globo &longs;upra planum con&longs;titu<lb/>to liceat dicere, illum ad motum &longs;upra planum, &longs;eu ad <lb/>volutionem ita propendere, vt minimo pul&longs;u, ac ve<lb/>luti nutu talem motum &longs;ubeat, ip&longs;oque ita afficiatur, <lb/>vt depo&longs;iturus illum nunquam &longs;it, ni&longs;i planum defece<lb/>rit, aut facta aliunde fuerit re&longs;i&longs;tentia. </s>

<s>Ni&longs;i verò ille <lb/>motus non e&longs;t dicendus maximè &longs;ecundum mobilis <lb/>naturam, qui &longs;emel inditus, &longs;it ex &longs;e perpetuus, ac præ<lb/>tereà æquabilis, vniu&longs;que tenoris? <emph type="italics"/>At,<emph.end type="italics"/> inquis, <emph type="italics"/>natu-<emph.end type="italics"/><pb pagenum="239"/><emph type="italics"/>ralis nondicitur motus, ni&longs;i ab interno principio, ip&longs;aque rei <lb/>natura effectiuè procedat.<emph.end type="italics"/> Sed quid-ni ille quoque di<lb/>catur, qui ab externo e&longs;t, effectiuéque ab alio e&longs;t; &longs;i mo<lb/>dò <expan abbr="&longs;ecund&utilde;">&longs;ecundum</expan> mobilis <expan abbr="naturã">naturam</expan>, ac di&longs;po&longs;itionem, non ve<lb/>rò contra illam &longs;it; & qua&longs;i fiat, quod dicitur, <foreign lang="greek"><gap/>sont<gap/><lb/>o)t<gap/>w<gap/><gap/>n</foreign>; <emph type="italics"/>in&longs;tigare iam fe&longs;tinantem?<emph.end type="italics"/> Et nonne ip&longs;e <lb/>fateris cum Ari&longs;totele motum rerum grauium e&longs;&longs;e na<lb/>turalem, quem ille tamen vult ab externo, non ab in<lb/>terno e&longs;&longs;e principio? </s>

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<s>Dicis po&longs;teà, <emph type="italics"/>forè, vt mihi Eruditi omnes conce<lb/>dant accelerationem e&longs;&longs;e violentam, &longs;i illam, vt quid &longs;uper<lb/>ueniens, mente &longs;ecernamus ab ip&longs;o de&longs;cen&longs;u.<emph.end type="italics"/> Non e&longs;t porrò <lb/>cur dubites, quin ip&longs;e quoque mente &longs;ecernam motum <lb/>illum &longs;implicem, quo lapis fertur deor&longs;um, quemque <lb/>tu de&longs;cen&longs;um appellas, ab omnibus, qui &longs;uperueniunt, <lb/>giadibus accelerationis. </s>

<s>Quippe id abunde expre&longs;&longs;i, <lb/>cùm dixi <emph type="italics"/>eum motum, &longs;eclu&longs;a acceleratione, fore ex &longs;e æqua<lb/>bilem, &longs;ed imperceptibilem tamen, ob incredibilem &longs;egnitiem.<emph.end type="italics"/><lb/>Non e&longs;t proinde etiam, cur hæreas, quin illum e&longs;&longs;e na<lb/>turalem, & &longs;ine reluctatione agno&longs;cam; quippe qui <lb/>eum faciam, quantum e&longs;t ex &longs;e, æquabilem, perpetuum, <lb/>ac talem, qui &longs;it imprimendus etiam lapidi ex&longs;i&longs;tenti <lb/>in vacuo, vbi mobile nullam habet ad motum repu<lb/>gnantiam, quocumque ver&longs;um tandem agatur: verum <lb/>quòd eiu&longs;modi motus cen&longs;eri naturalis po&longs;&longs;it, non id<lb/>circò cen&longs;eo ca&longs;um lapidis habendum e&longs;&longs;e naturalem. <lb/>Quoniam tamet&longs;i talis motus in hoc ca&longs;u interueniat, <lb/>euane&longs;cit tamen, &longs;iue nullus e&longs;t, re&longs;pectu accelerationis, <pb pagenum="241"/>quæ ip&longs;i &longs;uperuenit, quæque vtramque paginam facit; <lb/>& quam ip&longs;e quoque fateris violentam. </s>

<s>Quoniam tamet&longs;i talis motus in hoc ca&longs;u interueniat, <lb/>euane&longs;cit tamen, &longs;iue nullus e&longs;t, re&longs;pectu accelerationis, <pb pagenum="241"/>quæ ip&longs;i &longs;uperuenit, quæque vtramque paginam facit; <lb/>& quam ip&longs;e quoque fateris violentam. </s>

<s>Atque vt per&longs;<lb/>picuè appareat cuius momenti &longs;it ille motus, &longs;iue, vt <lb/>tu vocas, de&longs;cen&longs;us, ab acceleratione &longs;ecretus, & cum <lb/>ip&longs;a tamen comparatus; age Experiamur, &, exempli <lb/>gratiâ, altitudin m accipiamus non immanem <expan abbr="aliquã">aliquam</expan>, <lb/>&longs;ed qualem &longs;olùm vulgò v&longs;urpant inter tabulatum, & <lb/>laquear, duarum videlicet orgyiarum. </s>

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<s>Erunt proin<lb/>de in vno minuto horæ &longs;ecundo minuta decima <lb/>167961600000000. Quoniam autem lapistotis i&longs;tis <lb/>decimis &longs;ucce&longs;&longs;iue fluentibus percurrit &longs;ucce&longs;&longs;iuè &longs;pa<lb/>tium duarum orgyiarum, illiu&longs;ve particulas; ideò cùm <lb/>iuxta memoratam, ob&longs;eruatamque proportionem, &longs;pa<lb/>tia &longs;int inter&longs;e vt quadrata temporum, intelligi opor<lb/>tebit di&longs;tingui &longs;patij particulas 3821109907456 <lb/>0000000000000000. Exinde verò &longs;ict, vt cùm pri<lb/>mo momento lapis non percurrat ni&longs;i vnam huiu&longs;mo<lb/>di particularum, nece&longs;&longs;e &longs;it, vt acceleratione &longs;eclu&longs;a, & <lb/>non percurrendo quolibet con&longs;e quentium momento<lb/>rum, plu&longs;quam vnam particulam, totidem a&longs;&longs;ignentur <pb pagenum="242"/>decima minuta, &longs;eu momenta primo æqualia, quot <lb/>&longs;unt particulæ &longs;patij memoratæ. </s>

<s>Reducamus itaque <lb/>huiu&longs;cemodi decima minuta in prima, in horas, in dies, <lb/>in annos; procreabuntur certè anni Iuliani, &longs;eu quales <lb/>nobis v&longs;ui &longs;unt 5322381, cum vno ferè anno prætereà. <lb/>Igitur hic erit numerus annorum, quo demùm exacto <lb/>lapis ex laqueari ad tabulatum petueniet. </s>

<s>Igitur hic erit numerus annorum, quo demùm exacto <lb/>lapis ex laqueari ad tabulatum petueniet. </s>

<s>Heinc, &longs;i <lb/>inter varianteis Chronologorum opiniones, &longs;uppona<lb/>mus Mundum fui&longs;&longs;e conditumà &longs;ex mille annis; vides, <lb/>vt &longs;i lapis ab initio Mundi occ&oelig;pi&longs;&longs;et cadere, non<lb/>dum cecidi&longs;&longs;et temporibus no&longs;tris vna &longs;eptima parte <lb/>digiti; vtque oporteret ad <expan abbr="perficiend&utilde;">perficiendum</expan> <expan abbr="mot&utilde;">motum</expan> durare ad<lb/>hûc <expan abbr="Mund&utilde;">Mundum</expan> <expan abbr="plu&longs;quã">plu&longs;quam</expan> octingenteis, octogies, & &longs;epties, <lb/>quàm durauerit hactenus. </s>

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<s>Quid verò, &longs;i acciperemus <lb/>pro momento primo non momentum horæ <expan abbr="decim&utilde;">decimum</expan>, <lb/>&longs;ed cente&longs;imum, &longs;ed mille&longs;imum; quàm multæ myria<lb/>des durationum Mundi nece&longs;&longs;ariæ forent, ptin&longs;quàm <lb/>illo motu digitus vnus peruaderetur? </s>

<s>Sed ne eò v&longs;que <lb/>rem deducam, quæ&longs;o te&longs;olùm, tamet&longs;i is motus con<lb/>cedatur & naturalis, & à principio intrin&longs;eco; cùm in<lb/>&longs;en&longs;ibilis tamen &longs;it non modò intra vnum minutum <lb/>&longs;ecundum, &longs;ed etiam intra centum annos, quibus totis <lb/>apparere non po&longs;&longs;it cente&longs;ima parte digiti promotior: <lb/>quæ&longs;o te, inquam, an-non ca&longs;us lapidis valeat potiùs <lb/>denominari ab acceleratione violentus, quàm ab illo <lb/>naturalis; cùm quicquid &longs;en&longs;ibile habet, ab acceleratio. <lb/>ne obtineat. </s><pb pagenum="243"/>

<s>ne obtineat. </s><pb pagenum="243"/>

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<s>Dicis <emph type="italics"/>te non intelligere quomodò ea<emph.end type="italics"/><pb pagenum="247"/><emph type="italics"/>&longs;int à me &longs;eriò &longs;cripta:<emph.end type="italics"/> &longs;ed potui non &longs;eria &longs;eriò &longs;cribere; <lb/>hoc e&longs;t non ioco, &longs;ed vt eruditi, quæ magis &longs;eria habue<lb/>rint, doceant. </s>

<s>Neque enim e&longs;t, cur exi&longs;times i&longs;tis me <lb/>nugis ita hærere, vt ip&longs;as qua&longs;i veritatem ip&longs;i&longs;&longs;imam <lb/>habeam, aut colam, &longs;ed cùm totus Mundus &longs;it nuga<lb/>rum plenus, & videre videar nugas quoque e&longs;&longs;e, quæ <lb/>vulgò habentur &longs;eria maximè; &longs;upere&longs;&longs;e exi&longs;timo, vt <lb/>eas nugas deligam, quæ e&longs;&longs;e minùs nugæ videantur. <lb/>Quæris, <emph type="italics"/>Ecquid nam proferam, cur non poßint grauia deor<lb/>&longs;um moueri naturâ?<emph.end type="italics"/> Sed protuli primùm illud argumen<lb/>tum, quod mox antè repetij. </s>

<s>Quæris, <emph type="italics"/>Ecquid nam proferam, cur non poßint grauia deor<lb/>&longs;um moueri naturâ?<emph.end type="italics"/> Sed protuli primùm illud argumen<lb/>tum, quod mox antè repetij. </s>

<s>Deinde, vnde colligis <lb/>inficiari me moueri lapidem naturâ? </s>

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<s>Subinde ergo comparo cum immoto globo <lb/>Tellurem, cum circum-ductis Sidera; & dico, &longs;icut glo<lb/>bus ille emoueri pote&longs;t à loco, in quo e&longs;t, & promoue<lb/>ri ver&longs;us alium; &longs;ic po&longs;&longs;e ip&longs;am quoque Tellurem emo<lb/>ueri à loco, in quo e&longs;t, & promoueri ver&longs;us Lunam; <lb/>addoque, vt globus ille in quocumque alio aquæ loco <lb/>reponatur, in eo pari modo quie&longs;cet, neque priorem <lb/>repetet: &longs;ic & Tellurem, in quocumque loco con&longs;titu<lb/>ta fuerit, in eo man&longs;uram, nec pri&longs;tinum repetituram. <lb/>Et dicis tu quidem <emph type="italics"/>attolli,<emph.end type="italics"/> quod ego heic &longs;impliciter <lb/>dico <emph type="italics"/>emoueri:<emph.end type="italics"/> &longs;ed nimirùm, quia concipis infimum e&longs;&longs;e <lb/>in Mundo locum, & Terram ip&longs;um occupare: cùm &longs;u<lb/>perum tamen, & inferum comparatè &longs;olùm ad nos, & <lb/>re&longs;pectu globi, quem inhabitamus, videatur e&longs;&longs;e acci<lb/>piendum. </s>

<s>Et dicis tu quidem <emph type="italics"/>attolli,<emph.end type="italics"/> quod ego heic &longs;impliciter <lb/>dico <emph type="italics"/>emoueri:<emph.end type="italics"/> &longs;ed nimirùm, quia concipis infimum e&longs;&longs;e <lb/>in Mundo locum, & Terram ip&longs;um occupare: cùm &longs;u<lb/>perum tamen, & inferum comparatè &longs;olùm ad nos, & <lb/>re&longs;pectu globi, quem inhabitamus, videatur e&longs;&longs;e acci<lb/>piendum. </s>

<s>Ex hoc certè intelligo, tran&longs;latà Terrâ ver&longs;us <lb/>Lunam ad Antipodas ex&longs;i&longs;tentem, nos non propterea <lb/>auolaturos in derelictum à Terra locum; vt neque <lb/>etiam Antipodas, tran&longs;latâ Terra ver&longs;us Lunam factam <lb/>nobis ad verticem: &longs;ed & illos, & nos perinde in ea<lb/>dem antiqua &longs;ede ver&longs;aturos, tanquam &longs;imùl tran&longs;lato <lb/>Terræ centro, re&longs;pectu cuius, & comparatè ad &longs;itum <lb/>capitis, pedumque no&longs;trorum, cen&longs;ebimur &longs;emper a&longs;<lb/>cendere, & de&longs;cendere, &longs;iue locum &longs;ur&longs;um, deor&longs;um<lb/>que habere; non autem &longs;impliciter re&longs;pectu loci, in <lb/>quo Terra aut erit, aut fuerit, & qui &longs;eu centrum Mun<lb/>di &longs;it, &longs;eu non &longs;it, nihil ad a&longs;cen&longs;um, aut de&longs;cen&longs;um <lb/>&longs;acit. </s>

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<s>An non, vt fiat incitatio, e&longs;&longs;e alia pars inci<lb/>tans, & alia incitata debet? </s>

<s>Idem certè mouere &longs;eip&longs;um, <lb/>ni&longs;i parteis habeat mouentem, & motam, cùm iis, quos <lb/>tu vocas Eruditos, aduer&longs;atur; tum communi etiam no<lb/>tioni repugnat, cui Ari&longs;toteles inhærens, impo&longs;&longs;ibilo <lb/>e&longs;&longs;e cen&longs;et, vt id &longs;eip&longs;um moueat, quod e&longs;t <foreign lang="greek">s<gap/>exe\<gap/></foreign>, <lb/><emph type="italics"/>continuum<emph.end type="italics"/> &longs;<gap/>u <emph type="italics"/>vniu&longs;modi, rigidum, inarticulatum.<emph.end type="italics"/> Non<lb/>ne verò &longs;unt huius generis tam Magnes, quàm Ferrum? <lb/>De altero ergo vt &longs;olùm loquamur, quænam in Ferro <lb/>parsincitans? </s>

<s>De altero ergo vt &longs;olùm loquamur, quænam in Ferro <lb/>parsincitans? </s>

<s>Et quid illam mouet vt incitet aliam? <lb/></s>

<s>Et quid illam mouet vt incitet aliam? <lb/>Et, quonam motus genere illam in citat? </s>

<s>Et, quonam motus genere illam in citat? </s>

<s>Pul&longs;u-ne, an <lb/>tractu, an alio? </s>

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<s>Sed hæc vt præteream; cùm videamus <lb/>Ferrum non ex quacumque di&longs;tantia in amplexum <lb/>Magnetis accurrere, &longs;ed accurrere &longs;olum, v. </s>

<s>c. ab vno <lb/>palmo; quo modo vis intelligamus incitari ferrum <lb/>&longs;ponte naturæ in di&longs;tantia palmi, non in di&longs;tantia cubi<lb/>ti? </s>

<s>ab vno <lb/>palmo; quo modo vis intelligamus incitari ferrum <lb/>&longs;ponte naturæ in di&longs;tantia palmi, non in di&longs;tantia cubi<lb/>ti? </s>

<s>An in di&longs;tantia cubiti &longs;uæ &longs;pontis non e&longs;t? </s>

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<s>quî po&longs;&longs;it iure potiore Ferrum ad &longs;uper<lb/>ex&longs;tantem Magnetem, ni&longs;i traxent ip&longs;um Magnes? </s>

<s>An <lb/>&longs;uæ &longs;pontis magis e&longs;t, pote&longs;tque magis agere &longs;ponte? <lb/>An cùm homo pedibus pul&longs;et, prematque fru&longs;trà aë<lb/>rem, Ferrum id præ&longs;tat appo&longs;itè magis? </s>

<s>An <lb/>&longs;uæ &longs;pontis magis e&longs;t, pote&longs;tque magis agere &longs;ponte? <lb/></s>

<s>An cùm homo pedibus pul&longs;et, prematque fru&longs;trà aë<lb/>rem, Ferrum id præ&longs;tat appo&longs;itè magis? </s>

<s>Si non capia<lb/>mus igitur quomodò &longs;eu homo, &longs;eu Ferrum incitare <lb/>po&longs;&longs;it &longs;eip&longs;um, & Ferrum certè magis, quàm homo, <pb pagenum="260"/>defectu firmitudinis, re&longs;i&longs;tentiæque in aëre, propter in<lb/>nixum, &longs;ine quo non videtur fieri po&longs;&longs;e incitatio: quid <lb/>e&longs;t, cur, vt homo, dum &longs;ur&longs;um effertur, arguit e&longs;&longs;e à <lb/>quo trahatur, non &longs;ic Ferrum arguat, dum &longs;ursùm ef<lb/>fertur? </s>

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<s>Sed nihil &longs;anè nece&longs;&longs;e e&longs;t inductio<lb/>nem texam innumerarum rerum in&longs;en&longs;ilium, oculi&longs;ve <lb/>imperceptarum, quas tamen & dari, & vehementibus <lb/>motibus præditas e&longs;&longs;e ambigat nemo. </s>

<s>Nihil etiam <lb/>nece&longs;&longs;e e&longs;t, vt argumenta congeram, quibus huiu&longs;ce<lb/>modi rescontexi ex corpu&longs;culis in&longs;en&longs;ibilibus quidem, <lb/>&longs;ed præditis nihilominùs &longs;pecialibus figuris, probem. <lb/>Nihil prætereà, vt vrgeam ex attractionis effectu ar<lb/>gui, organa illa in&longs;en&longs;ilia debere analoga e&longs;&longs;e, aut &longs;i<lb/>mile quidpiam habere cum ijs, quibus attractiones <lb/>&longs;en&longs;ibiliùs fiunt; quòd à &longs;en&longs;ibilioribus ad in&longs;en&longs;ibilio<lb/>ra procedendo &longs;eruari videamus analogiam: quódque <lb/>mens humana non capiat attractionem fieri, & ratione <lb/>quadam cum his &longs;en&longs;ibilibus analoga non fieri. </s>

<s>Nihil prætereà, vt vrgeam ex attractionis effectu ar<lb/>gui, organa illa in&longs;en&longs;ilia debere analoga e&longs;&longs;e, aut &longs;i<lb/>mile quidpiam habere cum ijs, quibus attractiones <lb/>&longs;en&longs;ibiliùs fiunt; quòd à &longs;en&longs;ibilioribus ad in&longs;en&longs;ibilio<lb/>ra procedendo &longs;eruari videamus analogiam: quódque <lb/>mens humana non capiat attractionem fieri, & ratione <lb/>quadam cum his &longs;en&longs;ibilibus analoga non fieri. </s>

<s>Ni<lb/>hil, inquam, nece&longs;&longs;e e&longs;t, vt hæc, & &longs;imilia quædam <pb pagenum="261"/>pro&longs;equar, quandò tu ea rides, & iure forta&longs;&longs;is; &longs;ed <lb/>non ea ratione, quæ &longs;it mihi facta per&longs;picua. </s>

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<s>Verba tua de<lb/>inde &longs;unt; <emph type="italics"/>Quo enim &longs;en&longs;u catenas illas tuas percepisti, qui<lb/>bus, ne &longs;ur&longs;um auoles, Terræ alligatum te cen&longs;es?<emph.end type="italics"/> Nempe <lb/>me voce qua&longs;i cen&longs;oria cen&longs;ui&longs;ti e&longs;&longs;e admonendum, vt <lb/>in memet de&longs;cenderem. </s>

<s>Accipio, & hoc &longs;olùm dico, <lb/>non magis &longs;entire me catenas, quibus trahor tamen; <lb/>quàm oculus &longs;pecies memoratas, dum videt tamen. <lb/>Rogas con&longs;equenter, <emph type="italics"/>Cur verear negraue deor&longs;um, & <lb/>Ferrum ad Magnetem, cæteraque corpora ad electrica, &longs;ine <lb/>&longs;en&longs;u concurrere non poßint?<emph.end type="italics"/> Sed quamobrem verear, ex<lb/>po&longs;itum habes. </s>

<s>Accipio, & hoc &longs;olùm dico, <lb/>non magis &longs;entire me catenas, quibus trahor tamen; <lb/>quàm oculus &longs;pecies memoratas, dum videt tamen. <lb/></s>

<s>Rogas con&longs;equenter, <emph type="italics"/>Cur verear negraue deor&longs;um, & <lb/>Ferrum ad Magnetem, cæteraque corpora ad electrica, &longs;ine <lb/>&longs;en&longs;u concurrere non poßint?<emph.end type="italics"/> Sed quamobrem verear, ex<lb/>po&longs;itum habes. </s>

<s>XIX. Pergis, <emph type="italics"/>Ad hos certè effectus abundè &longs;ufficit re<lb/>bus omnibus à &longs;apientißimo earum opifice indita naturalis <lb/>inclinatio ad con&longs;eruationem, perfectionemque propriam; ad<lb/>de, &longs;i veles, ad con&longs;eruandum vniuer&longs;i ordinem, vt opus non<emph.end type="italics"/><pb pagenum="262"/><emph type="italics"/>&longs;it ad figmenta hæc tua confugere.<emph.end type="italics"/> Sed, Vir religio&longs;i&longs;&longs;ime, <lb/>inter nos non ambigitur, &longs;it-ne naturalis inclinatio <lb/>hi&longs;ce rebus ab Opifice &longs;apienti&longs;&longs;imo indita; quippe <lb/>quali&longs;cumque ea &longs;it, tam ego illam e&longs;&longs;e à Deo agno&longs;<lb/>co, & fateor, quam tu: &longs;ed hoc &longs;olùm ambigitur, qua<lb/>lis nimirùm illa &longs;it? </s>

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<s>Et, &longs;i &longs;it &longs;olùm propendentia, quomo<lb/>do ab illa non &longs;it &longs;olus ca&longs;us? </s>

<s>Quomodo etiam actio? <lb/>Quomodo non &longs;ine delectu? </s>

<s>Quomodo etiam actio? <lb/></s>

<s>Quomodo non &longs;ine delectu? </s>

<s>cæteraque id genus alia, <lb/>quæ no&longs;&longs;e foret operæ-pretium. </s>

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<s>Atque eadem quidem erit cau&longs;&longs;a, quare <lb/>acceptis pedibus altitudinis aliquot, &longs;iue ad fa&longs;tigium, <lb/>&longs;iue ad medium, &longs;iue ad pedem turris, lapis eos vbivis <lb/>æquè velociter percurrat; quoniam & &longs;implex attractio <lb/>erit ad &longs;en&longs;um eadem; & compo&longs;ita pari modo ad ac<lb/>celerationem conducet. </s>

<s>Heinc &, cùm paucis inter<lb/>po&longs;itis in eandem &longs;ententiam concludis, <emph type="italics"/>euidens e&longs;t igi<lb/>tur grauia Magneticè deorsùm à Terra non trahi:<emph.end type="italics"/> vides, vt <lb/>hoc euidens fiat, euidens priùs fieri debere, attractio<lb/>nem ferri à Magnete &longs;en&longs;ibiliorem e&longs;&longs;e vna digiti mil<lb/>le&longs;ima parte prope ip&longs;um Magnetem, quàm duabus. <lb/>Quippe &longs;eruanda proportio e&longs;t inter attrahentia, attra<lb/>cta, & interualla attractionis. </s><pb pagenum="267"/>

<s>Quippe &longs;eruanda proportio e&longs;t inter attrahentia, attra<lb/>cta, & interualla attractionis. </s><pb pagenum="267"/>

<s><emph type="center"/><emph type="italics"/>Non e&longs;&longs;e Atomorum minùs, quàm Aristoteleæ Materiæ <lb/>tolerabilem in Religione Po&longs;itionem.<emph.end type="italics"/><emph.end type="center"/></s>

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<s>Quid, quòd cæteræ non modò non <lb/>&longs;ub&longs;i&longs;tunt, &longs;ed neque dici quidem pote&longs;t, quid, aut vnde <lb/>habeant, vt &longs;ub&longs;tantiæ dicantur, ac &longs;int, & di&longs;tinctæ <lb/>quidem ab ip&longs;a materia; quandò &longs;uam illam &longs;ub&longs;tan<lb/>tialem &longs;uíque <expan abbr="propriã">propriam</expan> <expan abbr="entitat&etilde;">entitatem</expan> neque habent à nihilo, <lb/>ex quo fieri non admittuntur: neque ab ip&longs;a materia, <lb/>ex &longs;ub&longs;tantiali cuius entitate detrahi nihil volunt, quod <lb/>in formam abeat: adeò proinde, vt commentum inex<lb/>plicabile &longs;it, quòd interim Formas educi ex materia, il<lb/>liu&longs;ve potentia dicunt. </s>

<s>Nam & quòd eò adiguntur, vt <lb/>explicent Formam educi ex materia, nihil e&longs;&longs;e aliud, <lb/>quàm fieri in materia, & dependenter ab illa; tum di<lb/>cunt prorsùs aliud, quàm quid &longs;it educi, &longs;iue extrò tra<lb/>his; tum non declarant vnde habeat e&longs;&longs;e, &longs;uamve enti<lb/>tatem hæc formæ &longs;ub&longs;tantia, quæ iam e&longs;t, & antè non <lb/>erat; quandò id totum non denotat ex quo facta, &longs;iue <lb/>vnde accepta &longs;it i&longs;ta realis entitas, quæ neque materia <lb/>&longs;it, neque vlla portio ip&longs;ius (cùm ob ip&longs;am eductam, <lb/>materia non cen&longs;eatur aliquid reale, &longs;eu entitatem vl<lb/>lam realem priùs habitam ami&longs;i&longs;&longs;e) & ip&longs;a proinde <pb pagenum="272"/>dependentiæ vox nihil al ud, quàm caliginem auget, <lb/>dum in quo con&longs;i&longs;tat, dici, concipique non pote&longs;t. <lb/>Quid etiam, quòd ip&longs;e Ari&longs;toteles &longs;ententiam &longs;uam ita <lb/>expo&longs;uit, Græcique eius Interpretes illam nobis &longs;ic tra<lb/>diderunt, vt planè videatur non alias, quàm acciden<lb/>taleis formas cognoui&longs;&longs;e? </s>

<s>Quid etiam, quòd ip&longs;e Ari&longs;toteles &longs;ententiam &longs;uam ita <lb/>expo&longs;uit, Græcique eius Interpretes illam nobis &longs;ic tra<lb/>diderunt, vt planè videatur non alias, quàm acciden<lb/>taleis formas cognoui&longs;&longs;e? </s>

<s>Accidentaleis, inquam, <lb/>prout accidens &longs;ub&longs;tantiæ opponitur, non e&longs;&longs;entiæ: <lb/>nam alioquin tam materiam, quàm formam, quàm <lb/>compo&longs;itum, eo e&longs;&longs;e &longs;en&longs;u <foreign lang="greek"><gap/>si/as</foreign> dixit, quo tam diffe<lb/>rentiam, quam genus, quam &longs;peciem <foreign lang="greek"><gap/>n <gap/> ti/<gap/>s<gap/></foreign> dixit <lb/>prædicati. </s>

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<s>XXIV. <emph type="italics"/>Si enim,<emph.end type="italics"/> inquis, <emph type="italics"/>alterationes quoque omnes, <lb/>quibus calor, frigus, humor, &longs;iccitas, itemque color, odor, &longs;apor, <lb/>& qualitates aliæ gignuntur, nihil e&longs;&longs;e aliud videntur, præter <lb/>localeis tenuißimorum corporum motiones: formæ igitur acci<lb/>dentariæ nullæ &longs;unt, mulióque minùs inueniri, & e&longs;&longs;e po&longs;&longs;unt <lb/>ab omni &longs;ub&longs;tantia &longs;eparatæ. </s>

<s>Quid &longs;anctioribus igitur no<lb/>&longs;træ Religionis my&longs;teriis fiet?<emph.end type="italics"/> At imprimis vides non e&longs;&longs;e <lb/>timendum, <emph type="italics"/>ne accidentales formæ nullæ &longs;int;<emph.end type="italics"/> quippe quæ <lb/>e&longs;&longs;e &longs;upponantur, & &longs;peciali &longs;olùm explicentur modo. <lb/>Suusigni &longs;eruatur calor: &longs;uum frigus glaciei: &longs;uus &longs;apor <lb/>melli: &longs;uus odor ro&longs;æ: &longs;uus tympano &longs;onus: &longs;uus can<lb/>dor niui; &longs;ua lux Soli, &c. </s>

<s>Suusigni &longs;eruatur calor: &longs;uum frigus glaciei: &longs;uus &longs;apor <lb/>melli: &longs;uus odor ro&longs;æ: &longs;uus tympano &longs;onus: &longs;uus can<lb/>dor niui; &longs;ua lux Soli, &c. </s>

<s>Cùm ex vulgari autem &longs;en<lb/>tentia explicari nequeat, in quónam con&longs;i&longs;tat energia, <lb/>& modus agendi illius eiu&longs;dem caloris, frigoris, &longs;aporis, <lb/>cæterarumque qualitatum; tentatur, an id declarari <lb/>ex tali hypothe&longs;i valeat. </s>

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<s>Quia enim iure <lb/>obiici potuit, fru&longs;trà in&longs;inüari à me conquirendas e&longs;&longs;e <pb pagenum="278"/>alias rationes, cùm illæ iam & conqui&longs;itæ, & adinuen<lb/>tæ fuerint; ideò vi&longs;us &longs;um non debere cæteras intactas <lb/>prætermittere, vt o&longs;tenderem quatenus eas quoque ar<lb/>bitrarer e&longs;&longs;e infirmas. </s>

<s>Exi&longs;timaui autem, &longs;i licuit eam <lb/>&longs;uffodere, quæ qua&longs;i murus aheneus erat, & quam tu <lb/>t<gap/>et, ip&longs;um pridem improba&longs;&longs;e te&longs;tatus es; nihil pro<lb/>hibere quò minùs cæteræ &longs;altem mediocri ar<gap/>atione <lb/><expan abbr="impeter&etilde;tur">impeterentur</expan>: neque enim illas aut e&longs;&longs;e &longs;anctior<gap/>s, vt in<lb/>uiolatiores manerent: aut magis extra aleam, vt vel <lb/>non po&longs;&longs;ent, vel non deberent parem experiri <expan abbr="fortunã">fortunam</expan>. <lb/>Quod autem &longs;imùl interrogaui, aut exaggeraui <gap/>am <lb/>aliquid in Copernicanorum gratiam; id egi, vt difficul<lb/>tates vberiùs innote&longs;cerent, patefaceremque quibus <lb/>argumentis, cuique rationum oppo&longs;itarum probabili<lb/>tati occurrendum &longs;it, &longs;i quis aduer&longs;us Copernicanos <lb/>præ&longs;tare voluerit rationem inuictam. </s>

<s>Quod autem &longs;imùl interrogaui, aut exaggeraui <gap/>am <lb/>aliquid in Copernicanorum gratiam; id egi, vt difficul<lb/>tates vberiùs innote&longs;cerent, patefaceremque quibus <lb/>argumentis, cuique rationum oppo&longs;itarum probabili<lb/>tati occurrendum &longs;it, &longs;i quis aduer&longs;us Copernicanos <lb/>præ&longs;tare voluerit rationem inuictam. </s>

<s>Et quæris, <lb/><emph type="italics"/>Quid ampliùs eram facturus, &longs;i eam &longs;ententiam animo de&longs;ti<lb/>nato a&longs;&longs;erendam, propugnandamque a&longs;&longs;ump&longs;i&longs;&longs;em?<emph.end type="italics"/> At nihil <lb/>&longs;anè ampliùs facturus fui, qui neid quidem fui a&longs;&longs;um<lb/>pturus. </s>

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<s>Nec verò ip&longs;is di&longs;plicet modò concitati&longs;&longs;imus <lb/>ille motus, attributus vulgò primo mobili Sidera om<lb/>nia circum-rapienti; &longs;ed etiam inconcinnitas, qua ne<lb/>ce&longs;&longs;e e&longs;t Planetarum directiones, regre&longs;&longs;iones, &longs;tatio<lb/>nes, & non pauca alia ab Heraclide quoque, & Eephan<lb/>to &longs;aluentur. </s>

<s>Quod autem &longs;pectat ad portento&longs;a, quæ <lb/>dicis ab&longs;urda, & incommoda; ip&longs;i nulla e&longs;&longs;e agno&longs;cunt: <lb/>vnde & ni&longs;i aduer&longs;am habeant &longs;acræ Scripturæ autho<lb/>ritatem, exi&longs;timant &longs;e prorsùs nihil intolerabile tueri. <lb/>Sequitur adhûc, <emph type="italics"/>Memini&longs;&longs;e &longs;emper oportet nos non Philo&longs;o<lb/>phos tantum e&longs;&longs;e, &longs;ed etiam Chri&longs;tianos, Philo&longs;ophiamque <lb/>no&longs;tram nec debere, nec verò etiam po&longs;&longs;e à Chri&longs;tiana fide <lb/>di&longs;crepare.<emph.end type="italics"/> Id verò e&longs;t &longs;anè tua pietate dignum; ip&longs;eque <lb/>non modò a&longs;&longs;entior, verùm etiam palam profiteor, ac <pb pagenum="280"/>iuro. </s>

<s>Sequitur adhûc, <emph type="italics"/>Memini&longs;&longs;e &longs;emper oportet nos non Philo&longs;o<lb/>phos tantum e&longs;&longs;e, &longs;ed etiam Chri&longs;tianos, Philo&longs;ophiamque <lb/>no&longs;tram nec debere, nec verò etiam po&longs;&longs;e à Chri&longs;tiana fide <lb/>di&longs;crepare.<emph.end type="italics"/> Id verò e&longs;t &longs;anè tua pietate dignum; ip&longs;eque <lb/>non modò a&longs;&longs;entior, verùm etiam palam profiteor, ac <pb pagenum="280"/>iuro. </s>

<s>Id vnum &longs;upere&longs;t, vt no&longs;catur, quid Philo&longs;ophia <lb/>proferat à Chri&longs;tiana di&longs;crepans fide. </s>

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<s>Augu&longs;tinus allato exem<lb/>plo præclarè in&longs;inüat; cùm difficultate propo&longs;ita, <emph type="italics"/>Quo<lb/>modo non &longs;it <expan abbr="contrari&utilde;">contrarium</expan> ijs, qui figuram Sphæræ cælo tribuunt, <lb/>quod &longs;criptum est in libris no&longs;tris, Qui extendit cælum &longs;icut <lb/>Pellem?<emph.end type="italics"/> Re&longs;pondet; S<emph type="italics"/>it &longs;anè contrarium, &longs;i fal&longs;um e&longs;t, quod <lb/>illi dicunt; hoc enim verum e&longs;t, quod diuina dicit authoritas, <lb/>potiu&longs;quàm illud, quod humana infirmitas coniicit. </s>

<s>Sed &longs;i <lb/>fortè talibus illi documentis probare potuerint, vt dubitari inde <lb/>non debeat; demon&longs;trandum est, hoc, quod apud nos est de Pelle <lb/>dictum, veris illis rationibus non e&longs;&longs;e contrarium.<emph.end type="italics"/> Et rursùs, <lb/><emph type="italics"/><expan abbr="Tãdiù">Tandiù</expan> non e&longs;t extra fidem, donecveritate certißima refellatur. <lb/>Quod &longs;i factum fuerit, non hoc habebat diuina Scriptura; &longs;ed <lb/>hoc &longs;en&longs;erat humana ignorantia.<emph.end type="italics"/> Haud-dubium proinde, <lb/>quin &longs;anctus Doctor, &longs;i in no&longs;tra incidi&longs;&longs;et tempora; <lb/>aut &longs;i eius temporibus fui&longs;&longs;et tota Terra, vt nuper e&longs;t <lb/>factum, circum-nauigata: tum agniturus Antipodas <lb/>fui&longs;&longs;et, tum ad humanam potiùs ignorantiam, quàm <lb/>ad Scripturæ diuinæ &longs;en&longs;um, præhabitam &longs;uam relatu<lb/>rus &longs;ententiam, quam vidi&longs;&longs;et certi&longs;&longs;ima experientiæ <lb/>veritate refelli. </s>

<s>Quod &longs;i factum fuerit, non hoc habebat diuina Scriptura; &longs;ed <lb/>hoc &longs;en&longs;erat humana ignorantia.<emph.end type="italics"/> Haud-dubium proinde, <lb/>quin &longs;anctus Doctor, &longs;i in no&longs;tra incidi&longs;&longs;et tempora; <lb/>aut &longs;i eius temporibus fui&longs;&longs;et tota Terra, vt nuper e&longs;t <lb/>factum, circum-nauigata: tum agniturus Antipodas <lb/>fui&longs;&longs;et, tum ad humanam potiùs ignorantiam, quàm <lb/>ad Scripturæ diuinæ &longs;en&longs;um, præhabitam &longs;uam relatu<lb/>rus &longs;ententiam, quam vidi&longs;&longs;et certi&longs;&longs;ima experientiæ <lb/>veritate refelli. </s>

<s>Quæ memoro &longs;olùm, vt intelligamus, <lb/>non quicquid Philo&longs;ophia docet, quod videatur prima <lb/>fronte à Literis &longs;acris e&longs;&longs;e di&longs;crepans, proptereà verè <lb/>di&longs;crepare. </s><pb pagenum="281"/>

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<s>Nimirùm contendent, cùm Terra id <lb/>iuris habuerit, vt inter Planetas ver&longs;ata, heinc Vene<lb/>rem, Mercurium, Solem, illeinc Martem, Iouem, Satur<lb/>num, ac aliunde circum &longs;e Lunam proximè circumdu<lb/>ctam &longs;ortiatur; non idem iuris proptereà aliis Planetis <lb/>competere, quos propterillam Deus creârit. </s>

<s>Neminem <lb/>proinde &longs;anæ mentis colligere po&longs;&longs;e e&longs;&longs;e aut in Luna, <lb/>aut in aliis Planetis, Stelli&longs;que fixis incolas, qui autho<lb/>mines &longs;int, aut &longs;imilitudinem cum hominibus habeant. <lb/>quoniam, &longs;i non omnis tellus omnia fert; & Europa, <lb/>Americáque, Scythia, & Libya, quæ eiu&longs;dem globi <lb/>partes &longs;unt, diuer&longs;i&longs;&longs;ima proferunt; quantò æquius &longs;it <lb/>reputare, non po&longs;&longs;e eadem na&longs;ci, educari, degere in <lb/>Luna, atque cæteris, qui &longs;unt orbes planè diuer&longs;i? </s>

<s>quoniam, &longs;i non omnis tellus omnia fert; & Europa, <lb/>Americáque, Scythia, & Libya, quæ eiu&longs;dem globi <lb/>partes &longs;unt, diuer&longs;i&longs;&longs;ima proferunt; quantò æquius &longs;it <lb/>reputare, non po&longs;&longs;e eadem na&longs;ci, educari, degere in <lb/>Luna, atque cæteris, qui &longs;unt orbes planè diuer&longs;i? </s>

<s>Si <lb/>quædam proinde oriantur, & intereant aut in Planetis <lb/>cæteris, aut in aliis Siderum globis, non po&longs;&longs;e illa e&longs;&longs;e <lb/>præ&longs;tantiora homine; quatenùs nihil e&longs;&longs;e pote&longs;t aut <lb/>ratione præclarius, aut &longs;upernaturalibus donis, quibus <lb/>ille &longs;olus donatur, diuinius. </s>

<s>Cæterùm enim po&longs;&longs;e e&longs;&longs;e <lb/>corpora maiora, robu&longs;tiora, durabiliora, aut aliis qui<lb/>bu&longs;dam adiunctis perfectiora, quàm homines, id ne <lb/>negari quidem po&longs;&longs;e; cùm etiam in ip&longs;amet Terra mul<lb/>ta corpora id genus na&longs;cantur. </s>

<s>Et non proptereà Ge<lb/>ne&longs;in in &longs;u&longs;picionem po&longs;&longs;e vocari; quoniam ea docet, <pb pagenum="285"/>quod non negatur, feci&longs;&longs;e Deum Solem, & Lunam, ac <lb/>Stellas, vt Terram illuminent, &longs;intque in&longs;igna, & tem<lb/>pora; & non docet tamen Sidera ad hec &longs;olùm facta. <lb/>Alioquin enim inferretur, e&longs;&longs;e quidem factum Solem, <lb/>vt illuminet Terram, &longs;ed non vt Lunam, aut Venerem, <lb/>quod Gene&longs;is tacet: &, Lunam e&longs;&longs;e quidem factam, vt <lb/>Terram illuminet; &longs;ed non vt (quod mox dictum e&longs;t) <lb/>tenebras in ip&longs;am inducat; nam & Gene&longs;is id non dicit. <lb/>Vt prætereatur, &longs;i, quia Gene&longs;is aliud non declarat, ni<lb/>hil agitur aliud à Sideribus; non igitur Solem calefa<lb/>cere, vrere, fouere, &c. </s>

<s>Alioquin enim inferretur, e&longs;&longs;e quidem factum Solem, <lb/>vt illuminet Terram, &longs;ed non vt Lunam, aut Venerem, <lb/>quod Gene&longs;is tacet: &, Lunam e&longs;&longs;e quidem factam, vt <lb/>Terram illuminet; &longs;ed non vt (quod mox dictum e&longs;t) <lb/>tenebras in ip&longs;am inducat; nam & Gene&longs;is id non dicit. <lb/></s>

<s>Vt prætereatur, &longs;i, quia Gene&longs;is aliud non declarat, ni<lb/>hil agitur aliud à Sideribus; non igitur Solem calefa<lb/>cere, vrere, fouere, &c. </s>

<s>neque Lunam &longs;peciale impe<lb/>rium in res humidas exercere, in <expan abbr="cõchylia">conchylia</expan>, animalium <lb/>medullas, & id genus &longs;imilia. </s>

<s>Non item &longs;u&longs;pectam <lb/>reddi Verbi Incarnati &oelig;conomiam, veritatem Euan<lb/>gelicam, totam ip&longs;am fidem Chri&longs;tianam; quoniam ea <lb/>perinde illibata conferuatur; quatenus nullæ aliæ na<lb/>turæ rationales, & redemptionis, gratiæ, gloriæque &longs;u<lb/>pernaturalis capaces vlla ratione colligi po&longs;&longs;unt ex&longs;i<lb/>&longs;tere, præter homines in Terris degenteis; in quibus &longs;o<lb/>lis incarnatus Dei Vnigenitus vi&longs;us e&longs;t, & cum homi<lb/>nibus conuer&longs;atus. </s>

<s>Neque verò cæteros globos, &longs;i in <lb/>ip&longs;is creaturæ quædam generantur, & corrumpuntur, <lb/>dici magis po&longs;&longs;e ab ijs habitari, quàm dicantur loca <lb/>Terræ de&longs;erta à &longs;axis, herbis, culicibus, cæteri&longs;que id <lb/>genus rebus; neque proptereà dici po&longs;&longs;e incolas habere, <lb/>qui &longs;int homines, aut cum hominibus comparandi. <lb/>Nam &longs;upponere quidem, & docere Fidem &longs;acram, non <lb/>habitari Sidera ab aliis aut hominibus, aut naturis, quæ <lb/>pari modo vel ratiocinentur, vel participes &longs;int dono<lb/>rum &longs;upernaturalium: at non &longs;upponere, nec docere, <pb pagenum="286"/>nihil in ip&longs;is e&longs;&longs;e ortui, interituique obnoxium; & ne <lb/>maculas quidem in Sole na&longs;ci, ac perire; non in cælo <lb/>reliquo Cometas, atque nouas Stellas. </s>

<s>Nam &longs;upponere quidem, & docere Fidem &longs;acram, non <lb/>habitari Sidera ab aliis aut hominibus, aut naturis, quæ <lb/>pari modo vel ratiocinentur, vel participes &longs;int dono<lb/>rum &longs;upernaturalium: at non &longs;upponere, nec docere, <pb pagenum="286"/>nihil in ip&longs;is e&longs;&longs;e ortui, interituique obnoxium; & ne <lb/>maculas quidem in Sole na&longs;ci, ac perire; non in cælo <lb/>reliquo Cometas, atque nouas Stellas. </s>

<s>Nec porrò <lb/>&longs;acrum ip&longs;um Textum, cùm dicit Solem, & cætera Si<lb/>dera facta, vt Terram illuminent, negare prop tereà, <lb/>quin ip&longs;a aliude &longs;int in &longs;eip&longs;is, ac præter lucem aliquid; <lb/>& id genus alia, quæ tamen non dicit, vt nec cætera, <lb/>quæ no&longs;&longs;e nihil intere&longs;t ad &longs;upernaturalem &longs;alutem. <lb/>Scilicet præclarè &longs;anctus ille Doctor, <emph type="italics"/>Breuiter,<emph.end type="italics"/> inquit, <lb/><emph type="italics"/>dicendum e&longs;t, hoc &longs;ci&longs;&longs;e Authores no&longs;tros, quod veritas habet: <lb/>&longs;ed Spiritum Dei, qui per ip&longs;os loquebatur, nolui&longs;&longs;e i&longs;ta docere <lb/>bomines, nulli ad &longs;alutem profutura.<emph.end type="italics"/> Eiu&longs;modi &longs;unt, alia<lb/>que affinia, quæ prædixi vereri me, ne illi fuerint re&longs;<lb/>pon&longs;uri. </s>

<s>Scilicet præclarè &longs;anctus ille Doctor, <emph type="italics"/>Breuiter,<emph.end type="italics"/> inquit, <lb/><emph type="italics"/>dicendum e&longs;t, hoc &longs;ci&longs;&longs;e Authores no&longs;tros, quod veritas habet: <lb/>&longs;ed Spiritum Dei, qui per ip&longs;os loquebatur, nolui&longs;&longs;e i&longs;ta docere <lb/>bomines, nulli ad &longs;alutem profutura.<emph.end type="italics"/> Eiu&longs;modi &longs;unt, alia<lb/>que affinia, quæ prædixi vereri me, ne illi fuerint re&longs;<lb/>pon&longs;uri. </s>

<s>XXXI. Subiicis, <emph type="italics"/>Vides igitur, quàm i&longs;ta periculosè in <lb/>publicum diuulgentur, & à viris præ&longs;ertim, qui &longs;ua authori<lb/>tate fidem facere videantur; & quàm non immeritò iam inde <lb/>à Copernici tempore Eccle&longs;ia &longs;emper huic &longs;e errori oppo&longs;ue<lb/>rit: eumque etiam nouißimè non<emph.end type="italics"/> C<emph type="italics"/>ardinales tantum aliqui, vt <lb/>ais, &longs;ed &longs;upremum Eccle&longs;iæ caput Pontificio decreto in Galileo <lb/>damnauerit, & vt ne in posterùm verbo, aut &longs;cripto docere<lb/>tur, &longs;anctißimè prohibuerit.<emph.end type="italics"/> Heic non repeto, quod illi <lb/>tuebuntur, non &longs;equi ex ea, quam diuulgant, &longs;ententia <lb/>id, quod tu times, periculum. </s>

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<s>Sed e&longs;to, vt dicis; quandò Copernicani <lb/>&longs;unt, qui illam magnitudinem tribuere Stellis non <lb/>erube&longs;cunt. </s>

<s>Pro&longs;equeris, <emph type="italics"/>Quod &longs;i' tibi ab&longs;urdum, atque <lb/>ab omni ratione abhorrens non videtur, quid, amabò, iudica<lb/>bis ab&longs;urdum?<emph.end type="italics"/> Id verò tu mihi potes dicere, neque ego <lb/>abnuo, &longs;ed ad&longs;tipulor; At quæ&longs;o te tamen, quid &longs;im <lb/>re&longs;pon&longs;urus, &longs;i cùm idem obiecero, illi ita exceperint? <lb/>Tu id ab&longs;urdum, & ab omni ratione e&longs;&longs;e abhorrens <lb/>iudicas: & quam-nam tandem affers rationem? </s>

<s>Tu id ab&longs;urdum, & ab omni ratione e&longs;&longs;e abhorrens <lb/>iudicas: & quam-nam tandem affers rationem? </s>

<s>An-ne <lb/>quòd exinde Stellæ inerrantes molis &longs;int nimis prodi<lb/>gio&longs;æ? </s>

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<s>An-non, &longs;i id, quod dicimus, tuo &longs;en&longs;u ab&longs;urdum <lb/>e&longs;t: &longs;ecundum magis, & minus &longs;olùm erit di&longs;crimen <lb/>ab&longs;urditatis? </s>

<s>Habes-ne verò interim vllum omninò <lb/>argumentum, quo Stellas e&longs;&longs;e tantas &longs;ic probes, vt &longs;i<lb/>mùl probes aut non e&longs;&longs;e, aut non po&longs;&longs;e e&longs;&longs;e maiores? <lb/>Non certè; &longs;ed penitùs gratis in ea con&longs;i&longs;tis magnitu<lb/>dine; neque e&longs;t tibi maior ratio quærendi ex nobis, <lb/>cur procedamus vlteriùs: quàm nobis quærendi ex te, <lb/>quamobrem con&longs;i&longs;tas citeriùs. </s>

<s>Non certè; &longs;ed penitùs gratis in ea con&longs;i&longs;tis magnitu<lb/>dine; neque e&longs;t tibi maior ratio quærendi ex nobis, <lb/>cur procedamus vlteriùs: quàm nobis quærendi ex te, <lb/>quamobrem con&longs;i&longs;tas citeriùs. </s>

<s>Dicere ad &longs;ummum <lb/>potes, tibi &longs;ic videri; & quia &longs;ic videtur, nos à ratione <lb/>abhorrere: quid-ni & nobis pari iure dicere dete idem <lb/>liceat? </s>

<s>Quanquam & nobis ratio e&longs;t, tum admiranda <lb/>concinnitas, quæ hac &longs;uppo&longs;ita amplitudine ob&longs;erua<lb/>tur; tum commendatio operum Dei, quæ tu, quantum <lb/>potes, extenuas, dum ea non maiora tuo captu facis. <lb/>Quippe huiu&longs;modi amplitudo diuinæ potentiæ, &longs;a<lb/>pientiæ, & magni&longs;icentiæ con&longs;entanea e&longs;t: neque e&longs;t, <lb/>cur tu ab&longs;que vlla aut ob&longs;eruatione, aut ratione illam <lb/>contrahas, vel ab&longs;urdam putes. </s>

<s>Quippe huiu&longs;modi amplitudo diuinæ potentiæ, &longs;a<lb/>pientiæ, & magni&longs;icentiæ con&longs;entanea e&longs;t: neque e&longs;t, <lb/>cur tu ab&longs;que vlla aut ob&longs;eruatione, aut ratione illam <lb/>contrahas, vel ab&longs;urdam putes. </s>

<s>Quæ&longs;o te, inquam, Vir <lb/>Religio&longs;i&longs;&longs;ime, ecquid-nam illis dicturus &longs;im, cùm <lb/>hæc, & &longs;imilia reponent? </s><pb pagenum="291"/>

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<s>Non e&longs;to Sol, non &longs;unto Fixæ in tanta à Terris <lb/>di&longs;tantia, quanta à nobis a&longs;&longs;eritur: e&longs;to minima, & qua<lb/>lem Tycho po&longs;uit, nulla &longs;anè ob&longs;eruatione (quod ad <lb/>Fixas pr&ecedil;&longs;ertim &longs;pectat) verùm coniectatione mera, <lb/>meróque arbitrio inductus. </s>

<s>Di&longs;&longs;idebit à Terra Sol, <lb/>cùm di&longs;&longs;ebit mediocriter, terrenis &longs;emidiametris mille <lb/>centum, & quinquaginta, & Fixæ quater-decies nulle. <lb/>Finge igitur Solem quantu&longs;-quantus e&longs;t, tran&longs;latum <lb/>e&longs;&longs;e v&longs;que ad Fixas: cùm diameter eius apparens im-<pb pagenum="292"/>minuenda &longs;it pro ratione di&longs;tantiæ, diuide Fixarum <lb/>di&longs;tantiam per di&longs;tantiam Solis à Terra, fiet quotiens <lb/>amplius, quàm duodecim. </s>

<s>Di&longs;&longs;idebit à Terra Sol, <lb/>cùm di&longs;&longs;ebit mediocriter, terrenis &longs;emidiametris mille <lb/>centum, & quinquaginta, & Fixæ quater-decies nulle. <lb/></s>

<s>Finge igitur Solem quantu&longs;-quantus e&longs;t, tran&longs;latum <lb/>e&longs;&longs;e v&longs;que ad Fixas: cùm diameter eius apparens im-<pb pagenum="292"/>minuenda &longs;it pro ratione di&longs;tantiæ, diuide Fixarum <lb/>di&longs;tantiam per di&longs;tantiam Solis à Terra, fiet quotiens <lb/>amplius, quàm duodecim. </s>

<s>Et quia Solis diameter ap<lb/>paret iam nobis dimidij gradus, &longs;iue minutorum tri<lb/>ginta; &longs;equitur vt Sole inter Fixas ex&longs;i&longs;tente, eius dia<lb/>meter apparitura non &longs;it, ni&longs;i pars huius duodecima, <lb/>&longs;iue minutorum duorum cùm &longs;emi&longs;&longs;e. </s>

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<s>Sed vide, quæ&longs;o, vt non dicam e&longs;&longs;e eam Stellam <lb/>vi&longs;ibilem &longs;ub huiu&longs;modi angulo: verùm eam Stellam, <lb/>quæ vi&longs;ibilis e&longs;t &longs;ub angulo &longs;emi&longs;&longs;is minuti, &longs;iue trigin<lb/>ta <expan abbr="&longs;ecundor&utilde;">&longs;ecundorum</expan>, comprehen&longs;a nempe circumradiatione, <lb/>non habere <expan abbr="diametr&utilde;">diametrum</expan> veram, circum-radiationeve &longs;po<lb/>liatam, &longs;extante &longs;ecundi maiorem. </s>

<s>At hoc ip&longs;um quo<lb/>que e&longs;t, inquies, quod omni figmento e&longs;t maius, tam <lb/>minutulum punctulum ita po&longs;&longs;e circum-radiare, vt fu<lb/>turum aliàs planè incon&longs;picuum, effici vi&longs;ibile po&longs;&longs;it. <lb/>Verùm, quid res &longs;it, vt percipi po&longs;&longs;it: e&longs;to candelæ flam<lb/>mula cra&longs;&longs;itudinis &longs;emidigitalis; ea poterit nocte ob<lb/>&longs;cura &longs;pectari à tribus pa&longs;&longs;uum millibus. </s>

<s>Verùm, quid res &longs;it, vt percipi po&longs;&longs;it: e&longs;to candelæ flam<lb/>mula cra&longs;&longs;itudinis &longs;emidigitalis; ea poterit nocte ob<lb/>&longs;cura &longs;pectari à tribus pa&longs;&longs;uum millibus. </s>

<s>Fac verò an<lb/>gulum, &longs;ub quo vi&longs;ibilis efficietur, non e&longs;&longs;e dimidio <lb/>minuti maiorem, ita vt flammula appareat, qua&longs;i ma<lb/>gnitudinis &longs;extæ Stella; quæ&longs;o te, quantus angulus erit, <lb/>qui ab ip&longs;ius flammulæ vera diametro &longs;ubtendetur? <lb/>Profecto vix maior &longs;emi&longs;&longs;e &longs;ecundi. </s>

<s>Profecto vix maior &longs;emi&longs;&longs;e &longs;ecundi. </s>

<s>Cùm in tribus <lb/>enim pa&longs;&longs;uum millibus &longs;int trecenta, & &longs;exaginta &longs;e<lb/>midigitorum millia: &longs;i, vt hic numerus &longs;e habet ad <lb/>vnum, ita centum millia, &longs;eu radium feceris ad aliud; <lb/>procreabuntur &longs;olum quinque decima octaua vnius, <lb/>&longs;eu tangens &longs;eptuncis vnius &longs;ecundi. </s>

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<s>I&longs;ta <lb/>vberius non pro&longs;equor; ne cau&longs;&longs;eris non po&longs;&longs;e me meis <lb/>figmentis facere finem. </s>

<s>Adnoto tamen; cùm ex iam <lb/>dictis, Stella magnitudinis &longs;extæ e&longs;&longs;e non debeat Sole <lb/>maior; ecquid-nam dicturus de figmento fui&longs;&longs;es, &longs;i <lb/>propo&longs;ui&longs;&longs;em cum Land&longs;bergio Stellam magnitudinis <lb/>&longs;extæ e&longs;&longs;e vicies quinquies ip&longs;o Orbe magno maiorem? <lb/>Et ille tamen vi&longs;us e&longs;t &longs;ibi ex certis principiis demon<lb/>&longs;tra&longs;&longs;e omnia: quanquam illud &longs;altem non cauit, quod <lb/>circum-radiatio imponit circa magnitudinem veram: <lb/>quodque proinde diameter vna Stellæ magnitudinis <lb/>&longs;extæ e&longs;t longè minor quinque &longs;ecundis, &longs;ecùs quàm <lb/>ab illo &longs;uppo&longs;itmu e&longs;t. </s>

<s>Et ille tamen vi&longs;us e&longs;t &longs;ibi ex certis principiis demon<lb/>&longs;tra&longs;&longs;e omnia: quanquam illud &longs;altem non cauit, quod <lb/>circum-radiatio imponit circa magnitudinem veram: <lb/>quodque proinde diameter vna Stellæ magnitudinis <lb/>&longs;extæ e&longs;t longè minor quinque &longs;ecundis, &longs;ecùs quàm <lb/>ab illo &longs;uppo&longs;itmu e&longs;t. </s>

<s><emph type="center"/><emph type="italics"/>Hûc accommodari non potui&longs;&longs;e cau&longs;&longs;am quæ redditur vulgò, <lb/>quare flammæ noctu maiores appareant.<emph.end type="italics"/><emph.end type="center"/></s>

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<s>Itaque aliam requi&longs;iui (affectionem <lb/>putà in pupilla, acretina) quæ vt effectui in candela ap<lb/>parenti congrueret, ita lucidis omnibus, quorum &longs;pe<lb/>cies noctu incre&longs;cit, accommodari congruè po&longs;&longs;et. </s>

<s>Hu<lb/>iu&longs;modi maximè &longs;unt tam Luna, quàm Stellæ, &longs;eu <lb/>Errantes, &longs;eu <expan abbr="Inerrãtes">Inerrantes</expan>: nam Lunæ quidem diametrum <lb/>non &longs;emel ob&longs;eruauimus octaua propè &longs;ui parte noctu, <lb/>quàm interdiù maiorem: Veneris vero diametrum <lb/>multis maiorem vicibus; & Iouis con&longs;imiliter (quippe <lb/>qui fuerit etiam nobis &longs;æpenumerò ob&longs;eruatus inter<lb/>diù) con&longs;tatque vniuersè Stellas cæteras, cùm interdiù <lb/>&longs;int incon&longs;picuæ, in gruente tamen crepu&longs;culo æger<lb/>rimè primùm ob exilitatem videri, ac deinde magis, <lb/>magi&longs;que, dum &longs;en&longs;im grande&longs;cunt, vi&longs;ibileis fieri. <lb/>Quæ&longs;o verò i&longs;ta-ne valeant ad halituo&longs;as aliquas par<lb/>teis, quæ vt à flamma, &longs;ic à Luna, Stelli&longs;que diffugiant, <lb/>referri; & non potiùs ad vberiorem tum pupillæ dila<lb/>tationem, tum impre&longs;&longs;ionem retinæ factam, donec <lb/>oculus in tenebris degit? </s>

<s>Quæ&longs;o verò i&longs;ta-ne valeant ad halituo&longs;as aliquas par<lb/>teis, quæ vt à flamma, &longs;ic à Luna, Stelli&longs;que diffugiant, <lb/>referri; & non potiùs ad vberiorem tum pupillæ dila<lb/>tationem, tum impre&longs;&longs;ionem retinæ factam, donec <lb/>oculus in tenebris degit? </s>

<s>At hæc tamen cau&longs;&longs;a, in-<pb pagenum="305"/>quies, quid ad Solem? </s>

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<s>Tu verò &longs;ic interrogas, <lb/>vt &longs;i cen&longs;erem ex ea di&longs;tantia tum magnum Orbem <lb/>appariturum eiu&longs;dem, qua propè amplitudinis; tum <lb/>Solem non modò maiorem, quàm heinc con&longs;piciatur; <lb/>&longs;ed etiam quantus Orbis magnus ex Marte, v. </s>

<s>g. aut <lb/>Ioue con&longs;piceretur, appariturum. </s>

<s>aut <lb/>Ioue con&longs;piceretur, appariturum. </s>

<s>Quòd verò &longs;ic in<lb/>terrogas, eo permotus argumento, <emph type="italics"/>quòd con&longs;tet Lu<lb/>nam, ac Martem, ip&longs;umque etiam Solem quò propiùs acce<lb/>dunt ad nos, eò maiores con&longs;pici; quò longiùs ab&longs;cedunt,<emph.end type="italics"/><pb pagenum="306"/><emph type="italics"/>minores:<emph.end type="italics"/> vides rem e&longs;&longs;e incohærentem. </s>

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<s>Neque enim re<lb/>quiritur, cur Mars v. </s>

<s>g. dum e&longs;t perigeius, terri&longs;ve pro<lb/>pinquior, appareat maior, quàm apogeius, &longs;eu à terris <lb/>remotior, & in eodem quidem tenebrarum gradu: &longs;ed <lb/>cur in eadem propinquitate, aut in eadem remotione <lb/>maior, & minor appareat, prout in variis gradibus ob<lb/>&longs;curitatis con&longs;picitur; vt claro adhûc crepu&longs;culo, & no<lb/>cte iam facta profunda. </s>

<s>dum e&longs;t perigeius, terri&longs;ve pro<lb/>pinquior, appareat maior, quàm apogeius, &longs;eu à terris <lb/>remotior, & in eodem quidem tenebrarum gradu: &longs;ed <lb/>cur in eadem propinquitate, aut in eadem remotione <lb/>maior, & minor appareat, prout in variis gradibus ob<lb/>&longs;curitatis con&longs;picitur; vt claro adhûc crepu&longs;culo, & no<lb/>cte iam facta profunda. </s>

<s>Quare & ad hoc non ad il<lb/>lud &longs;imilitudo candelæ facit; & ad hoc, non verò ad <lb/>illud, quam cau&longs;&longs;am e&longs;&longs;e prætermittendam cen&longs;ui&longs;ti, <lb/>referenda fuit. </s>

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<s>Quantò verò <lb/>magis hoc loco id volui; vbi &longs;ententiam non tam pro<lb/>priam, quàm alienam expo&longs;ui! Heinc & quæ dicere <lb/>iam pergo, non vt propugnans &longs;ententiam, quæ mihi <lb/>rata fixa &longs;it: &longs;ed tanquam tentans quid iuxta ip&longs;am &longs;it <lb/>vero &longs;imile, in&longs;inuo: & dum tu &longs;ubdis, <emph type="italics"/>ne&longs;cire te, an ex <lb/>tarditate ingenij tui, an aliunde accidat, vt longè aliter, quàm <lb/>ego, hactenus hac in re &longs;en&longs;eris:<emph.end type="italics"/> id &longs;ic accipio, qua&longs;i velis <lb/>non me &longs;entire &longs;ecus, quàm te, quod ad rem ip&longs;am at<lb/>tinet; &longs;ed quod ad ea, quæ opinioni de motu Terræ <lb/>&longs;unt con&longs;entanea. </s>

<s>Non e&longs;t profectò interim, cur vl<lb/>lam in te &longs;u&longs;piceris tarditatem ingenij: ego illam in <lb/>me recipio, qui agno&longs;co me non potui&longs;&longs;e ex tot opi<lb/>nionibus aliis, quæ hac de re circumferuntur, aliquam <lb/>deprehendere, quæ non videretur, quàm i&longs;ta nugacior. <lb/>Gratum feci&longs;&longs;es, &longs;i in&longs;inua&longs;&longs;es ecquæ-nam tibi proba<lb/>tior foret: &longs;pes enim fui&longs;&longs;et quidpiam tua dignum &longs;o<lb/>lertia cogno&longs;cendi. </s>

<s>Gratum feci&longs;&longs;es, &longs;i in&longs;inua&longs;&longs;es ecquæ-nam tibi proba<lb/>tior foret: &longs;pes enim fui&longs;&longs;et quidpiam tua dignum &longs;o<lb/>lertia cogno&longs;cendi. </s>

<s>Nam quod ais quidem G<emph type="italics"/>alileum <lb/>cogi in &longs;ocietatem cau&longs;&longs;æ Lunam ad&longs;ci&longs;cere,<emph.end type="italics"/> non au&longs;im ita <lb/>interpretari, qua&longs;i tu proptereà totum hunc effectum, <lb/>aut quæ &longs;unt certè <foreign lang="greek">sumw<gap/>w/ma<gap/></foreign> illius præcipua, referas <lb/>in Lunam. </s>

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<s>Nam <lb/>primùm quidem, <emph type="italics"/>non e&longs;&longs;e quoddam paullatim factum in<lb/>crementum; &longs;ed repentè maximos æstus in Plenilunio<emph.end type="italics"/> Æ<emph type="italics"/>qui<lb/>noctium con&longs;equente contingere,<emph.end type="italics"/> hoc e&longs;t, quod neque <lb/>ob&longs;eruaui, neque ab alio quoquam accepi: cùm potiùs, <lb/>vt æ&longs;tus &longs;pectati per quadranteis men&longs;is, minimi circa <lb/>quadraturas, maximi circa &longs;yzygias, &longs;en&longs;im per inter<lb/>ceptos dies, & maximi ex minimis, & minimi ex ma<lb/>ximis euadunt; ita &longs;i &longs;pectentur per quadranteis anni, <lb/>audierim &longs;emper minimos fieri circa tempora inter <lb/>cardines tempe&longs;tatum media; maximos circa cardines <lb/>(ac præ&longs;ertim Æquinoctialeis) per tempora autem in<lb/>tercepta maximos &longs;en&longs;im ex minimis, minimos ex ma<lb/>ximis fieri: quantumcumque per aliquos dies ab&longs;que <lb/>apparente incremento, tam &longs;ub quadraturas, & &longs;yzy<lb/>gias, quàm &longs;ub Æquinoctia, Sol&longs;titiáque e&longs;&longs;e videan<lb/>tur. </s>

<s>Deinde, <emph type="italics"/>e&longs;&longs;e maximos æ&longs;tus qua&longs;i alligatos Plenilunio <lb/>proximè, primúmve post Æquinoctium contingenti,<emph.end type="italics"/> hoc e&longs;t <lb/>mihi &longs;eu iuxta propriam, &longs;eu iuxta alienam <expan abbr="experien-tiã">experien<lb/>tiam</expan> nouum; cùm con&longs;tare potiùs videatur idem Noui<lb/>lunio, quod & Plenilunio competere iuris; & neque <lb/>facto paulò ante Æquinoctium Plenilunio, ex&longs;pecte<lb/>tur ferè po&longs;t men&longs;em Plenilunium con&longs;equens, vt ma<lb/>ximi in eo &longs;int æ&longs;tus: neque non &longs;int æ&longs;tus maiores <lb/>Plenilunio, Nouilunióque ante <expan abbr="Æquinocti&utilde;">Æquinoctium</expan> proximè <pb pagenum="310"/>contingente, quàm contingente procùl po&longs;t ip&longs;um. <lb/>Quòd <emph type="italics"/>tales porrò æstus non contingant ex&longs;istente Terra in <lb/>ip&longs;is æquinoctialibus punctis,<emph.end type="italics"/> ideò e&longs;t, quia cau&longs;&longs;a, quæ <lb/>varietatem in ip&longs;is creat, neque &longs;ola e&longs;t, neque per dies <lb/>aliquot variatur &longs;en&longs;ibiliter: &longs;ed &longs;uperuenit illa cau&longs;&longs;a <lb/>alia, varietatis &longs;cilicet men&longs;truæ, quæ, quòd in Plenilu<lb/>niis, Nouilunii&longs;que potenti&longs;&longs;ima &longs;it: ideo illi coniuncta <lb/>æ&longs;tus maximè &longs;en&longs;ibileis creat. </s>

<s>Quòd <emph type="italics"/>tales porrò æstus non contingant ex&longs;istente Terra in <lb/>ip&longs;is æquinoctialibus punctis,<emph.end type="italics"/> ideò e&longs;t, quia cau&longs;&longs;a, quæ <lb/>varietatem in ip&longs;is creat, neque &longs;ola e&longs;t, neque per dies <lb/>aliquot variatur &longs;en&longs;ibiliter: &longs;ed &longs;uperuenit illa cau&longs;&longs;a <lb/>alia, varietatis &longs;cilicet men&longs;truæ, quæ, quòd in Plenilu<lb/>niis, Nouilunii&longs;que potenti&longs;&longs;ima &longs;it: ideo illi coniuncta <lb/>æ&longs;tus maximè &longs;en&longs;ibileis creat. </s>

<s>Quòd verò, <emph type="italics"/>cau&longs;&longs;a &longs;uf<lb/>ficiens exinde reddatur, cur tunc æstus fiant adeò magni præ <lb/>cæteris:<emph.end type="italics"/> ex eo e&longs;t, quòd vtraque cau&longs;&longs;a tunc temporis <lb/>vigeat: cùm aliàs in ip&longs;o Æquinoctio (ni&longs;i ca&longs;u quo<lb/>dam) vigor Plenilunij, Nouiluniive non &longs;it; aut in Ple<lb/>nilunio, Nouiluniove, vigor Æquinoctii. </s>

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<s>Et quia propter <lb/>hanc communionem efficitur, vt motus diurnus non <lb/>&longs;it integer accipiendus, ni&longs;i po&longs;tquàm non modò Ter<lb/>ra ex meridiano quopiam digre&longs;&longs;a ad eundem meridia<lb/>num redit, &longs;ed po&longs;tquàm ip&longs;a etiam Luna meridianum <lb/>eundem repetit: inde e&longs;t, cur Luna illum dietim repe<lb/>tente, vnâ prope hora, &longs;eu quatuor quintis horæ tar<lb/>diùs; cur, inquam, alteratio illa, atque adeò æ&longs;tus con<lb/>tingat dietim tanto tempore: quatuor &longs;cilicet horæ <lb/>quintis tardiùs. </s>

<s>Prætereo autem, cùm Luna ad datum <lb/>meridianum eádem diei hora, ni&longs;i po&longs;t men&longs;em non <lb/>redeat, excur&longs;us tamen, & recur&longs;us maris eadem hora <lb/>po&longs;t dies quindecim in&longs;taurari; quòd ij geminentur <lb/>in dies &longs;ingulos, ac eadem hora eueniant, non <lb/>modò cùm Luna e&longs;t nobis in mendiano &longs;upra horizon<lb/>tem, &longs;ed etiam cùm infià, in meridiano Antipodum. <lb/>Adeò proinde, vt dici po&longs;&longs;it, quemadmodum Luna <lb/>intra men&longs;em apparet reuolui circa Terram vna vice <lb/>minùs, quàm Sol; ita Mare affluere, & refluere duabus <lb/>vicibus minùs, quàm afflueret, ac reflueret, ab&longs;que illa <pb pagenum="317"/>retar datione. </s>

<s>Adeò proinde, vt dici po&longs;&longs;it, quemadmodum Luna <lb/>intra men&longs;em apparet reuolui circa Terram vna vice <lb/>minùs, quàm Sol; ita Mare affluere, & refluere duabus <lb/>vicibus minùs, quàm afflueret, ac reflueret, ab&longs;que illa <pb pagenum="317"/>retar datione. </s>

<s>Prætereo quoque hanc retardationem, <lb/>quatenus ex aquæ &longs;luore, lentoréque &longs;imùl dependet, <lb/>confirmari po&longs;&longs;e videri ex con&longs;imili retardatione aëris, <lb/>de qua in Epi&longs;tolis dictum; cùm ventus illo continuus, <lb/>& æquabilis ab ortu in occa&longs;um, quem experiuntur <lb/>nautæ in alto, non videatur po&longs;&longs;e explicari <expan abbr="cõmodiùs">commodiùs</expan> <lb/>quàm ex retardatione aëris, ob fluiditatem &longs;uam inca<lb/>pacis, qui con&longs;equatur præci&longs;e motum Telluris conti<lb/>nuum, & æquabilem ver&longs;us ortum. </s>

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<s>Pari&longs;iis, VI. Eid. </s>

<s>Decembris. <lb/>M. DC. XLII. </s>

<s>Decembris. <lb/></s>

<s><emph type="center"/>FINIS.<emph.end type="center"/><lb/><figure id="fig47"></figure><pb pagenum="319"/><gap desc="hr tag"/></s>

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<s>Operam verò imprimis <lb/>da, vt qui te authore amare me c&oelig;pit, me porrò, te <lb/>quoque promotore, amet. </s>

<s>Nimirùm tantus ille e&longs;t <lb/>vir, vt maximi ducam eius amicitiam, & tibi, cui ip&longs;am <lb/>debeo &longs;olidam, me &longs;ummoperè ob&longs;trictum agno&longs;cam. <lb/>Vale. </s>

<s>Nimirùm tantus ille e&longs;t <lb/>vir, vt maximi ducam eius amicitiam, & tibi, cui ip&longs;am <lb/>debeo &longs;olidam, me &longs;ummoperè ob&longs;trictum agno&longs;cam. <lb/></s>

<s>Pari&longs;iis, VI. Eid. </s>

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

<s>IVxta Priuilegium à Rege Chri&longs;tiani&longs;&longs;imo conce&longs;<lb/>&longs;um, cautum e&longs;t, ne quistoto Regnoimprimat, alibi<lb/>ve impre&longs;&longs;as diuendat PETRI GASSENDI <emph type="italics"/>De <lb/>Proportione, qua grauia decidentia accelerantur, Epi&longs;tolas <lb/>treis,<emph.end type="italics"/> præter LVD. DE HEVQVEVILLE, Bibliopolam <lb/>Pari&longs;ien&longs;em, idque in decennium, &longs;ub &longs;olitis p&oelig;nis. <lb/>Datum Pari&longs;iis 8. April. </s>

<s>Datum Pari&longs;iis 8. April. </s>

<s>1642. Signatum CEBERET. </s> </chap> </body> <back></back> </text></archimedes>

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