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| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
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| date | Wed, 29 Nov 2017 16:55:37 +0100 |
| parents | 22d6a63640c6 |
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<?xml version="1.0"?> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink" > <info> <author>Gassendi, Pierre</author> <title>De proportione qua gravia decidentia accelerantur</title> <date>1646</date> <place>Paris</place> <translator></translator> <lang>la</lang> <cvs_file>gasse_propo_028_la_1646.xml</cvs_file> <cvs_version></cvs_version> <locator>028.xml</locator> </info> <text> <front> </front> <body> <chap> <pb xlink:href="028/01/001.jpg"></pb> <p type="main"> <s id="s.000001"><emph type="center"></emph><emph type="italics"></emph>PETRI GASSENDI<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000002"><emph type="center"></emph>DE PROPORTIONE, <lb></lb>QVA GRAVIA DECIDENTIA <lb></lb>ACCELERANTVR.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000003"><emph type="center"></emph>EPISTOLÆ TRES.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000004"><emph type="center"></emph><emph type="italics"></emph>Quibus ad totidem Epiſtolas R. P.<emph.end type="italics"></emph.end> PETRI CAZRÆE <lb></lb><emph type="italics"></emph>Societatis<emph.end type="italics"></emph.end> IESV <emph type="italics"></emph>Reſpondetur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <figure id="id.028.01.001.1.jpg" xlink:href="028/01/001/1.jpg"></figure> <p type="main"> <s id="s.000005"><emph type="center"></emph>PARISIIS,<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000006"><emph type="center"></emph>Apud LVDOVICVM DE HEVQVEVILLE, via Iacobæa, <lb></lb>ſub ſigno Pacis.<emph.end type="center"></emph.end><lb></lb></s> </p> <p type="main"> <s id="s.000007"><emph type="center"></emph>M. DC. XLVI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000008"><emph type="center"></emph><emph type="italics"></emph>CVM PRIVILEGIO REGIS<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <pb xlink:href="028/01/002.jpg"></pb> <pb xlink:href="028/01/003.jpg"></pb> <figure id="id.028.01.003.1.jpg" xlink:href="028/01/003/1.jpg"></figure> <p type="main"> <s id="s.000009"><emph type="center"></emph>EPISTOLARVM<emph.end type="center"></emph.end><emph type="center"></emph>SVMMVLÆ.<emph.end type="center"></emph.end><lb></lb></s> </p> <p type="main"> <s id="s.000010"><emph type="center"></emph>EPISTOLÆ PRIMÆ.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000011">ART. I. </s> <s id="s.000012">Scribendi Occaſio. </s> </p> <p type="main"> <s id="s.000013"><emph type="italics"></emph>CVm enim ante annos treis Author edidiſſet duas Epiſto<lb></lb>las<emph.end type="italics"></emph.end> De Motu impreſſo à Motore tranſlato <emph type="italics"></emph>inſcrip<lb></lb>tas, R. P. Cazræus Societatis<emph.end type="italics"></emph.end> IESV <emph type="italics"></emph>tum Diuionenſis Collegij <lb></lb>Rector ſcripſit ad ipſum <expan abbr="Epiſtolã">Epiſtolam</expan>, qua reprehendit capita varia <lb></lb>tam circa cætera de Motu conſcripta, quàm circa diſputata ſpe<lb></lb>ciatim de Motu Terra attributo. </s> <s id="s.000014">Itaque Author ad illum reſ<lb></lb>cripſit eâ Epiſtolâ, quæ heic bhbetur ordine tertia, quàmque pri<lb></lb>mam legere ſi libet, licet, imò & non <expan abbr="incongruũ">incongruum</expan> eſt. </s> <s id="s.000015">Quia verò <lb></lb>R. P. cætera inter obiecerat, non fuiſſe Authorem probatu<lb></lb>rum<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei ſententiam circa Proportionem, qua grauia de<lb></lb>cidentia accelerantur, ſi commiſſum à<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileo Paralogiſmum <lb></lb>animaduertiſſet; & Author responderat ſe nec potuiſſe nec<lb></lb>dum poſſe Paralogiſmum vllum videre; ac optare adeò, <lb></lb>vt R. P. tum illum retegeret, tum proportionem quam crede<lb></lb>ret eſſe veriorem manifeſtaret; idcircò R. P. conſcripſit, edi<lb></lb>ditque nuper Epistolam aliam hocce Titulo,<emph.end type="italics"></emph.end> Phyſica <pb xlink:href="028/01/004.jpg"></pb>Demonſtratio, qua ratio, menſura, modus, ac poten<lb></lb>tia accelerationis motus in naturali deſcenſu grauium <lb></lb>determinantur; aduerſus nuper excogitatam à <emph type="italics"></emph>G<emph.end type="italics"></emph.end>alileo <lb></lb>Galilei Florentino Philoſopho, ac Mathematico de <lb></lb>eodem motu Pſeudo ſcientiam. <emph type="italics"></emph>Hæc ergo Epiſtola eſt, <lb></lb>ad quam heic primùm Respondetur.<emph.end type="italics"></emph.end> A pag. </s> <s id="s.000016">1. in 3. </s> </p> <p type="main"> <s id="s.000017">ART. II. III. IV. V. </s> <s id="s.000018">Status Controuerſiæ. </s> </p> <p type="main"> <s id="s.000019"><emph type="italics"></emph>Quæritur nimirùm, An, cùm lapide, v. c. ex alto cadente, <lb></lb>accipere liceat primum quoddam spatium, vt vnam orgyiam; <lb></lb>& habe re pro momento, ſeu tempore primo illud quod effluit, <lb></lb>donec lapis per hanc orgyiam decidit: & pro gradu celeritatis <lb></lb>primo eam celeritatem, quæ in fine primi huius temporis acqui<lb></lb>ſita eſt: An inquam, acceptis deinceps æqualibus ſpatijs, tempo<lb></lb>ribus, & gradibus, cenſeri debeat lapis motuſ-ve ipſius tum <lb></lb>acquiſiiſſe duos celeritatis gradus, cùm eſt ſuperata ſecunda <lb></lb>orgyia, licet ſecundum tempus nondum totum effluxerit, ac <lb></lb>pari modo treis, cùm tertia, quatuor cum quarta, &c. </s> <s id="s.000020">adeò vt <lb></lb>ſemper velocitates ſe habeant ſicut ſpatia, quòd R. P. conten<lb></lb>dit: An potiùs cenſeride beat <expan abbr="tũ">tum</expan> acquiſiiſſe duos celeritatis gra<lb></lb>dus, cùm effluxit ſecundum tempus, licet plura spatia, quàm <lb></lb>duo ſuperata ſint: ac pari modo treis, cùm tertium, quatuor, <lb></lb>cùm quartum, &c. </s> <s id="s.000021">adeò vt ſemper velocitates ſe habeant ſicut <lb></lb>tempora; quæ eſt Galilei ſententia. </s> <s id="s.000022">Ex qua aliunde ſequitur, <lb></lb>vt temporibus æqualibus ſpatia ſuperentur iuxta numeros ab <lb></lb>vnitate impareis: ita vt ſi primo tempore lapis decidat per <lb></lb>vnam orgyiam, decidat ſecundo per treis, tertio per quinque, <lb></lb>quarto per ſeptem, &c. </s> <s id="s.000023">atque idcircò spatia in fine cuiuſque <lb></lb>temporis à principio vſque aggregata habeant ſe ſicut quadra<lb></lb>ta temporum; hoc eſt, vt spatia ſuperata ſint in fine vnius <emph.end type="italics"></emph.end><pb xlink:href="028/01/005.jpg"></pb><emph type="italics"></emph>temporis vnum, in fine duorum quatuor; in fine trium nouem; <lb></lb>in fine quatuor ſexdecim, &c. </s> <s id="s.000024">Quæ omnia liceat repræſentare <lb></lb>in maiuſculo quodam Triangulo, cuius lateribus, ac baſi in par<lb></lb>teis æqualeis diuiſis, interductiſque lineis aream diſpeſcentibus <lb></lb>in minores, mutuò æqualeis, ſimileiſque triangulos, partes <lb></lb>vtriuſvis lateris (incipiendo ab apice) habeantur pro tempori<lb></lb>bus; baſes triangulorum ipſis respondentium pro gradibus ce<lb></lb>leritatis; & intercepta triangula, ipſorumve areæ pro spatiis. <lb></lb></s> <s id="s.000025">Vide & totius Epiſtolæ ſiue Diſſertationis ſeriem.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000026">3. in 9. </s> </p> <p type="main"> <s id="s.000027">ART. VI. VII. VIII. </s> <s id="s.000028">De Motus æquabiliter <lb></lb>accelerati definitione. </s> </p> <p type="main"> <s id="s.000029"><emph type="italics"></emph>Definit<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus Motum æquabiliter acceleratum (qua<lb></lb>lis grauibus decidentibus competit) illum,<emph.end type="italics"></emph.end> qui à quiete rece<lb></lb>dens, temporibus æqualibus æqualia celeritatis mo<lb></lb>menta acquirit. <emph type="italics"></emph>Jd autem improbans R. P. contendit po<lb></lb>tiùs definiendum cum vulgari ſententia illum,<emph.end type="italics"></emph.end> qui æquali<lb></lb>bus ſpatiis æqualia celeritatis augmenta acquirit. <emph type="italics"></emph>Quan<lb></lb>quam ex Galilei definitione præclarè intelligitur accelerationis <lb></lb>æquabilitas: prout increſcens celeritas ſe habet vt linea inter <lb></lb>latera memorati Trianguli ab apice vſque in baſim increſcens <lb></lb>& hæc linea ideò increſcit æquabiliter, quòd ſecundum parteis <lb></lb>laterum æqualeis (per quas dictum eſt repræſentari tempora) <lb></lb>additamenta continuò æqualia acquirat.<emph.end type="italics"></emph.end> E<emph type="italics"></emph>x definitione au<lb></lb>tem R. </s> <s id="s.000030">Patri probata, nihil tale potest intelligi: cùm nulla <lb></lb>facta temporis mentione, & ſumptis partibus lateris trianguli <lb></lb>pro spatiis, & interceptis triangulis pro celeritatis gradibus, <lb></lb>conſtet, ſi totidem ſemper addantur triangula, quot lateris par<lb></lb>tes, creatum iri triangulum totalem, cuius area inæquabiliſ<lb></lb>ſimè ab apice in baſim increſcat.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000031">9. in 14. </s> </p> <pb xlink:href="028/01/006.jpg"></pb> <p type="main"> <s id="s.000032">ART. IX. X. XI. XII. </s> <s id="s.000033">De Paralogiſmo, <lb></lb>qui Galileo Definitionem ſpuriam impugnan<lb></lb>ti obiicitur. </s> </p> <p type="main"> <s id="s.000034"><emph type="italics"></emph>Impugnat<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus definitionem R. </s> <s id="s.000035">Patri probatam, <lb></lb>quòd ſi velocitates eſſent, vt emenſa ſpatia, atque idcircò <lb></lb>ſpatium v. c. duplum percurreretur velocitate dupla illius, qua <lb></lb>dimidium: ſequeretur duplum, & dimidium, ſeu totum, & <lb></lb>partem, eodem, aut æquali tempore percurri. </s> <s id="s.000036">Nempe ſeu <lb></lb>motus æquabilis, ſeu acceleratus æquabiliter ſit, non potest ce<lb></lb>leritas eſſe dupla per duplum ſpatij, quin ea exſiſtente vbique <lb></lb>dupla, duplæ partes percurrantur quibuſlibet temporibus, ſic<lb></lb>que perueniatur eodem tempore ad dupli, & ad dimidij finem. <lb></lb></s> <s id="s.000037">Contendit R. P. committi heic Paralogiſmum: & nullam <lb></lb>tamen rationem profert, quàm quæ continetur his verbis,<emph.end type="italics"></emph.end><lb></lb>Si graue deſcendens per AB, tempus quodcum<lb></lb><figure id="id.028.01.006.1.jpg" xlink:href="028/01/006/1.jpg"></figure><lb></lb>que inſumat, putà quadrantem; ac deinde BC <lb></lb>ipſi AB æquale dimidio quadrante percurrat: <lb></lb>quis neget in C duplam haberi velocitatem eius, <lb></lb>quæ fuit in B? & tamen idem graue totam AC, <lb></lb>& dimidium eius AB non percurreret. <emph type="italics"></emph>Vbi ſanè <lb></lb>nihil aliud, quàm rem controuerſam ſupponit, habetque <lb></lb>pro principio: videlicet ſecundam partem percurri di<lb></lb>midio temporis, quo primam. </s> <s id="s.000038">Atque id quidem præter Incom<lb></lb>modum ex poſitione hac conſequens, quòd cùm oporteat pari <lb></lb>modo percurri partem tertiam dimidio temporis, quo ſecun<lb></lb>dam; quartam, quo tertiam, &c. </s> <s id="s.000039">debeat cum effluxu temporis <lb></lb>ſecundi percurri spatium infinitum: quatenus omnia illa di<lb></lb>midiorum dimidia, ſiue fragmenta temporis non poſſunt<emph.end type="italics"></emph.end><pb xlink:href="028/01/007.jpg"></pb><emph type="italics"></emph>æquari vni integro (cuius ſemper relinquitur inexhaustum <lb></lb>aliquid) niſi priùs omnia, hoc eſt infinita, fuerint numerata.<emph.end type="italics"></emph.end><lb></lb>A. p. </s> <s id="s.000040">14. in 21. </s> </p> <p type="main"> <s id="s.000041">ART. XIII. XIV. XV. XVI. XVII. <lb></lb>XVIII. </s> <s id="s.000042">De Poſtulato Galilei circa motum <lb></lb>ſuper æque-altis, non æque-inclinatis planis. </s> </p> <p type="main"> <s id="s.000043"><emph type="italics"></emph>Cùm experientiâ conſtet accelerationem eadem ratione <lb></lb>fieri, ſiue ad perpendiculum graue decidat, ſiue ſupra planum <lb></lb>inclinatum delabatur; candidè egit<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus, dum aſſumens<emph.end type="italics"></emph.end><lb></lb>Gradus velocitatis eiuſdem mobilis ſuper diuerſas pla<lb></lb>norum inclinationes acquiſitos tum eſſe æqualeis, cùm <lb></lb>eorumdem planorum eleuationes ponuntur æquales: <lb></lb><emph type="italics"></emph>id extulit, non vt demonſtratum (tametſi Torricellius posteà <lb></lb>demonſtrationem attulerit) ſedvt eatenus probabile, quatenus <lb></lb>deductæ ex eo concluſiones cum experientia conſentirent. </s> <s id="s.000044">Id <lb></lb>tamen R. P. exagitat, vti & confirmationem, non incongruè <lb></lb>alioquin petitam ex pendulis, quæ longioribus, breuioribuſque <lb></lb>filis illigata, & ex eadem tamen altitudine vibrari permiſſa, ad <lb></lb>eandem proximè aſſurgant, ſicque debeant omnia parem impe<lb></lb>tum (ſeu velocitatem) deſcendendo acquirere: vtcumque per <lb></lb>arcus inæqualeis procurrant. </s> <s id="s.000045">Neque verò etiam R. P. licet <lb></lb>difficilia obiiciat, proptereà infirmat<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei experimenta (qui<lb></lb>bus Author habet aliqua ſimilia) ad probandum grauia tam <lb></lb>decidentia, quàm delabentia conficere primo tempore vnum ſpa<lb></lb>tium, ſecundo tria, tertio quinque, &c.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000046">21. in 32 </s> </p> <pb xlink:href="028/01/008.jpg"></pb> <p type="main"> <s id="s.000047">ART. XIX. XX. XXI. XXII. </s> <s id="s.000048">De <lb></lb>Experimento circa ictum, impetumve grauium <lb></lb>cadentium, ad explorandum impetuſ-ne, vt <lb></lb>ſpatium increſcat. </s> </p> <p type="main"> <s id="s.000049"><emph type="italics"></emph>Tametſi conſtet grauia, quò ex altiore decidunt loco, eò <lb></lb>maiore impetu eſſe, vehementiuſque percutere, ac tantam eſſe <lb></lb>velocitatem, quantus impetus, & percußio est: non ideò tamen <lb></lb>conſtat vllis (qualia R. P. dicit in quolibet graui clara, facilia, <lb></lb>indubitata) experimentis, graue decidens ex altitudine duplæ <lb></lb>duplò fortiùs percutere, triplò ex tripla, quadruplò ex quadru<lb></lb>pla, &c. </s> <s id="s.000050">Quin-etiam ſunt Experimenta, quæ impetum, per<lb></lb>cußionemque non eſſe duplò maiorem inſinuant, niſi ex altitu<lb></lb>dine quadrupla; triplò, niſi ex nonupla; quadruplò, niſi ex ſe<lb></lb>decupla. </s> <s id="s.000051">Huiuſcemodi ſunt illa de Aqua cylindrico vaſe con<lb></lb>tenta; cuius duplum non exſilit tempore æquali, niſi altitudo <lb></lb>quadrupla ſit; nec triplum, niſi nonupla; quadruplum, niſi ſe <lb></lb>decupla: & de Chorda tenſa, cuius vibratæ itus, redituſque <lb></lb>dupli non ſunt, niſi quadruplo pondere tendatur; tripli, niſi <lb></lb>nonuplo; quadrupli, niſi ſedecuplo: ac rursùs de Penſilibus, <lb></lb>quorum vibrationes ad perpendiculum peruenientes non acqui<lb></lb>runt impetum duplum, niſi altitudo deſcenſus ſit quadrupla, <lb></lb>triplum, niſi nonupla, quadruplum, niſi ſedecupla, &c.<emph.end type="italics"></emph.end><lb></lb>A p. </s> <s id="s.000052">32. in 41. </s> </p> <p type="main"> <s id="s.000053">ART. XXIII. XXIV. XXV. XXVI. XXVII. <lb></lb>XXVIII. </s> <s id="s.000054">De Experimento in Bilance facto, ac <lb></lb>aliud reuerâ probante, quàm velocitates eſſe <lb></lb>ſicut ſpatia. </s> </p> <p type="main"> <s id="s.000055"><emph type="italics"></emph>Fuere omnia Experimenta R. P. ad vnum redacta, vt <emph.end type="italics"></emph.end><pb xlink:href="028/01/009.jpg"></pb><emph type="italics"></emph>non modò probaret impetum, atque idcircò velocitatem ſicut <lb></lb>spatium increſcere; ſed speciatim quoque illud, quod edixit, <lb></lb>diametrum cuiuſlibet globi ita eſſe præciſam impetus illius <lb></lb>menſuram, vt ex altitudine duarum diametrorum præcisè, per<lb></lb>cutiat duplò fortiùs: ex altitudine trium triplo: ex altitudine <lb></lb>quatuor quadruplò, &c. </s> <s id="s.000056">Iußit autem Experimentum in Bi<lb></lb>lance peragi, qua ruè ſuſpenſa, & alterâ lancium per aërem <lb></lb>liberâ, alterâ ſuffulta, & pondere exæquatâ cum libera, glo<lb></lb>bóque ſimùl, ſi deinceps, inquit, dimittatur globus in liberam <lb></lb>ex vna ſui diametro, is percußionis impetu attollet ſuffultam <lb></lb>cùm ſuper-addito præci è vno ſui pondere; ſi ex duabus, cum <lb></lb>ſuper-addito duplo: ſi ex tribus, cum triplo: ſi ex quatuor, <lb></lb>cum quadruplo. </s> <s id="s.000057">Et permirum tamen id Experimentum de<lb></lb>prehendi falſum; quatenus dimiſſus globus ex altitudine dia<lb></lb>metri vnius, non modò attollit cum altera lance (eo, quo dictum <lb></lb>eſt, modo exæquata) ponderis tantumdem, quanto ipſe eſt, ve<lb></lb>rùm etiam <expan abbr="duplũ">duplum</expan>, etiam ad vſque <expan abbr="ſeptuplũ">ſeptuplum</expan>: & tantum idem <lb></lb>aliunde attollit non modò ex diametro vna altitudinis, verùm <lb></lb>etiam ex diametri ſemiſſe, imo ex quadrante, imò ex octante, <lb></lb>imò & ex vncia. </s> <s id="s.000058">Quin-etiam eius ponderis, quod eleuat ſum<lb></lb>mum ex diametro vna, duplum eleuat non ex diametris dua<lb></lb>bus, ſed ex quatuor: triplum non ex tribus, ſed ex <lb></lb>nouem: quadruplum non ex quatuor, ſed ex ſedecim: adeò <lb></lb>proinde vt proprio R. P. experimento eius ſententia euertatur, <lb></lb>&<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileana confirmetur. </s> <s id="s.000059">Adde &, ſi velocitatis gradus <lb></lb>pro ratione diametrorum creſcerent, euenturum, vt dimißis ex <lb></lb>eadem altitudine duobus globis ex eadem materia, quorum <lb></lb>vnus eſſet diametro decies maiore, quàm alius, minor caderet <lb></lb>decuplo velociùs, ac decuplò citiùs perueniret in terram, quàm <lb></lb>maior; cùm experientia tamen doceat cadere æque-velociter,<emph.end type="italics"></emph.end><pb xlink:href="028/01/010.jpg"></pb><emph type="italics"></emph>temporéque eodem peruenire in terram: vtcúmque aliunde <lb></lb>Ariſtoteles cenſeat cadere maiorem velociùs, & peruenire <lb></lb>citiùs.<emph.end type="italics"></emph.end> A p 41. in 53. </s> </p> <p type="main"> <s id="s.000060">ART. XXIX. XXX. XXXI XXXII. XXXIII. <lb></lb></s> <s id="s.000061">De Tempore, quo R. P. colligit parteis ſpatij <lb></lb>ſingulas decurſum non iri. </s> </p> <p type="main"> <s id="s.000062"><emph type="italics"></emph>Origo fuit mali, quòd R. P. & Experimentum falſum <lb></lb>(ſeu quod nul um eſſet) pro vero habuerit. </s> <s id="s.000063">& illam Motus <lb></lb>æquabiliter accelerati definitionem aſſumpſerit, quæ traditur <lb></lb>nulla temporis mentione: <expan abbr="cũ">cum</expan> impoßibile tamen ſit ſeu celerita<lb></lb>tem, ſeu accelerationem, maximéque æquabilem, intelligi, ſine <lb></lb>comparatione ad tempus. </s> <s id="s.000064">Et quia ſupponendo velocitates <lb></lb>acquiri, vt spatiæ, manifeſtè ſequitur, vt ſecundum æquale <lb></lb>spatium decurratur dimidio temporis, quo primum; tertium <lb></lb>triente, quartum quadrante, &c. (quippe tempore ſemper <lb></lb>exſiſtente ad velocitatem increſcentem ſubmultiplo) cum heic <lb></lb>tamen conſequantur incommoda varia, ac illud speciatim, <lb></lb>quod acceleratio fieret, vt difformiter. </s> <s id="s.000065">ſic in ratione pluſquam <lb></lb>tripla: ideò oſtendit quidem R.<emph.end type="italics"></emph.end> P. <emph type="italics"></emph>ex quibuſdam incommodis <lb></lb>fieri non poſſe vt decurrantur ſpatia temporibus huiuſmodi; <lb></lb>ſed <expan abbr="oſtẽdit">oſtendit</expan> tamen aduerſus ſeipſum, quatenus decurri neceſſariò <lb></lb>ſequitur ex ea poſitione, quod velocitates ſe habeant vt ſpatia.<emph.end type="italics"></emph.end><lb></lb>A p. </s> <s id="s.000066">13. in 63. </s> </p> <p type="main"> <s id="s.000067">ART. XXXIV. XXXV. XXXVI. XXXVII. <lb></lb>XXXVIII. </s> <s id="s.000068">De Tempore, quo R. P. colligit <lb></lb>ſingulas parteis decurſum iri. </s> </p> <p type="main"> <s id="s.000069"><emph type="italics"></emph>Diuiſo caſus spatio in parteis æqualeis quotcumque,<emph.end type="italics"></emph.end><pb xlink:href="028/01/011.jpg"></pb><emph type="italics"></emph>accipit R. P. punctum infimum primæ partis, & ab ipſo <lb></lb>ſurſum eiuſdem primæ partis dimidium, trientem, quadran<lb></lb>tem, & vniuersè tot fragmenta, quot ſunt inferiùs partes <lb></lb>æquales; ac tum contendit, quanto tempore dimidium inferius <lb></lb>primæ partis percurritur, tanto deinceps partem ſecundam <lb></lb>æqualem percurri; quanto triens, tanto tertiam; quanto qua<lb></lb>drans, tanto quartam, &c. </s> <s id="s.000070">adeò proinde, vt in inferiore pri<lb></lb>mæ partis dimidio contineantur ſigillatim omnia tempora, qui<lb></lb>bus omnes ſuperſtites æquales partes percurruntur. </s> <s id="s.000071">Attamen <lb></lb>abs re, & omninô gratis negligit ſuperius dimidium, nullam<lb></lb>que eius rationem habet; à cuius tamen initio, non fine, motus <lb></lb>incipit, & per quod iam acceleratur, cùm pauciores parteis, <lb></lb><expan abbr="quã">quam</expan> inferius non habeat. </s> <s id="s.000072">Gratis <expan abbr="quoq;">quoque</expan> vſurpat inferius, ipſique <lb></lb>fata omnium partium inferiorum alligat: nam & quòd vult <lb></lb>ſecundam partem eſſe huius dimidij duplam, atque ideo eſſe <lb></lb>velocitatem duplam, & tempus æquale: nihil aliud; quàm <lb></lb>quæſitum petit. </s> <s id="s.000073">Aliunde autem variis argumentis conficitur, <lb></lb>vt aſſumpto quocumque primo tempore, tam inferius dimidium, <lb></lb>quàm ſecunda pars tempore breuiore, breuioreque in infinitum <lb></lb>percurrantur (ſubdiuiſo nempe priore dimidio in duo alia, & <lb></lb>rurſus priore in alia, &c.) vt <expan abbr="itẽ">item</expan> tam inferius dimidium, qua <lb></lb>ſecunda pars percurrantur dimidio temporis, quo integra pri<lb></lb>ma: vt tempus per ſecundam partem ſeſquialterum ſit, non <lb></lb>duplum ad illud, quo percurritur inferius dimidium: vt tam <lb></lb>prima pars ſola, quàm prima, & ſecunda ſimùl, hoc eſt pars, <lb></lb>& totum eodem, aut æquali percurrantur tempore; atque id <lb></lb>genus cætera, quæ proportione etiam obiici in trientem, qua<lb></lb>drantem, fragmentaque alia aſſumptæ primæ partis poſſunt.<emph.end type="italics"></emph.end><lb></lb>A p. </s> <s id="s.000074">63. in 72. </s> </p> <pb xlink:href="028/01/012.jpg"></pb> <p type="main"> <s id="s.000075">ART. XXXIX. XL. XLI. XLII. <lb></lb></s> <s id="s.000076">De Ratione continuò dupla, qua ſpatia de<lb></lb>curri temporibus æqualibus R. P. contendit. </s> </p> <p type="main"> <s id="s.000077"><emph type="italics"></emph>Diuiſo eodem caſus ſpatio in quotcúmque æqualeis parteis, & <lb></lb>parte prima ſubdiuiſa in duo dimidia; aſſumit R. P. illud <expan abbr="tẽpus">tempus</expan>, <lb></lb>quo inferius <expan abbr="dimidiũ">dimidium</expan> percurritur, pro tempore primo: ac vult <lb></lb>tempore æquali ſecundo percurri partem ſecundam, quæ est <lb></lb>nempe dupla illius dimidij: ac tertio parteis tertiam, & quar<lb></lb>tam, quæ iunctim ſunt duplum ſecundæ: & quarto quintam, <lb></lb>ſextam, ſeptimam, octauam, quæ iunctim ſunt duplum tertiæ, <lb></lb>& quartæ; & quinto octo ſuccedenteis, ſexto ſequenteis ſex<lb></lb>decim: atque ita porrò in ratione continuò dupla. </s> <s id="s.000078">At verò <lb></lb>heic quoque abs re præteritur primum primæ partis dimidium: <lb></lb>& maximè cùm requiratur, quæ accelerationis ſit ratio non <lb></lb>à medio vſque primæ partis, ſed ab eius vſque initio. </s> <s id="s.000079">Peruer<lb></lb>tit etiam R. P. </s> <s id="s.000080">Arithmeticam progreßionem, qua ſuperiùs <lb></lb>ſtatuens velocitates eſſe, vt ſpatia, voluit vni parti integræ, non <lb></lb>eius dimidio competere vnum celeritatis gradum, duobus <lb></lb>duos, &c. </s> <s id="s.000081">Conficitur rurſus heic quoque, vt totum, & pars <lb></lb>eodem tempore percurrantur; vt non ampliùs, quàm triens, & <lb></lb>quadrans exæquentur toti; vt item ſolæ partes quinta, ſexta, <lb></lb>ſeptima, octaua; atque ita de reliquis. </s> <s id="s.000082">Comficitur quoque, vt <lb></lb>decurrantur ſpatia non modò in ratione dupla, ſed etiam in <lb></lb>tripla, quadrupla, &c. </s> <s id="s.000083">Denique & illud inde ſequitur, <lb></lb>quod iam ante obiectum est; vt primo nimirùm tempore per<lb></lb>acto, effluere ſecundum æquale non poßit, quin decurſum fuerit <lb></lb>spatium infinitum.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000084">72. in 79. </s> </p> <pb xlink:href="028/01/013.jpg"></pb> <p type="main"> <s id="s.000085">ART. XLIII. XLIV. </s> <s id="s.000086">De Tempore, <lb></lb>quo globum ferreum caſurum ex Luna in <lb></lb>Terram contendit. </s> </p> <p type="main"> <s id="s.000087">C<emph type="italics"></emph>ùm<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus ſupponendo eſſe à Luna in centrum Ter<lb></lb>ræ milliaria Jtalica<emph.end type="italics"></emph.end> 196000, <emph type="italics"></emph>deducat ex obſeruatione, ac <lb></lb>proportione à ſe instituta decurſum iri id spatium à globo fer<lb></lb>reo è Luna dimiſſo intra horas<emph.end type="italics"></emph.end> 3. <emph type="italics"></emph>minuta<emph.end type="italics"></emph.end> 22. <emph type="italics"></emph>& ſecunda<emph.end type="italics"></emph.end> 4. <lb></lb><emph type="italics"></emph>deducit R. P. iuxta ſuam illam progreßionem in ratione con<lb></lb>tinuò dupla, decurſum iri id spatium intra minuta non omninò <lb></lb>duo.<emph.end type="italics"></emph.end> I<emph type="italics"></emph>mmanis ſanè pernicitas, & quam refellit etiam ex<lb></lb>perientia, qua cùm constet globum non conficere amplius vno <lb></lb>ſemi-minuto, quàm milliare vnum altitudinis; & ſeruata <lb></lb>etiam acceleratione in ratione dupla, non poßit ſecundo ſemi<lb></lb>minuto, niſi duo conficere: tertio, niſi quatuor: quarto, niſi octo: <lb></lb>manifeſtum fit ex ijs aggregatis non poſſe intra duo minuta <lb></lb>confici milliaria pluſquam quindecim. </s> <s id="s.000088">Quàm ingenti verò <lb></lb>diſcrimine hic numerus abeſt à milliaribus<emph.end type="italics"></emph.end> 196000. <emph type="italics"></emph>ſeu ab <lb></lb>ijs potiùs, quæ ille vult intra duo minuta integra percurri,<emph.end type="italics"></emph.end><lb></lb>1677721 1/2: <emph type="italics"></emph>& mira quidem incohærentia, quatenus de<lb></lb>bent primo ſemi-minuto percurri<emph.end type="italics"></emph.end> 6, <emph type="italics"></emph>cum proximè triente: <lb></lb>ſecundo<emph.end type="italics"></emph.end> 403, <emph type="italics"></emph>cum vna quinta: tertio<emph.end type="italics"></emph.end> 25804, <emph type="italics"></emph>cum quatuor <lb></lb>quintis: & quarto<emph.end type="italics"></emph.end> 1651507, <emph type="italics"></emph>cum vna quinta?<emph.end type="italics"></emph.end> A p. </s> <s id="s.000089">79. in 82. </s> </p> <p type="main"> <s id="s.000090">ART. XLV. XLVI. XLVII. </s> <s id="s.000091">De Tem<lb></lb>pore per primas parteis obſeruatione determi<lb></lb>nando; pauca de cauſſa Phyſica, déque lapſu <lb></lb>circa cam admiſſo. </s> </p> <p type="main"> <s id="s.000092">I<emph type="italics"></emph>ngenuè quidem R. P. fatetur non habere ſe vnde tempus <emph.end type="italics"></emph.end><pb xlink:href="028/01/014.jpg"></pb><emph type="italics"></emph>determinet, qua ſecunda pars, quo primæ dimidia ſigillatim <lb></lb>percurruntur: ac alios ideò prouocat, vt rem experiantur in <lb></lb>turri pedes ducentos alta (vtcumque ipſe præ cæteris videatur <lb></lb>fuiſſe experturus) ac non videtur<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileum id determinantem <lb></lb>ex obſeruatis proprijs ſufficienter refellere: dum ait duntaxat, <lb></lb>eſſe verendum, ne cùm in alijs magnoperè errauerit, heic quo<lb></lb>que ſit hallucinatus. </s> <s id="s.000093">Quippe neque oſtenſum eſt erraſſe ipſum <lb></lb>in alijs, neque heic habet aliquid non experientiæ conſonum, <lb></lb>maximéque illud effatum,<emph.end type="italics"></emph.end> ſi à lationis principio duo quæ<lb></lb>libet ſpatia ſumantur, tempora ipſorum fore inter ſe, <lb></lb>vt alterum eorum ad ſpatium medium proportionale <lb></lb>inter ipſa: <emph type="italics"></emph>iuxta quod quidem promptum eſt, quanto specia<lb></lb>tim tempore & ſecunda pars, & duo primæ dimidia percur<lb></lb>rantur, determinare. </s> <s id="s.000094">Excuſatione, dilationeque vtitur R. P. <lb></lb>circa cauſſam Phyſicam, de qua videbatur ipſe titulus feciſſe <lb></lb>aliquid sperandum. </s> <s id="s.000095">Circa hanc cauſſam lapſus admiſſus in <lb></lb>Epistolis<emph.end type="italics"></emph.end> de. </s> <s id="s.000096">Motu impreſſo: <emph type="italics"></emph>quatenus in ea explicanda ipſi <lb></lb>gradus velocitatis facti æquales spatijs ſunt; & intercepta <lb></lb>triangula, de quibus ſuprà, aſſumpta ſunt non modò pro ſpa<lb></lb>tijs, verùm etiam pro gradibus; pro quibus aſſumendæ potiùs <lb></lb>triangulorum baſes fuerunt.<emph.end type="italics"></emph.end> A. p. </s> <s id="s.000097">82. in 96. </s> </p> <p type="main"> <s id="s.000098"><emph type="center"></emph>ART. XLV. CONCLVSIO.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000099"><emph type="italics"></emph>Ex præteritione eorum, quæ R. P. anacephalæoſi quadam <lb></lb>exaggerat; non oblitus etiam quantum condoluerit, habitam ab <lb></lb>Authore fuiſſe<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei principijs fidem: neque id ſine ſolita <lb></lb>beneuolentiæ ſignificatione.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000100">86. in 88. </s> </p> <pb xlink:href="028/01/015.jpg"></pb> <p type="main"> <s id="s.000101"><emph type="center"></emph>EPISTOLÆ SECVNDÆ<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000102">ART. I. </s> <s id="s.000103">Scribendi Occaſio. </s> </p> <p type="main"> <s id="s.000104"><emph type="italics"></emph>Reu. Pater viſo ſuperioris Epistolæ autographo, ipſam <lb></lb>edi non improbauit, ſi modò attexeretur alia, quam ſubinde <lb></lb>ſcripſit, inſcripſitque<emph.end type="italics"></emph.end> Vindicias Phyſicæ Demonſtratio<lb></lb>nis. <emph type="italics"></emph>Qùia verò R. P. profitetur ſeſe in ea ignotam Authori <lb></lb>veritatem maiori iam luce illuſtratam aperire, & ab errore <lb></lb>vindicatam exhibere; ac aliunde queritur frequens ea ſibi af<lb></lb>fingi quæ nec dixerit, nec ex traditis à ſe principijs potuerint <lb></lb>deduci; idcircò ſic edi viſum eſt Vindicias, vt Exceptio inter<lb></lb>ſeratur, ad explorandum quî fieri poßit, vt veritatem ſic il<lb></lb>luſtratam, vindicatamque Author non videat, & ad eluen<lb></lb>dum labem illam, qua adſpergi perſenſit ſe, ob affictionem to<lb></lb>ties obiectam.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000105">89. in 93. </s> </p> <p type="main"> <s id="s.000106">ART. II. III. IV. V. </s> <s id="s.000107">De Statu Controuerſiæ. </s> </p> <p type="main"> <s id="s.000108"><emph type="italics"></emph>Quòd perſtet R. P. pro Demonſtratione habere eam <lb></lb>Epiſtolam, in quam ſuperior conſcripta eſt; ideò vt Status <lb></lb>controuerſiæ luculentior fiat, ac ſimùl appareat, qualis<emph.end type="italics"></emph.end> D<emph type="italics"></emph>emon<lb></lb>ſtratio hæc ſit; placet ipſam eruere ex eius totius Epistolæ textu, <lb></lb>ac reducere, analyſi facta, in hypotheticum Syllogiſmum, qui <lb></lb>eſſe poßit huiuſmodi.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000109"><emph type="italics"></emph>Si in motu accelerato grauium decidentium velocitates <lb></lb>acquiſitæ ſe habent vt emenſa ſpatia, neceſſe eſt ſpatia decurri <lb></lb>temporibus æqualibus in ratione continuò dupla:<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000110"><emph type="italics"></emph>Atqui in motu accelerato grauium decidentium veloci-<emph.end type="italics"></emph.end><pb xlink:href="028/01/016.jpg"></pb><emph type="italics"></emph>tates acquiſitæ ſe habent vt emenſa spatia:<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000111"><emph type="italics"></emph>Igitur in motu accelerato grauium decidentium neceſſe est <lb></lb>ſpatia decurri temporibus æqualibus in ratione continuò <lb></lb>dupla.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000112"><emph type="italics"></emph>Nimirùm, vt ex ſerie ſuperioris Epiſtolæ patet, factum eſt <lb></lb>initium ab Aſſumptionis confirmatione, dum in<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileum <lb></lb>diſputatum eſt; tum gradus ad eiuſdem-met Aſſumptionis pro<lb></lb>bationem factus, dum palmare illud Bilancis Experimentum <lb></lb>eſt narratum; ac tandem ventum ad probandum conſequutio<lb></lb>nem Propoſitionis, dum explicitus est conatus circa Rationem <lb></lb>ſpatiorum duplam, quæ eadem concluſio fuit Demonſtrationis.<emph.end type="italics"></emph.end><lb></lb>A p 93. in 97. </s> </p> <p type="main"> <s id="s.000113">AD ART. VI. VII. VIII. </s> <s id="s.000114">De Motus <lb></lb>æquabiliter accelerati Definitione. </s> </p> <p type="main"> <s id="s.000115"><emph type="italics"></emph>Conſtat ſemper, quam Galileus Definitionem tradidit. <lb></lb></s> <s id="s.000116">Neque enim poſſunt velocitatis gradus per triangulorum re<lb></lb>præſentari baſeis, ſi per parteis laterum repræſententur ſpatia, <lb></lb>vt R. P. vult; tum quòd nulla habita temporis mentione in<lb></lb>telligi poßit difformitas mira; tum quòd gradus ſemel acqui<lb></lb>ſitus aut perire debeat, aut nihil agere, neque poßit duplum <lb></lb>illius, qui acquiritur; tum quòd ſit futurum vt ſecundo tempo<lb></lb>re octo penè spatia primo æqualia percurrantur. </s> <s id="s.000117">Confundit <lb></lb>R. P. </s> <s id="s.000118">Vniformitatem cum Proportione, dum progreßiones <emph.end type="italics"></emph.end><lb></lb><emph type="italics"></emph>Geometricas non minùs eſſe vniformeis, quàm Arithmeticas <lb></lb>vult: ac in eadem rursùs incidit Incommoda, dum in difformi <lb></lb>Triangulo vult iteratò spatia per laterum parteis, potiuſ quàm <lb></lb>per triangulos interceptos repræſentari.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000119">97. in 1. 0. </s> </p> <pb xlink:href="028/01/017.jpg"></pb> <p type="main"> <s id="s.000120">AD ART. IX. X. XI. XII. </s> <s id="s.000121">De Paralogiſmo, <lb></lb>qui Galileo Definitionem ſpuriam impugnan<lb></lb>ti obiicitur. </s> </p> <p type="main"> <s id="s.000122"><emph type="italics"></emph>Magno quidem molimine conatur R. P. </s> <s id="s.000123">Paralogiſmum <lb></lb>oſtendere: ſed fruſtrà nihilominùs; cùm ſeu varios ſenſus <lb></lb>diſtinguat, ſeu propoſitiones retexat, ſeu conſequutionem ex<lb></lb>pendat, nihil aliud rursùs, quàm quæſitum, ſeu principium (vt <lb></lb>fuerat illi <expan abbr="obiectũ">obiectum</expan>) petat; aut in ſeipſum etiam, vbi retorquere <lb></lb>quidpiam vult, mutato nomine, concludat. </s> <s id="s.000124">Haud iure verò <lb></lb>conqueritur ſibi affingi, quòd dixerit, ſpatio in duas parteis <lb></lb>æqualeis diuiſo, poſteriorem percurri dimidio temporis, quo prio<lb></lb>rem (vnde illatum eſt<emph.end type="italics"></emph.end> I<emph type="italics"></emph>ncommodum de infinito spatio intra <lb></lb>ſecundum tempus percurrendo) cùm relata ipſißima illius ver<lb></lb>ba fuerint (de quadrante nempe, & dimidio quadrantis) ac, vt <lb></lb>poſſet Paralogiſmi Galileum conuincere, non fuerit alio prin<lb></lb>cipio vſus. </s> <s id="s.000125">Denique, ſi Paralogiſmus à<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileo admiſſus ſit, <lb></lb>oſtenditur R. P. alio loco aut nihil concluſiſſe, aut apertißimè <lb></lb>in eundem Paralogiſmum incidiſſe.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000126">110. 136. </s> </p> <p type="main"> <s id="s.000127">AD ART. XIII. XIV. XV. XVI. XVII. <lb></lb>XVIII. </s> <s id="s.000128">De Poſtulato Galilei circa motum <lb></lb>ſuper æque-altis, non æque-inclinatis planis. </s> </p> <p type="main"> <s id="s.000129">G<emph type="italics"></emph>alilei obſeruata ad Poſtulatum hoc confirmandum nul<lb></lb>lius hactenus falſitatis conuicta ſunt; poteſtque adeò eius do<lb></lb>ctrina potiore iure cenſeri Scientia, vt quæ experientiæ con<lb></lb>ſentanea ſit, quàm ea, quæ à R. P. traditur, vt quæ experien<lb></lb>tiæ repugnet, ac fundata ſit in Experimento, quod falſum de-<emph.end type="italics"></emph.end><pb xlink:href="028/01/018.jpg"></pb><emph type="italics"></emph>prehenſum eſt. </s> <s id="s.000130">Si planum, vt minùs decliue, ita etiam prolixius <lb></lb>ſit, potest profectò prolixitas paruitatem incrementorum <lb></lb>velocitatis ſic compenſare, vt acquiſita in fine motus veloci<lb></lb>tas ſitnihilo minor. </s> <s id="s.000131">Quod eſt allatum de pendulis exemplum <lb></lb>ſemper congruit: & ex quatuor pendulis, quæ prolixitate <lb></lb>ſint, primum vnius præcisè pedis, ſecundum quatuor, tertium <lb></lb>nouem, quartum ſedecim: peragit reuerâ, conſtanterque pri<lb></lb>mum vibrationes quatuor, eodem tempore, quo ſecundum <lb></lb>peragit treis, & tertium duas, & quartum vnam: ſi modò <lb></lb>quidem <expan abbr="eadẽ">eadem</expan> ſemper longitudine perſeuerent.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000132">136. in 141. </s> </p> <p type="main"> <s id="s.000133">AD ART. XIX. XX. XXI. XXII. <lb></lb></s> <s id="s.000134">De Experimentis circa ictum, impetumve gra<lb></lb>uium cadentium, ad explorandum, impetuſ<lb></lb>ne, vt ſpatium increſcat. </s> </p> <p type="main"> <s id="s.000135"><emph type="italics"></emph>Meritò fuere vno plura requiſita Experimenta, vbi <lb></lb>fuit iactatum peragi ea poſſe in grauibus quibuſlibet; tametſi <lb></lb>ne in vno quidem peragere fuerit conceſſum. </s> <s id="s.000136">Allata tria ex<lb></lb>perimenta quaſi ſupparia ad ſuadendum non increſcere impe<lb></lb>tum, velocitatemve ſicut spatia, ſed ſicut spatiorum radices, <lb></lb>attinent omninô ad rem; ac illud speciatim de Aqua ef<lb></lb>fluente ex vaſe cylindrico, quatenus ſumma aqua in foramen <lb></lb>decidens, non magis à ſibi ſubiecta, præeunteque impeditur, <lb></lb>quàm ſi per aërem caderet; quòd illa ſemper pari cum ipſa <lb></lb>velocitate ſeſe ſubducat, antecedenſque nihil officiat.<emph.end type="italics"></emph.end><lb></lb>A. p. </s> <s id="s.000137">141. in 146. </s> </p> <p type="main"> <s id="s.000138">AD ART. XXIII. XXIV. XXV. XXVI. XXVII. <lb></lb>XXVIII. </s> <s id="s.000139">De Experimento in Bilance facto, ac <pb xlink:href="028/01/019.jpg"></pb>aliud reuerâ probante, quàm velocitates eſſe <lb></lb>ſicut ſpatia. </s> </p> <p type="main"> <s id="s.000140"><emph type="italics"></emph>Quandoquidem iactatum illud tantopere Experimen<lb></lb>tum falſitatis conuictum eſt: mirum videri profectò potest, <lb></lb>quamobrum R. P. venditare pergat pro Demonſtratione ra<lb></lb>tiocinium, quod fuerit eo Experimento duntaxat ſuffultum; ac <lb></lb>potißimùm prouocando ad vberiorem experientiam, qua con<lb></lb>trouerſia dirimatur; quaſi verò ſinondum ſit dirempta contro<lb></lb>uerſia, eius Demonſtratio interim cohæreat? </s> <s id="s.000141">Fruſtrà iam ſol<lb></lb>licitus eſt de non aſſumendo ſupra æquilibrium exceſſu; cùm <lb></lb>agnoſcat iam quàm vanè vſurpet diametrum globi pro men<lb></lb>ſura præciſa altitudinum, ex quibus totidem pondera at<lb></lb>tollantur. </s> <s id="s.000142">Incommodum illud de globo diametri decuplò mi<lb></lb>noris, & decuplò citius caſuro ex eadem altitudine, obiectum <lb></lb>legitimè fuit, & R. P. eximere ſe ab illo nequicquam tenta<lb></lb>uit.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000143">146. in 157. </s> </p> <p type="main"> <s id="s.000144">AD ART. XXIX. XXX. XXXI. XXXII. XXXIII. <lb></lb></s> <s id="s.000145">De Tempore, quo R.P. colligit parteis ſpatij <lb></lb>ſingulas decurſum non iri. </s> </p> <p type="main"> <s id="s.000146"><emph type="italics"></emph>Haud abs re fuere obiecta illa de neglecto tempore in <lb></lb>tradenda motus æquabiliter accelerati definitione. </s> <s id="s.000147">Affictum <lb></lb>nihil fuit R. P. inter vrgendum incommoda; quæ ſi variata <lb></lb>interdum ſint, in cauſſa fuit variatio principiorum, quibus <lb></lb>ille eſt vſus. </s> <s id="s.000148">Nihil iteratò demonſtrat: verum aut ex falſis <lb></lb>concludit; aut in<emph.end type="italics"></emph.end> <emph type="italics"></emph>Diallellum incidit, circulum-ve, vt aiunt, <lb></lb>committit; aut prætereà inuoluit ſe multiplici contradictione. <lb></lb></s> <s id="s.000149">Quæſtio ne que eſt, neque fuit, an ostenderit (quod fuit conceſ<lb></lb>ſum) non poſſe partem spatij ſecundam decurri dimidio tem-<emph.end type="italics"></emph.end><pb xlink:href="028/01/020.jpg"></pb><emph type="italics"></emph>poris, quo primam, tertiam triente, &c. </s> <s id="s.000150">ſed an oſtenderit ad<lb></lb>uerſus ſeipſum; vt pote ex cuius principio, poſitioneve illud <lb></lb>ſequatur. </s> <s id="s.000151">Nequicquam conatur capita abſurda ſibi obiecta <lb></lb>retorquere; quaſi ſit perinde ſeu ſpatium, ſeu tempus cum <lb></lb>velocitate conferat; & ad hominem cum argumentatur, in <lb></lb>limine ipſo aberrat, dici vt putà id ſupponens, quod minimè <lb></lb>dicitur, & tempus cum velocitate ſecus conferri, quàm con<lb></lb>fertur. </s> <s id="s.000152">Tota gloriatio conſequens nihil habet, quod inuidea<lb></lb>tur; & dum ait impugnationem ſui ratiocinij, non poſſe, vt <lb></lb>inanem, ac vanam, inuenire plauſum, niſi apud minùs peritos; <lb></lb>ſatis eſt prouocare illum vt proferat vel vnicum, cui ſuam <lb></lb>ſententiam perſuadeat, peritum.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000153">157. in 181. </s> </p> <p type="main"> <s id="s.000154">ART. XXXIV. XXXV. XXXVI. XXXVII. <lb></lb>XXXVIII. </s> <s id="s.000155">De Tempore, quo R.P. colligit <lb></lb>ſingulas parteis decurſum iri. </s> </p> <p type="main"> <s id="s.000156"><emph type="italics"></emph>Non alia ratione probauit R. P. velocitatem per ſecun<lb></lb>dam partem eſſe duplam velocitatis per dimidium inferius pri<lb></lb>mæ, quàm quia ſpatium, duplum eſt: neque hanc conſequutio<lb></lb>nem vllo modo probauit; ſed ex eo ſolùm ſuppoſuit, quod ve<lb></lb>locitates ſicut spatia ſint, quæ est iterata principij petitio: cùm <lb></lb>hoc ipſum ſit, quod controuertitur, neque vllatenus inueniatur <lb></lb>oſtenſum; niſi ex falſo illo circa Bilancem experimento. </s> <s id="s.000157">Ex <lb></lb>varijs obiectionibus vna est delecta, cui reſponderetur, propter <lb></lb>errorem calami, quo in immenſa, importunaque literarum <lb></lb>farragine litera vna irrepſit pro alia. </s> <s id="s.000158">Beatus eſt R.<emph.end type="italics"></emph.end> P. <emph type="italics"></emph>cui <lb></lb>Author eſſe non videatur ingreſſus in controuerſiæ pene tralia, <lb></lb>quique eum æquè à dictis ſuis, atque à natura penitiùs inspi<lb></lb>ciunda arce at. </s> <s id="s.000159">Tempus minutorum ſex attributum primæ <emph.end type="italics"></emph.end><pb xlink:href="028/01/021.jpg"></pb><emph type="italics"></emph>parti, non ab Authore fuit delectum, ſed <expan abbr="ſuppeditatũ">ſuppeditatum</expan> à R. P. <lb></lb>qui tametſi alicubi non probet ex ijs ſex minutis quatuor priori <lb></lb>dimidio, & duo poſteriori attribui: id tamen tum ex varijs <lb></lb>eius principijs deducitur: tum recipit Author deducturum ſe <lb></lb>eadem, & plura incommoda, ex quacumque alia diſtributione <lb></lb>eius numeri, aut alterius à R. P. facienda: ſi modò ſemper <lb></lb>velocitates habere ſe vt spatia ſupponat.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000160">181. in 191. </s> </p> <p type="main"> <s id="s.000161">ART. XXXIX. XL. XLI. XLII. <lb></lb></s> <s id="s.000162">De Ratione continuò dupla, qua ſpatia de<lb></lb>curri temporibus æqualibus R. P. contendit. </s> </p> <p type="main"> <s id="s.000163"><emph type="italics"></emph>Mirum, velle adhûc R. P. incipere acceleratum motum <lb></lb>à primæ partis medio, non ab ipſo eius principio; & maximè <lb></lb>quidem, cùm aliunde velit velocitates eſſe vt spatia, spatiive <lb></lb>parteis, quarum vna ſit tota prima, non dimidium primæ: ac <lb></lb>inſignes prætereà ſuboriantur difficultates ex eo, quòd dum <lb></lb>ad obiecta de ſubdiuiſione prioris dimidij in alia, aliaque dimi<lb></lb>dia reſpondet, standum ait alicubi, quòd diuiſio eſſe in Phy<lb></lb>ſicas parteis infinita non valeat, & ibi tamen standum, vbi <lb></lb>tot partes adhûc ſuperſunt, vt ex ijs ratio accelerati motus <lb></lb>perfectè intelligatur. </s> <s id="s.000164">Quippe cùm inter cætera aſſumpto <lb></lb>caſu ex Luna, Sole, aut Firmamento, & aſſumpta particula <lb></lb>prima Phyſicè diuidua, in qua reperiri debeant dimidium <lb></lb>inferius, ac in ipſo triens, quadrans, & tot fragmenta cætera, <lb></lb>quot ſunt partes ipſi primæ æquales in toto illo ſpatio, quotque <lb></lb>etiam diſtingui poßunt in ſuperiore dimidio; incredibilis ſit <lb></lb>partium numerus, per quas in priore dimidio contentas opor<lb></lb>teat motum peragi, priuſquam incipiat accelerari; & in qui<lb></lb>bus tamen conſiſtendum ſit, quòd diuiſio vlteriùs fieri in duo<emph.end type="italics"></emph.end><pb xlink:href="028/01/022.jpg"></pb><emph type="italics"></emph>dimidia non valeat, ne ratio motus accelerati non perfectè in<lb></lb>telligatur. </s> <s id="s.000165">Quæſtio heic iterùm non eſt, an velocitas per <lb></lb>ſecundam partem ſit præcisè dupla velocitatis per primam: ſed <lb></lb>an id ſequatur (vt & abſurda quædam alia) ex R. P. prin<lb></lb>cipijs. </s> <s id="s.000166">Refugit R. P. prouocationem ad calculos, nec incom<lb></lb>moda clariùs pateant, ac illud speciatim, quod obiectum eſt <lb></lb>ex triente, & quadrante non componi integrum: neque item <lb></lb>ex partibus quinta, ſexta, ſeptima, octaua. </s> <s id="s.000167">Irrito cona<lb></lb>mine rationem duplam, vt ſolam congruam excuſare adniti<lb></lb>tur, eò quòd ipſa quoque ſeipſam euertat, quoties tempora aſ<lb></lb>ſumuntur maiora, vel minora dato, quæ ſint ipſa quoque inter <lb></lb>ſe æqualia: ſiquidem ea quoque deberent in eadem ratione <lb></lb>respondere spatijs: quod tamen non fit: vt in allato à R. P. <lb></lb>exemplo de caſu globi ex Luna monſtratur.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000168">191. in 208. </s> </p> <p type="main"> <s id="s.000169">AD ART. XLIII. XLIV. </s> <s id="s.000170">De Tempore, <lb></lb>quo globum ferreum caſurum ex Luna in <lb></lb>Terram contendit. </s> </p> <p type="main"> <s id="s.000171"><emph type="italics"></emph>Nihil eſſe heic videtur addendum ad ea, quæ obiecta ſunt <lb></lb>cùm R. P. fateatur non poſſe illam rapiditatem, quam priùs <lb></lb>aſſeruerat, inſanam eſſe adeò, vt globus id ſpatium minutis <lb></lb>non omninô duobus percurrat: tametſi lenire rem ſtudet, dum <lb></lb>naturam quidem id exigere, ſed medij tamen conditionem <lb></lb>obstare ait.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000172">208. in 209. </s> </p> <p type="main"> <s id="s.000173">AD ART. XLV. XLVI. XLVII. </s> <s id="s.000174">De <lb></lb>quodam lapſu emendando circa cauſſam Phy<lb></lb>ſicam accelerati grauium motus. </s> </p> <p type="main"> <s id="s.000175"><emph type="italics"></emph>Quod R. P. in Vindicijs ad Artic. XL. de Phyſica <emph.end type="italics"></emph.end><pb xlink:href="028/01/023.jpg"></pb><emph type="italics"></emph>cauſa accelerationis diſſerüerit, docendo ſolam grauitatem <lb></lb>eſſe cauſſam initij motus, & ſolùm medium, putà aërem eſſe <lb></lb>cauſſam accelerationis, quatenus à fronte reſiliens, & à tergo <lb></lb>clandem, graue vrget; cùm alioquin ſola grauitate agente, ſi<lb></lb>bique ſimili manente, vt in vacuo, deſcenſus foret vniformis, <lb></lb>ſimiliſque ſui perſeueraturus: idcircò anſa & accepta, & in <lb></lb>hunc locum dimiſſa eſt adiiciendi quidpiam de Phyſica cauſſa. <lb></lb></s> <s id="s.000176">Nam primùm quidem paulò fuſiùs deducitur lapſus indicatus <lb></lb>ad calcem ſuperioris Epistolæ: declarando videlicet, quo pro<lb></lb>greſſu tentatum fuiſſet in Epiſtolis<emph.end type="italics"></emph.end> de Motu impreſſo à <lb></lb>motore tranſlato <emph type="italics"></emph>cauſſam dicere, quamobrem grauia acce<lb></lb>lerentur iuxta progreßionem numerorum imparium ab vnita<lb></lb>te incœptorum; & quemadmodum talis cauſſa fuiſſet agnita <lb></lb>tum primo momento ſola attractrix Terræ vis, quæ imprime<lb></lb>ret ſingularem ictum: tum ſecundo, & reliquis tam eadem <lb></lb>attractrix, quàm aër à tergo ſuccedens, inſtanſque, adeò vt <lb></lb>quolibet momento duo quaſi ictus imprimerentur: ſicque & <lb></lb>primo momento vnus acquireretur velocitatis gradus, quo ſu<lb></lb>peraretur vnum ſpatium: ſequente autem quolibet ſuper-ad<lb></lb>derentur duo, eſſentque proinde tres, quinque, ſeptem, &c. <lb></lb></s> <s id="s.000177">quibus spatia totidem conſequenter ſuperarentur: vnde & <lb></lb>conſentaneum foret velocitates eſſe, vt spatia, quæ proinde ſi<lb></lb>mul repræſentari deberent per illas triangulorum areas: quod <lb></lb>animaduerſum eſt repugnare. </s> <s id="s.000178">Deinde verò oſtenditur, <lb></lb>quamobrem cùm cauſſa vnica ſufficiat, iuxta antè expoſita <lb></lb>(ſupponitur autem videri non eſſe ipſam aliam, quàm ipſam <lb></lb>vim Terræ tractricem) oſtenditur, inquam, vtramque à<emph.end type="italics"></emph.end><lb></lb>R. P. <emph type="italics"></emph>aßignatam videri eſſe reiiciendam, quatenus medium, <lb></lb>putà aër, ad accelerationem nihil confert, quin-etiam potiùs <emph.end type="italics"></emph.end><pb xlink:href="028/01/024.jpg"></pb><emph type="italics"></emph>officit, nec quantum obeſt, tantum iuuat, ac longè eſt adeò, vt <lb></lb>ſolus accelerationis ſit cauſſa: grauitas verò, ſeu qualitas graui <lb></lb>inſita, & ab attractione diſtincta, nulla eſt: neque proinde po<lb></lb>teſt motum ſeu in ſpatio vacuo, ſeu in aëre, (vt ſi ſolus aër in <lb></lb>vniuerſo eſſet) præſtare.<emph.end type="italics"></emph.end> A p 209. in 220. </s> </p> <p type="main"> <s id="s.000179">AD ART. XLVIII. </s> <s id="s.000180">De Reſponſionis <lb></lb>Concluſione. </s> </p> <p type="main"> <s id="s.000181"><emph type="italics"></emph>Licitum fuit amicitiæ (ſed ſeruata tamen illi reuerentiâ) <lb></lb>anteponere veritatem. </s> <s id="s.000182">Fuit in<emph.end type="italics"></emph.end> R.P. <emph type="italics"></emph>vt quaſcumque vellet, duce<lb></lb>ret lituras, aut etiam rem totam ſupprimi iuberet. </s> <s id="s.000183">Non capitur <lb></lb>quamobrem cenſeat ſe veritatem iam illuſtratam, & ab er<lb></lb>rore vindicatam exhibere: ac ſperet tamen, vt ex correcto <lb></lb>falſo ſuo Experimento veritas deinceps certiùs inueniatur. </s> <s id="s.000184">Ipſe <lb></lb>fuit<emph.end type="italics"></emph.end> R.P. <emph type="italics"></emph>qui Authori alioquin ignotus, prouocauit prior; & <lb></lb>cui tamen nihil aut reſponſum, aut oppoſitum ſaltem, fuiſſet, <lb></lb>ſi is fuiſſet creditus, qui ipſa rei nouitate, quod iam ait, per<lb></lb>celleretur, tanquam nemine alio hactenus inuento, qui in eius <lb></lb>aſſertionibus, ac decretis pugnam aliquam, contrarietatemque <lb></lb>aut inuenißet, aut obiecißet. </s> <s id="s.000185">Quare & eſſe ſecurus poteſt <lb></lb>iri deinceps nihil inquiſitum in ea, quæ ſe dicit habere <lb></lb>obſcuriora, incertioraque; fore autem, vt ſolitum affectum, <lb></lb>venerationemque ſemper experiatur.<emph.end type="italics"></emph.end><pb xlink:href="028/01/025.jpg"></pb></s> </p> <p type="main"> <s id="s.000186"><emph type="center"></emph>EPISTOLÆ TERTIÆ.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000187">ART. I. </s> <s id="s.000188">Scribendi Occaſio </s> </p> <p type="main"> <s id="s.000189"><emph type="italics"></emph>De hac iam dictum. </s> <s id="s.000190">Notandum ſolùm, Epistolas<emph.end type="italics"></emph.end> de <lb></lb>Motu impreſſo à motore tranſlato, <emph type="italics"></emph>pro quibus hac fuit <lb></lb>velut Apologia, ea occaſione fuiſſe conſcriptas, quòd fides <lb></lb>ægrè habita fuiſſet Experimentis ab Authore factis, adſtruen<lb></lb>do illi Theoremati,<emph.end type="italics"></emph.end> Si id corpus, cui inſiſtimus, trans<lb></lb>feratur, motus omneis noſtros, rerumque à nobis mo<lb></lb>bilium, perinde fieri, apparereque, ac ſi illud quieſceret. <lb></lb><emph type="italics"></emph>Ea autem fuerant præ cæteris, Quòd naui velocißimè abducta, <lb></lb>perinde atque quieſcente, proiectus ſursùm lapis ſecundum <lb></lb>mali longitudinem, tueretur ſemper tam aſcendendo, quàm <lb></lb>exſcendendo eandem a malo diſtantiam; & dimiſſus è carche<lb></lb>ſio ad pternam, ita caderet, vt neque ex parte puppis deſere<lb></lb>retur, neque ex parte proræ attingeretur à malo. </s> <s id="s.000191">Quòd pi<lb></lb>la ex prora in puppim, ex puppi in proram proiecta, pari im<lb></lb>petu ferri appareret, parque ſpatium conficeret; & neque tar<lb></lb>diùs perueniret ad colluſorem, tametſi aufugientem, qui ad <lb></lb>proram: neque citiùs ad alium, tametſi occurrentem, qui ad <lb></lb>puppim, donec volaret per aërem. </s> <s id="s.000192">Quòd è curru, aut equo <lb></lb>citißimè abrepto, perinde ac quieſcente, proiectæ ſursùm res in <lb></lb>ipſam manum reciderent: dimiſſæ cadere apparerent ſecun<lb></lb>dum perpendiculum; emiſſæ prorsùm, retrorſúmque, nec pro<lb></lb>piùs, nec longiùs caderent in terram. </s> <s id="s.000193">Quòd dimiſſa pila <lb></lb>ab incedente, currenteve per complanatum locum, antrorsùm <lb></lb>ſemper procurreret; pari vi antrorsùm, retrorſúmque proie<lb></lb>cta, pariabeſſet, dum à motu ceſſaret, à proiectore diſtantia; & <emph.end type="italics"></emph.end><pb xlink:href="028/01/026.jpg"></pb><emph type="italics"></emph>proiecta ſpeciatim retrorsùm, nunc aliquantúm excurreret, <lb></lb>nunc ad perpendiculum caderet, nunc proiectorem etiam ſeque<lb></lb>retur; prout adactio manus retrorsúm eſſet velocior, æquè ve<lb></lb>lox, aut minùs velox, quàm corporis prorsùm. </s> <s id="s.000194">Jtaque horum <lb></lb>aliorumque Experimentorum explicandæ caußæ deſtinata fue<lb></lb>rat Epiſtola Prior; ac fuerant ideò variæ de Motu attingendæ <lb></lb>difficultates. </s> <s id="s.000195">Fuerat & Poſterior speciatim conſcripta decla<lb></lb>randæ inanitati rationis illius, quæ aduerſus Aſſertores motus <lb></lb>Telluris peti ſoleret ex eo, quòd ſagitta ſursùm euibrata è <lb></lb>puppi, dum nauis moueretur, non in puppim recideret, ſed in <lb></lb>aquam à tergo puppis, quæ interim ſubducta foret: ac fuerat <lb></lb>conſequenter oſtenſa imbecillitas aliarum rationum complu<lb></lb>rium, quæ ſolent ijſdem obiici. </s> <s id="s.000196">Præstita, inquam, hæc fue<lb></lb>rant; cùm R. P. </s> <s id="s.000197">Epiſtolis viſis, ea ex vtraque impugnauit, <lb></lb>quæ potißimùm diſplicuerunt.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000198">227. in 228. </s> </p> <p type="main"> <s id="s.000199">ART. II. III. IIII. </s> <s id="s.000200">Nondum obſeruatum, <lb></lb>qui Galileo obiicitur, Paralogiſmum: &, Neu<lb></lb>tram duarum virium à Motore tranſlato im<lb></lb>preſſarum imminui ab alterutra. </s> </p> <p type="main"> <s id="s.000201"><emph type="italics"></emph>Qualem deinceps Paralogiſmum R. P. detexerit, ſatis <lb></lb>est, ſuperque in Epiſtolis ſuperioribus adnotatum. </s> <s id="s.000202">Quod ſu<lb></lb>perest: cùm mota, v. c. naui, lapis ex ea proiicitur ſursùm; is <lb></lb>apparet quidem tam proiectori, quàm omnibus, qui in naui <lb></lb>ſunt, aſcendere, deſcenderéque ſecundum perpendiculum: ſed <lb></lb>reuerâ tamen aſcendit, deſcenditque obliquè (vti & apparet <lb></lb>quieſcentibus in littore) deſcribit nempe lineam curuam, quam <lb></lb>dicunt parabolicam: cauſſaque eſt, quia manus proiiciens vt<lb></lb>cumque ſursùm moueri appareat, reuerâ tamen mouetur obli<lb></lb>què, deflexa nempe à motu nauis, qui illam, dum attollitur,<emph.end type="italics"></emph.end><pb xlink:href="028/01/027.jpg"></pb><emph type="italics"></emph>abducit vnà cum corpore ipſius proiectoris in latus, ſiue ſecun<lb></lb>dum horizontem. </s> <s id="s.000203">Et quoniam Author dixerat,<emph.end type="italics"></emph.end> Vim im<lb></lb>pellentem mobile ſursùm, non modò non deſtrui, ſed <lb></lb>ne vlla quidem ratione imminui à vi depellente in la<lb></lb>tus (<emph type="italics"></emph>quippe lapis ille neque minùs peruenit aliùm, quàm ſi <lb></lb>pari vi, naui quieſcente, proiiceretur à manu: vti neque mi<lb></lb>nùs in latus, quàm ſi immota manu veheretur ſolo motu nauis) <lb></lb>Idcircò R. P. iſtud improbans, obiicit, quod eſſe apud peritos <lb></lb>Effatum ait,<emph.end type="italics"></emph.end> Mobile quodcumque duobus motibus in <lb></lb>diuerſas parteis actis, tantò ſegniùs deferri in vnum <lb></lb>terminum, quantò fortiùs in alterum tendit. <emph type="italics"></emph>Sed cùm <lb></lb>hoc eſſe poßit verum, donec mobili iam ſeparato à motore ſu<lb></lb>peruenit vis, quæ ipſum deflectat: falſum eſt tamen, ſi nihil <lb></lb>noui à proiectore vſque interueniat, in quo & vis ipſius pro<lb></lb>pria, & vis corporis ipſum transferentis in vnam coïerint, quæ <lb></lb>tantùm ſit alterutrâ fortior, quantùm altera fortis eſt; vt in <lb></lb>exemplo allato conſtat, in quo quicquid eſt motus ſurſum, à ma<lb></lb>nu est; quicquid motus prorsùm, à naui; & quod deeſt virtuti <lb></lb>manus propriæ ad proiiciendum non minus altum ſecundum li<lb></lb>neam curuam, quàm ſecundum rectam, ſuppletur à vi tranſ<lb></lb>latitia nauis; vti & quod deest naui ad adigendum non mi<lb></lb>nus prorſum ſecundum curua, quàm ſecundum rectam, <lb></lb>ſuppletur à vi proiectitia manus. </s> <s id="s.000204">Habentur & alia de Ex<lb></lb>perimentis.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000205">228. in 235. </s> </p> <p type="main"> <s id="s.000206">ART. V. VI. VII. </s> <s id="s.000207">Poſſe varias Sectas <lb></lb>veritatis ſtudio tentari: ac, Poſſe animalis inceſ<lb></lb>ſum præ ſaltatione; & globi volutionem præ <lb></lb>adactione, dici naturalem. </s> </p> <p type="main"> <s id="s.000208"><emph type="italics"></emph>Quòd Author explicando cauſſas commemoratorum <expan abbr="Ex-perimentorũ">Ex<lb></lb>perimentorum</expan>, ſequutus fuerit alia quædam, quàm Ariſtotelea,<emph.end type="italics"></emph.end><pb xlink:href="028/01/028.jpg"></pb><emph type="italics"></emph>& vulgaria principia: id R. P. reprehendit, quaſi ſit viris <lb></lb>eruditis, pijſque minus placiturum: verùm, ſalua modò maneat <lb></lb>pietas, nihil eſt, quod vetet philoſophari liberè, nullique Sectæ <lb></lb>addictum eſſe Displicet illi conſequenter dici inceſſum ani<lb></lb>malis præ ſaltatione naturalem: ſed non apparet quid ſit in<lb></lb>congruum, quatenus motus naturalis notio eſt, vt sponte, aut <lb></lb>ſine repugnantia fiat; violenti, vt præter naturam, ſeu cum <lb></lb>aliqua repugnantia. </s> <s id="s.000209">Displicet & globi volutionem ſupræ <lb></lb>planum dici naturalem præ adactione eiuſdem per aërem: ſed <lb></lb>conſtat ſatis globum eſſe ſuapte natura comparatum, vt volua<lb></lb>tur potiùs ſupra planum (quod niſi aliunde deficeret, euaderet <lb></lb>motus vt æquabilis, ſic perpetuus) quàm vt per aërem adiga<lb></lb>tur (per quem aliunde inæquabiliter, & motu ſtatim finiendo <lb></lb>trans fertur.) Vt prætereatur eſſe hæc omnia Ariſtoteli conſona, <lb></lb>quem coryphæum <expan abbr="eruditorũ">eruditorum</expan> intelligit. </s> <s id="s.000210">R.P.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000211">235, in 240. </s> </p> <p type="main"> <s id="s.000212">ART. VIII. IX. X. </s> <s id="s.000213">Incredibilem fore <lb></lb>motus corporum decidentium ſegnitiem, ſi vt <lb></lb>incipit, ita pergeret; &, Non ſolùm acceleratio<lb></lb>nem, ſed ipſum quoque initium motus eſſe à <lb></lb>principio externo. </s> </p> <p type="main"> <s id="s.000214"><emph type="italics"></emph>Displicet rursus<emph.end type="italics"></emph.end> R. P. <emph type="italics"></emph>cenſeri caſum lapidis violentum <lb></lb>potiùs, quàm naturalem: nam quamuis accelerationem eſſe <lb></lb>violentam non deneget: ob deſcenſum tamen, ſeu ſimplicem <lb></lb>motum, cui illa ſuperuenit, contendit eſſe potius dicendum ca<lb></lb>ſum lapidis naturalem. </s> <s id="s.000215">Sed <expan abbr="primũ">primum</expan>, quia quicquid in hoc caſus <lb></lb>motu ſenſibile eſt, ex acceleratione eſt, ac ne millies quidem <lb></lb>milleſima eius pars ad ſimplicem motum, deſcenſumve ſpectat: <lb></lb>conſtat, ſi à potiore parte denominatio facienda ſit, dicendum<emph.end type="italics"></emph.end><pb xlink:href="028/01/029.jpg"></pb><emph type="italics"></emph>potius eſſe caſum ab acceleratione violentum, quàm à ſimplici <lb></lb>motu naturalem. </s> <s id="s.000216">Quàm parùm autem cenſendum ſit, quod <lb></lb>ex ſimplici motu eſt, ex eo probatur, quòd ſi qualis incipit mo<lb></lb>tus quo momento primo eſt adhûc ab acceleratione liber, talis <lb></lb>perſeueraret per duarum <expan abbr="orgyiarũ">orgyiarum</expan> altitudinem; ille, aſſumpto <lb></lb>pro primo momento, vno minuto ex ijs, quæ decima vocant, non<lb></lb>dum eſſet planè peractus poſt annos<emph.end type="italics"></emph.end> 5322380: <emph type="italics"></emph>neque adeò lapis, <lb></lb>ſi occœpiſſet illo motu ab vſque initio Mundi cadere, perfeciſſet <lb></lb>iam ſeptimam vnam digiti partem. </s> <s id="s.000217">Deinde, cùm illud vio<lb></lb>lentum dicatur, cuius principium extra eſt; etiam deſcenſus, ſeu <lb></lb>ſimplex motus eſſe comprobatur à principio externo, nempe à <lb></lb>virtute attractrice Terræ (credebatur tunc poſſe quoque aër à <lb></lb>tergo impellere) tum quia lapis ſeu intra vacuum (vbi nihil <lb></lb>cum Mundo, Terráque adeò communicaret, ac perinde illi fo<lb></lb>ret, ſeu eſſet, ſeu non eſſet Mundus) ſeu intra aërem infinitum <lb></lb>(ſi ſolus præter ipſum foret) talem motum nullum haberet: <lb></lb>tum quia quæ res ſunt intenſionis capaces, à qua cauſſa habent <lb></lb>gradus reliquos, ab ea nanciſcuntur & primum; atque adeò, <lb></lb>vti dum calefit aqua, non cæteri gradus ab externo ſunt, pri<lb></lb>mus ab interno principio, ſed omnes ab externo ſunt: ita dum <lb></lb>lapis deorsùm mouetur, non cæteræ motus partes ab externa <lb></lb>cauſſa, & prima ab interna ſunt; verùm ſunt omnes ab ex<lb></lb>terna.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000218">240. in 246. </s> </p> <p type="main"> <s id="s.000219">ART. XI. XII. XIII. XIV. </s> <s id="s.000220">Terram grauia <lb></lb>attrahere; &, Quid illi contingeret, ſi verſus <lb></lb>Lunam dimoueretur? </s> <s id="s.000221">Quid lapidi, ſi intra for<lb></lb>nicem ad centrum Terræ conſtitueretur? </s> </p> <p type="main"> <s id="s.000222"><emph type="italics"></emph>Cùm attrahi grauia à Terra videantur, ob cauſſam iam <lb></lb>expoſitam: Ad illud, quod quærit R. P. quid ipſi Terræ con-<emph.end type="italics"></emph.end><pb xlink:href="028/01/030.jpg"></pb><emph type="italics"></emph>tingeret, ſi verſus Lunam dimoueretur? </s> <s id="s.000223">Dicitur eſſe probabi<lb></lb>le, fore, vt vbicumque Terra conſtitueretur, illeic quieſceret <lb></lb>eo modo, quo corpus eiuſce materiæ, vt aquæ ſub pari mole <lb></lb>æquiponderet, vbicumque in imo, in ſummo, in medio, aut vbi<lb></lb>uis intra aquam ſtatuatur, conſiſtit. </s> <s id="s.000224">Nimirùm, quòd Terra <lb></lb>ſecundum ſi totam neque grauis ſit, neque leuis; & talis affe<lb></lb>ctio partium propria ſit, prout à tota diſtrahuntur: quódque in <lb></lb>Mundo spherico exſiſtente, medium quidem, & extremum <lb></lb>ſit, non item infimum, & ſummum; acta is conditio ſit <lb></lb>Terræ, globorumque Mundi cæterorum propria, propter <lb></lb>eandem partium diſtractionem, & retractionem, quæ ſigillatim <lb></lb>cum speciali cuiuſque centro comparatur. </s> <s id="s.000225">Non probatur etiam <lb></lb>aliunde Terram eſſe in Mundi medio; cùm etiam oppoſitum <lb></lb>arguant excentrici ſiderum motus: neque veriſimile eſt, ſi <lb></lb>Terra abduceretur in verticem Antipodum, vbi ſuper<lb></lb>ficies, cui inſiſtimus, excederet punctum, in quo fuiſſet centrum, <lb></lb>nos ibi hæſuros: aut abreptos vlteriùs, eò auolaturos, ſeu po<lb></lb>tiùs caſuros. </s> <s id="s.000226">Ad aliud, quod quærit, quid eueniret lapidi, ſi <lb></lb>intra cauernam in meditullio Terræ excauatam, oppletamque <lb></lb>aqua, aut aëre constitueretur? </s> <s id="s.000227">Dicitur probabile eſſe, ſi Terra <lb></lb>quidem quaſi magnes ſit, qui ſuis quaſi radijs emißis attrahat <lb></lb>terrena: euenturum, vt lapis ineam cauernæ partem feratur, è <lb></lb>qua radij plures, confertioreſque affluxerint; &, ſi ſupponan<lb></lb>tur ex æquo vndequàque affluere, fore, vtin medio ſuſpenſus <lb></lb>teneatur. </s> <s id="s.000228">Vnde &, quod rogat, cur lapis in puteum dimiſſus <lb></lb>fundum petat, non latera? </s> <s id="s.000229">Cauſſa eſt in promptu, quòd plu<lb></lb>res, denſioreſque radij exparte fundi, ad quam eſt tota Terræ <lb></lb>moles, adueniant, quàm ex parte vlla laterum aduenire <lb></lb>poßint.<emph.end type="italics"></emph.end> A p 247. in 254. </s> </p> <pb xlink:href="028/01/031.jpg"></pb> <p type="main"> <s id="s.000230">ART. XV. XVI. XVII. XVIII. XIX. XX. <lb></lb></s> <s id="s.000231">Et Magnetem ferrum, & Terram grauia trahe<lb></lb>re per inſenſilia organula: &, Cur attractio pro<lb></lb>pe Terram non ſit ſenſibilior, quàm procùl. </s> </p> <p type="main"> <s id="s.000232"><emph type="italics"></emph>Non ridet Author in ſinu, vt R. P. ait, dum Magne<lb></lb>tem non trahere ſine organulis corporeis contendit: neque non <lb></lb>agit ſeriò, dum hamulos, catenulaſque, quatenus patitur imbe<lb></lb>cillitas, fingit. </s> <s id="s.000233">Dum ait R.<emph.end type="italics"></emph.end> P. <emph type="italics"></emph>non alio modo tractionem fie<lb></lb>ri, quàm quòd Magnes, & ferrum ſponte naturæ incitata in <lb></lb>mutuos amplexus accurrant; id eleganter quidem, ſed non ita <lb></lb>vt res vocibus ſubiecta intelligi poßit: quomodo ſcilicet vtrum<lb></lb>uis, ac ſpeciatim ferrum inanime, ac inarticulatum, incitet <lb></lb>ſeipſum, & nullare à Magnete emiſſa, diuinet tamen, quando <lb></lb>eſt propè, & metiatur vireis, ac ſpatium, è quo verſus ipſum <lb></lb>inſiliat. </s> <s id="s.000234">Neque verò dicere poteſt emitti à Magnete quali<lb></lb>tatem quandam, quæ ſit merum accidens: cùm exinde diffi<lb></lb>cultatum inextricabilium ſeges ſubnaſcatur. </s> <s id="s.000235">Quod cauſſatur <lb></lb><expan abbr="autẽ">autem</expan> organula inſenſilia dicta: conſtat ſatis ea ſic dici, quòd nec <lb></lb>videri oculis, nec palpari manibus poßint. </s> <s id="s.000236">Iniuriâ traducit Au<lb></lb>thorem R. P. quaſi proptereà neget poſſe <expan abbr="Deũ">Deum</expan> Magneti talem <lb></lb>qualitatem, qualem deſcribit imprimere: <expan abbr="cũ">cum</expan> quæſtio non ſit, an <lb></lb>à Deo ſit, quicquid Magneti <expan abbr="impreßũ">impreßum</expan> eſt: ſed quale ſit, quod est <lb></lb>impreſſum. </s> <s id="s.000237">Quod obiicit verò, vt ferrum à Magnete fortiùs è <lb></lb>propinquo, quàm, è longinquo trahitur, non ſic obſeruari <lb></lb>trahi à terra lapidem, quatenus magis non ponderat, nec ve<lb></lb>locius initio cadit ad baſin turris, quàm ad fastigium: Patet <lb></lb>cauſſam eſſe, non quòd diſcrimen aliquod non ſit: ſed quòd <lb></lb>euadere ſenſibile non poßit, quouſque lapis ponderetur, inci<lb></lb>piatve cadere ex tanta altitudine, quæ non minorem habeat <emph.end type="italics"></emph.end><pb xlink:href="028/01/032.jpg"></pb><emph type="italics"></emph>rationem ad molem Telluris, quàm intercapedo, qua ferrum <lb></lb>trahitur, ad molem Magnetis.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000238">254. in 267. </s> </p> <p type="main"> <s id="s.000239">ART. XXI. XXII. XXIII. XXIV. XXV. <lb></lb></s> <s id="s.000240">Non eſſe Atomorum minùs, quàm Ariſtoteleæ <lb></lb>Materiæ tolerabilem in Religione poſitionem. </s> </p> <p type="main"> <s id="s.000241"><emph type="italics"></emph>Haud iure traducit R. P. ea, quæ de ortu, interitu, alte<lb></lb>ratione, calore, frigore, & cæteris rebus naturalibus iuxtæ <lb></lb>Atomorum ſuppoſitionem dicta ſunt, ad ſtatum ſupernatura<lb></lb>lem: ac præſertim cùm Atomi nihil aliud fint, quàm prima <lb></lb>Materies, quæ ſi prout aſſerta eſt ab Ariſtotele, toleretur, aſ<lb></lb>ſumendo ſolùm, quòd à Deo creata ſit: tolerari ſanè poßint <lb></lb>Atomi, prout aſſeruntur non modò ab<emph.end type="italics"></emph.end> E<emph type="italics"></emph>picuro, aut Democrito, <lb></lb>ſed etiam ab alijs, ac nominatim à Platone (qui cum illiſ-ne <lb></lb>iure exſulet, vt R. P. loquitur, à Regno Philoſophico, conſu<lb></lb>lendi Patres) aſſumendo ſolummodò, fuiſſe illas à Deo creatas. <lb></lb></s> <s id="s.000242">Satis eſſe vult R. P. ſi dicamus halitus calidos, &c. </s> <s id="s.000243">à corpori<lb></lb>bus exhalari: at non illi inepti, qui requirunt prætereà ex qui<lb></lb>buſ nam corpuſculis texantur iſti halitus, vt modum actionis <lb></lb>ipſorum condiſcant: quod & Plato poſt alios fecit, & Demo<lb></lb>critus speciatim ſic eſt exſequutus, vt ideò Platoni ab Ariſtotele <lb></lb>præſeratur, & à Cicerone, Plutarcho, alijſque mirè commen<lb></lb>detur. </s> <s id="s.000244">Exclamat R. P. conclamatum fore de Formis ſub<lb></lb>ſtantialibus, ſi ortus, & interitus nihil aliud ſint, quàm locales <lb></lb>quædam Atomorum motiones: exclamat, inquam, vt videtur, <lb></lb>ob Rationalem animam: cùm tamen, vt generali Effato de for<lb></lb>mis è materia e ducibilibus adhibetur exceptio Rationalis ani<lb></lb>mæ, ſic adhiberi poßit Effato de accidentalibus: ac ipſa Anima <lb></lb>aliunde ſit propriè futura ſubstantia, quatenus ſubſiſtit per<emph.end type="italics"></emph.end><pb xlink:href="028/01/033.jpg"></pb><emph type="italics"></emph>ſe, ſecus ac formæ cæteræ, quæ vnde, aut quomodo habeant <lb></lb>ſuam ſubſtantialem entitatem distinctam à materia, dicere <lb></lb>communis ſententia non poßit. </s> <s id="s.000245">Quærit & quò ſint abitura <lb></lb>ſanctiora Religionis noſtræ myſteria: idque, vt videtur, ob <lb></lb>mysterium auguſtißimum Tranſubſtantiationis: cùm tamen, <lb></lb>vt iuxta Ariſtotelea ſententiam exſiſtentia ſubſtantiæ ſine <lb></lb>accidentibus, aut accidentium ſine ſubſtantia defenditur vir<lb></lb>tute naturæ impoßibilis, ſed poßibilis virtute diuina: eodem <lb></lb>modo, ac ijſdem verbis iuxta Democriticam defendatur.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000246">267. in 276. </s> </p> <p type="main"> <s id="s.000247">ART. XXVI. XXVII. XXVIII. </s> <s id="s.000248">Actum <lb></lb>eſſe de Motu Terræ, proponendo, non aſſe<lb></lb>rendo; &, Ferant ne magis Sacræ literæ Ter<lb></lb>ram in centro, quàm extra centrum circum<lb></lb>uolui. </s> </p> <p type="main"> <s id="s.000249">C<emph type="italics"></emph>ùm ex diſputatis in Priore<emph.end type="italics"></emph.end> de Motu impreſſo à motore <lb></lb>tranſlato <emph type="italics"></emph>Epiſtola, deduci poſſet <expan abbr="nullũ">nullum</expan> eſſe, quod aduerſus mo<lb></lb>tum Telluris petitur vulgò argumentum ex ſagitta ſursùm è <lb></lb>naui emiſſa, neque in nauim recidente; nullum, inquam, prout <lb></lb>ſicuti mota naui, omnes motus ſiue nautarum, ſiue rerum, <lb></lb>quas ipſi mouent, perinde fiunt, apparentque, ac ſi nauis quieſ<lb></lb>ceret, miſſaque adeò ſursùm ſagitta in <expan abbr="eandẽ">eandem</expan> nauis, è qua fuerit <lb></lb>emiſſa, partem recidit: ita ſi Terram verſus ortum moueri <lb></lb>ſuppoſuerimus, omnes motus noſtri, rerumque à nobis mobi<lb></lb>lium, perinde fient, apparebuntque, ac ſi Terra quieſceret. <lb></lb></s> <s id="s.000250">lapisque adeò ſursùm proiectus, in eundem Terræ recidet lo<lb></lb>cum, è quo proiectus fuerit;<emph.end type="italics"></emph.end> S<emph type="italics"></emph>cilicet<emph.end type="italics"></emph.end> T<emph type="italics"></emph>erra transferens proiecto<lb></lb>rem, eiuſque manum, ſuperaddit, intercedente manu, tantum <lb></lb>impetus lapidi, quantum oportet, vt ſuperet mundanum<emph.end type="italics"></emph.end><pb xlink:href="028/01/034.jpg"></pb><emph type="italics"></emph> ſpatium æquale illi, quod ea pars Terræ, è qua facta fuerit <lb></lb>proiectio, interim peruadit; eodem modo, quo nauis transferens <lb></lb>ſuperaddit ſagittæ, intercedente arcu, tantum roboris, quantum <lb></lb>eſt neceſſe, vt ſuperet aëreum ſpatium æquale illi, quod peruadit <lb></lb>interim ea nauis pars, è qua facta emißio: Cùm, inquam, de<lb></lb>duci id poſſet; Author re ipsâ ita deduxit poſteriore Epiſtola, vt <lb></lb>admonuerit quærendam ergo, ad impugnandum Terræ motum, <lb></lb>rationem veriſimiliorem. </s> <s id="s.000251">Et quia poterat responderi alias <lb></lb>iam multas eſſe inuentas: ideò illas, eſſe oſtendit magna ex parte <lb></lb>haud magis firmas. </s> <s id="s.000252">Iam R. P. hoc non fert, ac ſuperiore <lb></lb>ratione euerſa, indignatur fuiſſe cæteras convulſas: quaſi aut <lb></lb>eas expendere præoccupando non licuerit, aut ſit, cur magis, <lb></lb>quàm ſuperior vocari in examen non poßint, nec debeant. </s> <s id="s.000253">Et <lb></lb>traducit quidem Authorem R. P. quaſi aſſeruerit moueri Ter<lb></lb>ram non diurna modò reuolutione circa axem proprium, verùm <lb></lb>etiam annuo motu circa Solem: vnde & ait tolerabilius fuiſſe, <lb></lb>etiam per ſacras Literas, ſi aſſertus fuiſſet diurnus dumtaxat. <lb></lb></s> <s id="s.000254">Attamen, neque aſſerendo, ſed proponendo ſolummodò de mo<lb></lb>tu Terræ actum eſt; neque ea loca Scripturæ ſacræ, quæ aduer<lb></lb>ſus motum Terræ obiiciuntur, comperiuntur minùs aduer<lb></lb>ſus diurnum, quàm aduerſus annuum eſſe comparata; neque <lb></lb>non præclare addit R. P. debere noſtram Philoſophiam fidei <lb></lb>Chriſtianæ eſſe conſonam; ſed ſupereſt noſſe quid ſit diſſonum; <lb></lb>cùm non statim quicquid videtur repugnare Literis ſacris id<lb></lb>circò reuerà repugnat, vt rectè oſtendit D. </s> <s id="s.000255">Auguſtinus ad<lb></lb>uerſus eos, qui dicunt cælum Sphæricum, cùm Scriptura dicat<emph.end type="italics"></emph.end><lb></lb>extenſum, vt pellem. </s> <s id="s.000256">A p. </s> <s id="s.000257">276. in 281. </s> </p> <p type="main"> <s id="s.000258">ART. XXIX. XXX. XXXI. </s> <s id="s.000259">De Con<lb></lb>ſequutionibus ex Terra Planetis interſita <pb xlink:href="028/01/035.jpg"></pb>ductis, déque ignorata Copernicanæ opinionis <lb></lb>improbatione. </s> </p> <p type="main"> <s id="s.000260">O<emph type="italics"></emph>biicit R. P. </s> <s id="s.000261">Si moueri Terram inter Planetas per<lb></lb>ſuaſum ſit, creditum quoque iri ipſam eſſe<emph.end type="italics"></emph.end> P<emph type="italics"></emph>lanetam; & eſſe in <lb></lb>alijs<emph.end type="italics"></emph.end> P<emph type="italics"></emph>lanetis, Stelliſque ſuosincolas; ac iri <expan abbr="vocatũ">vocatum</expan> in ſuſpicio<lb></lb>nem<emph.end type="italics"></emph.end> G<emph type="italics"></emph>eneſin,<emph.end type="italics"></emph.end> <emph type="italics"></emph>Incarnationem, Euangelium, fidem<emph.end type="italics"></emph.end> C<emph type="italics"></emph>hriſtia<lb></lb>nam, quæ docet Aſtra non ad hominum, aliarumve rerum ha<lb></lb>bitationem eſſe facta, ſed vt illuminent, fœcundentque Terram. <lb></lb></s> <s id="s.000262">Verùm legitimas non eſſe huiuſmodi conſequutiones, declara<lb></lb>tur, Tum ex eo, quòd oſtenditur pari ratione deduci eaſdem ex <lb></lb>placitis alijs, quæ à viris pijs, eruditiſque defenduntur (cuiuſ<lb></lb>modi ſunt illa de rotunditate Terræ; de Luna eclipſin patiente <lb></lb>ob Terram, vt Terra patitur ob Lunam; déque ipſius ſuperfi<lb></lb>cie montibus, & conuallibus, terrenæ inſtar interstincta: de <lb></lb>Terræ exilitate comparatè ad Stellas; aéque Luna adhûc lon<lb></lb>gè exiliore, quæ præ illis tamen habetur in magnis luminari<lb></lb>bus, atque ita de cæteris) Tum ex eò, quòd oſtenditur, quàm <lb></lb>malè cohæreant cum Antecedente, ex quo deducuntur. </s> <s id="s.000263">Quod <lb></lb>autem<emph.end type="italics"></emph.end> R. P. <emph type="italics"></emph>opinionem de motu Terræ fuiſſe Eccleſiæ ſuspe<lb></lb>ctam ait à<emph.end type="italics"></emph.end> C<emph type="italics"></emph>opernici vſque tempore; id Authori eſt incomper<lb></lb>tum, & quod iam demùm damnatam ait decreto Pontiſicio, <lb></lb>profitetur Author ſe vel ſola fama, ac non expectata promul<lb></lb>gatione legitima, ad id complectendum induci.<emph.end type="italics"></emph.end> A p. </s> <s id="s.000264">281 in 288. </s> </p> <p type="main"> <s id="s.000265">ART. XXXII. XXXIII. XXXIV. </s> <s id="s.000266">Sit<lb></lb>ne abſurdum reputare Orbem magnum (ſeu <lb></lb>cœlum Solis) eſſe quaſi punctum comparatum <lb></lb>ad Firmamentum; & Solem quaſi vnam Fixa-<pb xlink:href="028/01/036.jpg"></pb>rum, Fixas quaſi Soleis totidem habere. </s> </p> <p type="main"> <s id="s.000267"><emph type="italics"></emph>Si Terra moueatur circa<emph.end type="italics"></emph.end> S<emph type="italics"></emph>olem, tantum deſcribet circulum, <lb></lb>quantum Sol motus circa Terram; atque adeò quantum cælum <lb></lb>Solis eſt, tantum erit & cælum<emph.end type="italics"></emph.end> T<emph type="italics"></emph>erræ, quod dieunt potiùs<emph.end type="italics"></emph.end> O<emph type="italics"></emph>r<lb></lb>bem magnum.<emph.end type="italics"></emph.end> I<emph type="italics"></emph>taque R. P. pro abſurdo habet, quòd<emph.end type="italics"></emph.end> C<emph type="italics"></emph>oper<lb></lb>nicani aſſumunt tam immanem eſſe Fixarum à nobis diſtan<lb></lb>tiam, vt ſi<emph.end type="italics"></emph.end> O<emph type="italics"></emph>rbis magnus fingatur in earum regionem tranſla<lb></lb>tus, nobis heic remanentibus, ſit appariturus nobis quaſi pun<lb></lb>ctum: nimirùm ex hoc ſequitur,<emph.end type="italics"></emph.end> S<emph type="italics"></emph>tellas, quæ nobis ſunt qua<lb></lb>ſi puncta, fore hoc orbe non minores. </s> <s id="s.000268">Ac Author quidem <lb></lb>habet diuerſa, quod Stellæ ſunt, & quod apparent, vt dicendum <lb></lb>illicò eſt: interim autem illi reſpondent, cùm ea ſit Fixarum <lb></lb>diſtantia, vt nulla obſeruatio ſit, qua definire illam liceat, & <lb></lb>ab omnibus merè gratis, próque lubitu maior, aut minor aſſu<lb></lb>matur (nemine putà aliam rationem, quàm propriam ſiue opi<lb></lb>nionem, ſiue voluntatem habente) ideò tam poſſe ſe maiorem, <lb></lb>quàm alios minorem eam aſſumere: imò & tantò magis, quantò <lb></lb>exinde fit commendatior tum concinnitas, tum maiestas operum <lb></lb>Dei. </s> <s id="s.000269">Quod verò R. P. abſurdum habet cenſeri Solem, quaſi <lb></lb>vnam quampiam Fixarum, & Fixas eſſe quaſi totidem<emph.end type="italics"></emph.end> S<emph type="italics"></emph>oleis: <lb></lb>iubent illi attendere, vel iuxta ipſam communem ſententiam <lb></lb>(quæ tam propè admouet Fixas) ſi Sol recedat, quantum Fixæ, <lb></lb>Fixæ accedant, quantum<emph.end type="italics"></emph.end> S<emph type="italics"></emph>ol, fore vt<emph.end type="italics"></emph.end> S<emph type="italics"></emph>ol, quaſi vna Fixarum, <lb></lb>& vna Fixarum, quaſi<emph.end type="italics"></emph.end> S<emph type="italics"></emph>ol appareat.<emph.end type="italics"></emph.end> A p 288. in 293. </s> </p> <p type="main"> <s id="s.000270">ART. XXXIV. XXXV. XXXVI. XXXVII. <lb></lb></s> <s id="s.000271">Poſſe Solem è Fixis non minorem, quàm Or<lb></lb>bem magnum apparere: & veros omnium Stel<lb></lb>larum diſcos in vnum compoſitos vix apparen<lb></lb>ti diſco vnius mediocris Stellæ exæquatum iri. </s> </p> <pb xlink:href="028/01/037.jpg"></pb> <p type="main"> <s id="s.000272"><emph type="italics"></emph>Vtin lucernæ flammula inter nocturnas tenebras procùl <lb></lb>viſa diſtinguere licet diſcum apparentem à vero; cùm ille poſ<lb></lb>ſit eſſe pedalis, iſte (hoc eſt flammulæ facies ſecundum diame<lb></lb>trum tranſuerſam) ſemidigitali non maior; ita in<emph.end type="italics"></emph.end> S<emph type="italics"></emph>tellis, quæ <lb></lb>non videntur, niſi per tenebras nocturnas, diſtinguendi haud<lb></lb>dubiè ſunt diſci apparentes à veris. </s> <s id="s.000273">Itaque, ſi apparentes qui<lb></lb>dem<emph.end type="italics"></emph.end> S<emph type="italics"></emph>tellarum<emph.end type="italics"></emph.end> 1022. <emph type="italics"></emph>diſci in vnum quemdam compingerentur, <lb></lb>is triplò maior euaderet, quàm<emph.end type="italics"></emph.end> S<emph type="italics"></emph>olaris vulgò appareat.<emph.end type="italics"></emph.end> S<emph type="italics"></emph>in au<lb></lb>tem pari modo in vnum diſculi veri coaptarentur, is non maior <lb></lb>euaderet, quàm vnius<emph.end type="italics"></emph.end>Siellæ <emph type="italics"></emph>magnitudinis quartæ diſcus. </s> <s id="s.000274">Et <lb></lb>accepto harum<emph.end type="italics"></emph.end> S<emph type="italics"></emph>tellarum dimidio; quaſi non ampliùs (licet re<lb></lb>uerâ ampliùs) ſupra horizontem appareat; diſci quidem appa<lb></lb>rentes conficerent diſcum ad<emph.end type="italics"></emph.end> S<emph type="italics"></emph>olarem, ſeſquialterum; at veri <lb></lb>non <expan abbr="maiorẽ">maiorem</expan> eo, quo apparet vnica magnitudinis quintæ<emph.end type="italics"></emph.end> S<emph type="italics"></emph>tella. <lb></lb></s> <s id="s.000275">Ex quo efficitur, vt mirum non ſit, fi<emph.end type="italics"></emph.end> S<emph type="italics"></emph>tellæ tam parùm per <lb></lb><expan abbr="noctẽ">noctem</expan> colluſtrent, cùm illuſtrent per veros, & non per <expan abbr="apparẽteis">apparenteis</expan> <lb></lb>diſcos. </s> <s id="s.000276">Heinc autem responderi poteſt ad id, quod R.<emph.end type="italics"></emph.end> P. <emph type="italics"></emph>obii<lb></lb>cit de<emph.end type="italics"></emph.end> S<emph type="italics"></emph>ole è Fixis, aut heinc inter Fixas per immenſam illam <lb></lb>diſtantiam spectato; quaſi nimirùm conſtitutus in ipſo<emph.end type="italics"></emph.end> O<emph type="italics"></emph>rbis <lb></lb>magni centro, aut quaſi centrum eius exſiſtens, non poßit tantus <lb></lb>apparere, quantus ipſemet<emph.end type="italics"></emph.end> O<emph type="italics"></emph>rbis eſt.<emph.end type="italics"></emph.end> S<emph type="italics"></emph>cilicet exinde intelligitur, <lb></lb>futurum, vt<emph.end type="italics"></emph.end> S<emph type="italics"></emph>ole, quaſi<emph.end type="italics"></emph.end> S<emph type="italics"></emph>tellula facto, tametſi verus illius diſcus <lb></lb>foret exilißimus, apparens tamen tantus eſſet, qui totum ipſum<emph.end type="italics"></emph.end><lb></lb>Orbem<emph type="italics"></emph> magnum, aut etiam ampliùs, quaſi compleret: quod de<lb></lb>claratur pleniùs exemplo flammulæ per noctem conspectæ.<emph.end type="italics"></emph.end><lb></lb>A p. </s> <s id="s.000277">293. in 301. </s> </p> <p type="main"> <s id="s.000278">ART. XXXVIII. XXXIX. </s> <s id="s.000279">Hùc accom<lb></lb>modari non potuiſſe cauſſam, quæ redditur <lb></lb>vulgò, quare <expan abbr="flãmæ">flammæ</expan> noctu maiores appareant. </s> </p> <pb xlink:href="028/01/038.jpg"></pb> <p type="main"> <s id="s.000280"><emph type="italics"></emph>Quod vulgò dicunt <expan abbr="aẽrem">aerrem</expan>, qui proximè circumſtat flam<lb></lb>mam, ita per parteis halituoſas è flamma procedenteis vehe<lb></lb>menter illuminari, vt ab oculo computetur in vnam flammam <lb></lb>continuam: id tum repugnat (quatenus & nullum inter flam<lb></lb>mam veram, ſpuriamque apparet diſcrimen; &, ſi vera flam<lb></lb>ma occultetur ſola, nulla apparet ſpuria; &, ſi verâ flammâ <lb></lb>præter foramen visâ, aër occultetur, ſpuria nihilominùs appa<lb></lb>ret) tum aliunde accommodari nec Lunæ potest, nec ipſis<emph.end type="italics"></emph.end> S<emph type="italics"></emph>tel<lb></lb>lis, quarum ſpecies noctu magnoperè increſcit. </s> <s id="s.000281">Quamobrem <lb></lb>fuit longè commodiùs repetere cauſſam ex affectione oculi, pu<lb></lb>pillæ nempe dilatatione, & impreßione retinæ facta, donec ocu<lb></lb>lus in tenebris degit. </s> <s id="s.000282">Quippe cauſſa hæc non noſtris modò flam<lb></lb>mis, & tam Lunæ, quàm<emph.end type="italics"></emph.end> S<emph type="italics"></emph>tellis congruit; ſed congruet etiam <lb></lb>ipſi<emph.end type="italics"></emph.end> S<emph type="italics"></emph>oli, ſi in ipſam Fixarum regionem ſupponatur tranſla<lb></lb>tus. </s> <s id="s.000283">Videlicet tunc paradoxum non erit, videri noctu<emph.end type="italics"></emph.end> S<emph type="italics"></emph>olem, <lb></lb>ſeu oculum videntem<emph.end type="italics"></emph.end> S<emph type="italics"></emph>olem verſari in tenebris;<emph.end type="italics"></emph.end> S<emph type="italics"></emph>ole, vt putá, <lb></lb>facto, conspectóque quaſi vna quapiam<emph.end type="italics"></emph.end> S<emph type="italics"></emph>tellarum fixarum.<emph.end type="italics"></emph.end><lb></lb>A p. </s> <s id="s.000284">301. in 306. </s> </p> <p type="main"> <s id="s.000285">ART. XL. XLI. XLII. </s> <s id="s.000286">Qua mente, & qua<lb></lb>tenus ex motu Terræ æſtus Maris deductus; &, <lb></lb>Poſſe exinde explicari varietates, quæ tam per <lb></lb>Æquinoctia, & Solſtitia, quàm per Nouilunia, <lb></lb>& Plenilunia contingunt. </s> </p> <p type="main"> <s id="s.000287"><emph type="italics"></emph>Vt de motu Terræ eſt actum proponendo, non aſſerendo: ſic <lb></lb>& de ipſo Maris æſtu, quatenus eſt viſus cum hac motus Ter<lb></lb>ræ hypotheſi congruere; maximè verò quatenus aqua bis die<lb></lb>tim fluit, ac refluit, vt bis contingit in motu Terræ inæqualitas, <lb></lb>propter commiſtionem diurni, & annui, respectu partis eiuſ<lb></lb>dem Terræ, qua, vt vaſe, contenta aqua, dum inæquali ductu <emph.end type="italics"></emph.end><pb xlink:href="028/01/039.jpg"></pb><emph type="italics"></emph>mouetur, non poteſt non fluere, ac refluere. </s> <s id="s.000288">Quòd porrò ſicut <lb></lb>Iupiter ſuos ſatellites ſibi circumducens, dum interim vnà cum <lb></lb>ipſis motu duodecenni transfertur per<emph.end type="italics"></emph.end> Z<emph type="italics"></emph>odiacum, cenſetur eſſe <lb></lb>vnà cum ipſis totale quodam mobile; ita Terra Lunam ſibi <lb></lb>circumducens, dum interim vnà cum ipſa transfertur motu an<lb></lb>nuo per Zodiacum, vnum aliquod mobile totale cum ipſa cen<lb></lb>ſeatur:<emph.end type="italics"></emph.end> I<emph type="italics"></emph>deò, ſi aliunde ſupponatur<emph.end type="italics"></emph.end> S<emph type="italics"></emph>ol, dum ſibi circumuoluitur, <lb></lb>emittere quoſdam veluti magneticos radios, quibus<emph.end type="italics"></emph.end> P<emph type="italics"></emph>lanetas ſi<lb></lb>bi circumducat, ac ſpeciatim hoc mobile (Terram videlicet cum <lb></lb>Luna) Efficietur, vt quia hoc mobile pendebit à<emph.end type="italics"></emph.end> S<emph type="italics"></emph>ole per <expan abbr="radiũ">radium</expan>, <lb></lb>veluti plumbum à clauo per filum; efficietur, inquam, vt, Quem<lb></lb>admodum plumbum ſegniùs vibratur, ſi infra appendatur <lb></lb><expan abbr="plumbulũ">plumbulum</expan>, quo longius penſile euadat; aut ocyùs, ſi ſupra illige<lb></lb>tur <expan abbr="plumbulũ">plumbulum</expan>, à quo appetente redire celeriùs, reducatur citiùs: <lb></lb>Jta Terra per<emph.end type="italics"></emph.end> P<emph type="italics"></emph>lenilunium moueatur aliquantò pigriùs, quòd <lb></lb>tunc propter Lunam veluti infernè appenſam prolixius euadat <lb></lb>quaſi penſile; & per Nouilunium velociùs, quòd tunc Luna ve<lb></lb>luti ſupernè impendens acceleret nonnihil motum. </s> <s id="s.000289">Quare & <lb></lb>exinde ſuperuenit quædam tam in<emph.end type="italics"></emph.end> P<emph type="italics"></emph>lenilumo, quàm in Noui<lb></lb>lunio inæqualitas, ob <expan abbr="quã">quam</expan> tunc mare fluat, ac refluat, quàm per <lb></lb>quadraturas æſtuoſiùs. </s> <s id="s.000290">Quòd autem prætereà hi fluxus, re<lb></lb>fluxuſque intendantur ipſis Solſtitiorum,<emph.end type="italics"></emph.end> Æ<emph type="italics"></emph>quinoctiorumque <lb></lb>temporibus; cauſſa eſſe poteſt ſuperueniens tertia inæqualitas, <lb></lb>ob prolixiores, breuioreſque diurni motus arcus (parallelos ſem<lb></lb>per æquatori acceptos) per Zodiacum; atque ita quidem, vt cùm <lb></lb>in<emph.end type="italics"></emph.end> Æ<emph type="italics"></emph>quinoctiis motus diurnus per hoſce arcus ſit maximè ad<lb></lb>uerſus motui annuo ſecundum<emph.end type="italics"></emph.end> Z<emph type="italics"></emph>odiacum, efficiatur aliunde, <lb></lb>vt æstus ſint per<emph.end type="italics"></emph.end> Æ<emph type="italics"></emph>quinectia, quam per<emph.end type="italics"></emph.end> S<emph type="italics"></emph>olſtitia vehementiores.<emph.end type="italics"></emph.end><lb></lb>A p. </s> <s id="s.000291">306. in 313. </s> </p> <pb xlink:href="028/01/040.jpg"></pb> <p type="main"> <s id="s.000292"><emph type="center"></emph>ARTICVL. XLIII. XLIV. XLV.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000293">Poſſe & varietates alias ad locorum ſitus; & <lb></lb>acceſſus retardationem, quæ dietim fit, ad mo<lb></lb>tum Lunæ menſtruum, quatenus eſt idem cum <lb></lb>diurno Telluris, referri. </s> </p> <p type="main"> <s id="s.000294"><emph type="italics"></emph>Quæ varietas fluxus in fluminum ripis inæquabilibus ob<lb></lb>ſeruatur, eadem affluxus, & refluxus in litoribus Maris de<lb></lb>prehenditur; ſicque ad varios littorum ſitus referri poſſunt di<lb></lb>uerſitates, quæ mox memoratis generalibus accidentibus ſuper<lb></lb>ueniunt; vt vel exemplo nauiculæ, cui ſimiles inſint inæqualita<lb></lb>tes, intelligi potest. </s> <s id="s.000295">Quòd autem affluxus ad littora fiat <lb></lb>diebus ſingulis vnà propò horà (ſeu quatuor horæ quintis) tar<lb></lb>diùs, ex eo eſſe poteſt, quòd cùm, vt iam dictum, Terra, & Lu<lb></lb>na vnum totale mobile ſint, & Terra ſuo motu diurno ſic Lu<lb></lb>nam circum-rapiat, vt Luna tamen non penitùs, ob diſtantiam, <lb></lb>obſecundando, circulum vnum non abſoluat, niſi intra menſem; <lb></lb>ac die bus proinde ſingulis integra propè hora tardiùs ad meri<lb></lb>dianum perueniat, è quo pridie cum aliqua Terræ parte diſceſ<lb></lb>ſerit, Idcircò affluxus non præcisè redeat, cùm ipſa eadem<emph.end type="italics"></emph.end> T<emph type="italics"></emph>er<lb></lb>ræpars ad meridianum eumdem redit, ſed cùm redit Luna, quæ <lb></lb>est mobilis totalis quaſi complementum. </s> <s id="s.000296">Epistolæ concluſio.<emph.end type="italics"></emph.end><lb></lb>A p. </s> <s id="s.000297">313. in 318. </s> </p> <p type="main"> <s id="s.000298"><emph type="italics"></emph>Errata in his Summulis.<emph.end type="italics"></emph.end> fol. </s> <s id="s.000299"><expan abbr="ẽ">em</expan>, pag. </s> <s id="s.000300">1. l. 17. lege <emph type="italics"></emph>tantumdem.<emph.end type="italics"></emph.end> p 2. l. 16. <lb></lb><emph type="italics"></emph>heixc.<emph.end type="italics"></emph.end> p. </s> <s id="s.000301">6. l. 4. <emph type="italics"></emph>at non.<emph.end type="italics"></emph.end> l. 22 XLVIII. fol. </s> <s id="s.000302">1. p. </s> <s id="s.000303">6. l. 5. <emph type="italics"></emph>ne.<emph.end type="italics"></emph.end> fol <expan abbr="õ">om</expan> p. </s> <s id="s.000304">1 l. 17. <emph type="italics"></emph>conficere.<emph.end type="italics"></emph.end><lb></lb>p. </s> <s id="s.000305">3 l. 22. <emph type="italics"></emph>curuam Omiſſa in textu.<emph.end type="italics"></emph.end> p. </s> <s id="s.000306">293. l. 10. lege <foreign lang="grc">ὑπ' ἀλλοῦ. </foreign></s> <s id="s.000307">242. 13. <lb></lb>octingenties. </s> <s id="s.000308">430. 25. <foreign lang="grc">αὐ <gap></gap>υα<gap></gap>ις. </foreign></s> <s id="s.000309">255. 17. collinees, 256 28. voce non. </s> <s id="s.000310">270. <lb></lb>24. Anſtoteleæ ſententiæ. </s> <s id="s.000311">285, 2 ad hoc. <emph type="italics"></emph>In ipſis Errata.<emph.end type="italics"></emph.end> l. 10. lege 128. 26. </s> </p> <pb pagenum="1" xlink:href="028/01/041.jpg"></pb> <figure id="id.028.01.041.1.jpg" xlink:href="028/01/041/1.jpg"></figure> <p type="main"> <s id="s.000312"><emph type="center"></emph>DE PROPORTIONE, <lb></lb>QVA GRAVIA DECIDENTIA <lb></lb>ACCELERANTVR.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000313"><emph type="center"></emph>EPISTOLA PRIMA.<emph.end type="center"></emph.end><lb></lb> </s> </p> <p type="main"> <s id="s.000314"><emph type="center"></emph><emph type="italics"></emph>ADMODVM REVERENDO, <lb></lb>& religioſißimo, doctißimoque Viro,<emph.end type="italics"></emph.end> P. <lb></lb>PETRO CAZRÆO <emph type="italics"></emph>Societatis<emph.end type="italics"></emph.end> IESV, <lb></lb><emph type="italics"></emph>Metenſis Collegij Rectori ſapientißimo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000315"><emph type="center"></emph>PETRVS GASSENDVS S.<emph.end type="center"></emph.end>PELLEGI, optime Cazræe, quam dig<lb></lb>natus es ad me dare, ac publici iuris ſimul <lb></lb>facere <emph type="italics"></emph>Demonſtrationem Phyſicam,<emph.end type="italics"></emph.end> qua <lb></lb><emph type="italics"></emph>Ratio accelerationis in motu rerum grauium <lb></lb>naturali determinatur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000316"> Agnoui verò imprimis illam ſin<lb></lb>gularem beneuolentiam, qua perrexiſti obſtringere <lb></lb>me, quæque eſt ſanè tota ad tuam bonitatis eximiæ <lb></lb>indolem accepta ferenda. </s> <s id="s.000317">Promptum deinde fuit <lb></lb>meminiſſe eruditæ Epiſtolæ, qua ante duos annos ea <lb></lb>ſignificaſti, quæ in meis illis, <emph type="italics"></emph>de Motu impreſſo à motore <lb></lb>tranſlato,<emph.end type="italics"></emph.end> minimè probares; ac illud inter cætera, quòd <pb pagenum="2" xlink:href="028/01/042.jpg"></pb>ſenſiſſem cum Galileo, <emph type="italics"></emph>Motum naturalem rerum deci<lb></lb>dentium ea ratione accelerari, vt ſuperata ſpatia temporibus <lb></lb>æqualibus, numerorum imparium progreßionem imitarentur.<emph.end type="italics"></emph.end><lb></lb>Commemini etiam, cùm fuiſſem conatus facere ſatis <lb></lb>in cæteris, expetiiſſe me, vt quia neque Paralogiſmum, <lb></lb>quem in Galileo cauſabaris, animaduertiſſem, neque <lb></lb>experientia, aut ratio monſtraſſet quidpiam oppoſi<lb></lb>tum; dignareris ipſe tum mihi fallaciam Galilei rete<lb></lb>gere, tum inuentam illam à te progreſſionem me edo<lb></lb>cere. </s> <s id="s.000318">Voluiſti id porrò nunc <expan abbr="demũ">demum</expan> cumulatiſſimè præ<lb></lb>ſtare, ac me vel ex eo deuinxiſti, quòd euulgare Medi<lb></lb>tationes de motu præclaras aggreſſus, hanc eſſe pri<lb></lb>mam volueris, quam non creditori profectò, qualem <lb></lb>me habes, perſolueres; ſed debitori, qualem me potiùs <lb></lb>ingenuè fateor, oppignerares. </s> <s id="s.000319">Heinc eſt, cur licet ni<lb></lb>hil in me ſit, quod quaſi par pari rependam; adnitar <lb></lb>tamen, quantum licet, teſtari gratitudinem, eandem <lb></lb>tecum rem meditatus, ac eas dubitandi rationes, quæ <lb></lb>mihi ſeſe inter legendum vltrò obtulere, reponens. <lb></lb></s> <s id="s.000320">Quippe lógè abſum abeo, quem tu me eſſe pro tua illa <lb></lb>rara comitate voluiſti, dum decreuiſti <expan abbr="Iudicẽ">Iudicem</expan> tuæ hu<lb></lb>ius Demonſtrationis. </s> <s id="s.000321">Is nimirùm ſum, qui aliud <lb></lb>nihil valeam, quàm difficultates quaſdam excitare, ac <lb></lb>tibimet proponere, qui in hiſce rebus & diutiſſimè, & <lb></lb>curioſiſſimè verſatus, ipſas explanare facillimè poſſis. <lb></lb></s> <s id="s.000322">Interim autem non ſubuereor, ne tametſi videarabs te <lb></lb>diſſentire, neque illicò manus dare, tu idcircò mihi ſu<lb></lb>cenſeas: cùm ea ſis humanitate, eo in veritatem affe<lb></lb>ctu, vt non poſſis in me candorem, quem ego in te <lb></lb>probem, improbare. </s> </p> <pb pagenum="3" xlink:href="028/01/043.jpg"></pb> <p type="main"> <s id="s.000323"><emph type="center"></emph><emph type="italics"></emph>Status controuerſiæ.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000324">II. </s> <s id="s.000325">Principio verò, vt experiar, num rem ſatis ca<lb></lb>piam, de qua agitur; Quæri, ecce, mihi videtur, <emph type="italics"></emph>Qua <lb></lb>ratione, ſeu proportione celeritas rerum decidentium increſcæt?<emph.end type="italics"></emph.end><lb></lb>Videlicet ſupponimusrem nimis-quàm notam, <expan abbr="motũ">motum</expan> <lb></lb><expan abbr="rerũ">rerum</expan> grauium ex alto cadentium eſſe velociorem in fi<lb></lb>ne, quàm in medio; & in medio, quàm in ipſo princi<lb></lb>pio. </s> <s id="s.000326">Supponimus rurſus hanc velocitatem ita conti<lb></lb>nuò increſcere, vt ab ipſo vſque inſtanti, quo mobile à <lb></lb>quiete recedit, illius motus magis, magiſque continen<lb></lb>ter acceleretur; ſeu incrementa velocitatis plura ſem<lb></lb>per, ac plura vniformiter præacquiſitis ſuper-addan<lb></lb>tur. </s> <s id="s.000327">Supponimus tertiò iſthæc incrementa compa<lb></lb>rari poſſe aut cum partibus temporis, quæ vno tenore <lb></lb>ſuccedunt, aut cum partibus ſpatij, quæ plures, plureſ<lb></lb>que continenter per curruntur. </s> <s id="s.000328">Supponimus quartò <lb></lb>poſſe accipi, ſiue deſignari primum quoddam tem<lb></lb>pus, vt minutum horæ ſecundùm, ſiue interuallum in<lb></lb>ter duas pulſationes arteriæ, cui conſequentia tempora <lb></lb>æqualia poſſint deſignari; adeò vt totum illud tem<lb></lb>pus, quod in decidendo mobile inſumit, in plureis hu<lb></lb>iuſcemodi æqualeis parteis diſtinguatur. </s> <s id="s.000329">Supponimus <lb></lb>quintò poſſe accipi, ſiue deſignari primùm quoddam <lb></lb>ſpatium, quod tempore nempe primo percurratur, vt <lb></lb>putà orgyiam, aut aliam menſuram, cui aliæ æquales <lb></lb>poſſint accipi, in conſequente ſpatio, adeò vt totu illud <lb></lb>ſpatium, quod à mobili decidente peiuaditur, intelli<lb></lb>gatur eſſe in plureis huiuſmodi parteis diuiſum. </s> <s id="s.000330">Sup<lb></lb>ponimus demùm poſſe accipi, ſiue deſignari velocita-<pb pagenum="4" xlink:href="028/01/044.jpg"></pb>tem aliquam primam, quæ ſcilicet ſit acquiſita in fine <lb></lb>eiuſdem primi temporis, & cui per conſequentem <lb></lb>motum æquales aliæ ſuper-addantur, vt ſolent gra<lb></lb>dus gradibus in capacibus intenſionis qualitatibus ſu<lb></lb>per-addi; adeò vt, quæ velocitas in fine motus eſt ac<lb></lb>quiſita, ac intenſiſſima eſt, eſſe coalita cenſeatur ex om<lb></lb>nibus velocitatibus, ſiue gradibus, qui perſeuerante <lb></lb>motu acquiſiti fuerint, ijque interſe, & <expan abbr="cũ">cum</expan> primo illo <lb></lb>æquales. </s> <s id="s.000331">Hiſce autem ſuppoſitis, quia partes tempo<lb></lb>ris æquales, quæ primæ ſuccedunt, pauciores ſunt nu<lb></lb>mero, quàm quæ ſpatij partes æquales decurruntur <lb></lb>poſt primam; & qui velocitatis gradus acquiruntur <lb></lb>poſt primum, ac ſunt veluti incrementa ſupperaddita, <lb></lb>comparari poſſunt, vt iam dictum eſt, aut cum parti<lb></lb>bus æqualibus temporis, aut cum partibus æqualibus <lb></lb>ſpatij; ideò difficultas, ſeu quæſtionis ſtatus is videtur <lb></lb>potiſſimùm, <emph type="italics"></emph>Vtrum gradus velocitatis primo æquales tot <lb></lb>acquirantur; quot ſtuunt partes temporis: an potiùs, quot spa<lb></lb>tij partes percurruntur?<emph.end type="italics"></emph.end> Nempe non alio reſpicitur, cùm <lb></lb>requiritur, <emph type="italics"></emph>an velocitates ſi ut tempora, an ſicut spatia ſeſe <lb></lb>habeant?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000332">III. <expan abbr="Cæterũ">Cæterum</expan> ea eſt tua opinio, vt velocitates habeant <lb></lb>ſe quemadmodum ſpatia; ſeu, vt tot gradus velocitatis <lb></lb>æquales primo acquirantur, quot ſunt partes æquales <lb></lb>ſpatij, quæ poſt primum, primoque gradu ſuperatum <lb></lb>decurruntur. </s> <s id="s.000333">Siquidem toto ſpatio diuiſo in decem <lb></lb>v. c. orgyias; qualis, quantuſque eſt velocitatis gra<lb></lb>dus in fine primæ orgviæ acquiſitus, taleis, tantoſque <lb></lb>vis acquiſitos in fine ſecundæ duos, in fine tertiæ treis, <lb></lb>in fine quartæ quatuor, & ita deinceps, quovſque in <pb pagenum="5" xlink:href="028/01/045.jpg"></pb>fine decimæ ſint decem. </s> <s id="s.000334">At Galileus vult potiùs ſe ve<lb></lb>locitates habere ſicut tempora; ſiue gradus velocitatis <lb></lb>æqualeis primo tot acquiri, quot temporis partes pri<lb></lb>mæ æquales poſt ipſam fluunt. </s> <s id="s.000335">Addit verò ſpatij par<lb></lb>teis continuò acquiri per parteis temporis æqualeis, ea <lb></lb>ſerie continua, qua numeri impares ab vnitate pro<lb></lb>grediuntur; adeò vt ſi primo momento, ſeu prima <lb></lb>æquali parte temporis mobile deciderit per vnam or<lb></lb>gyiam, decidat ſecundo per treis, tertio per quinque, <lb></lb>quarto per ſeptem, ac ita deinceps. </s> <s id="s.000336">Addit rurſus, quia <lb></lb>numeros ſic progredienteis aggregando, quadrati con<lb></lb>tinuò numeri creantur; heinc fieri, vt ſi primo ſpatio <lb></lb>illa continuò aggregentur, quæ æqualia æqualibus <lb></lb>percurruntur temporibus, ſpatia tunc ſe habeant ſicut <lb></lb>quadrata temporum; hoc eſt, vt quemadmodum pri<lb></lb>mo tempore eſt ſuperatum vnum ſpatium, ſecundo <lb></lb>tempore ſint ſuperata quatuor, tertiò nouem, quaito <lb></lb>ſexdecim, & ſic conſequenter. </s> <s id="s.000337">Hæc autem melius in<lb></lb>telligi, declararique non valeant, quàm productis ex <lb></lb>eodem puncto duabus rectis lineis angulum in ipſo <lb></lb>creantibus, ac in parteis quotcumque æqualeis diuiſis, <lb></lb>interductiſque rectis lineis tum inter reſpondentia <lb></lb>ſingula heincinde diuiſionis puncta, tum à quouis hu<lb></lb>iuſmodi in vtraque linea puncto ſecundùm ductum <lb></lb>alteri lineæ parallelum. </s> <s id="s.000338">Tale eſt ſchema, quod exhi<lb></lb>bui ad calcem prioris mearum illarum Epiſtolarum, <lb></lb>quodque ſi heic iam repetiero, ac paulò accuratiùs, ob <lb></lb>factan. </s> <s id="s.000339">illam, de qua poſteà, æquiuocationem, expo<lb></lb>ſuero, erit fortaſſis operæ pretium. </s> </p> <p type="main"> <s id="s.000340">IIII. </s> <s id="s.000341">Itaque illud heic apponendo, vides primùm <pb pagenum="6" xlink:href="028/01/046.jpg"></pb>lineas AB, AC, angulum creanteis in A, ſic diuiſas eſſe <lb></lb>heinc inde in parteis æqualeis, ad puncta D, E, F, G, H, <lb></lb>I, K, L (poſſent autem in longè plureis continuatæ di<lb></lb>uidi) vt lineæ ductæ cùm inter ipſa puncta, tùm ex ipſis <lb></lb>in puncta M, N, O, totum ſpatium KAL diſpeſcant <lb></lb>in triangula inter <lb></lb><figure id="id.028.01.046.1.jpg" xlink:href="028/01/046/1.jpg"></figure><lb></lb>ſe ſimilia, ac pror<lb></lb>sù æqualia. </s> <s id="s.000342">Cùm <lb></lb>poſſimus porto <lb></lb>habere punctum <lb></lb>A pro initio tem<lb></lb>poris, pro initio <lb></lb>ſpatij, pro initio <lb></lb>velocitatis, quæ <lb></lb>tria heic in motu <lb></lb>ſpectantur, ac vna <lb></lb>cùm ipſo inci<lb></lb>piunt; Poſſumus imprimis habere parteis æqualeis al<lb></lb>terutrius, aut vtriuſque lineæ AB, AC pro partibus, <lb></lb>ſiue momentis æqualibus temporis ab initio fluentis, <lb></lb>adeòproinde, vt AE, v. g. repræſentet <expan abbr="primũ">primum</expan> momen<lb></lb>tum, EG ſecundum, GI: tertium, IL quartum. <lb></lb></s> <s id="s.000343">Poſſumus ſecundò habere æqualia illa triangula pro <lb></lb>æqualibus ſpatij partibus, quæ ab initio percurrun<lb></lb>tur; adeò vt ductâ ſeorſim lineâ PQ caſum refe<lb></lb>rente per orgyias ſexdecim, Triangulum ADE <lb></lb>repræſentet primam orgyiam PR, quæ primò mo<lb></lb>mento percurritur; tria proxima, treis orgyias RS, <lb></lb>quæ ſecundo; quinque ſequentia quinque orgyias <lb></lb>ST, quæ tertiò; & ſeptem ſuccedentia ſeptem or-<pb pagenum="7" xlink:href="028/01/047.jpg"></pb>gyias TQ, quæ quarto. </s> <s id="s.000344">Conſtat autem exinde ſpatia <lb></lb>aggregata ita ſe habere, ſicut quadrata tempo<lb></lb><figure id="id.028.01.047.1.jpg" xlink:href="028/01/047/1.jpg"></figure><lb></lb>rum; quandò ADE triangulum (ſpatiumve <lb></lb>PR) eſt vnum; quemadmodum quadratum <lb></lb>ipſius AE, hoc eſt temporis vnius, eſt vnum; & <lb></lb>aggregatum AFG (ſeu PS) eſt quatuor; quem<lb></lb>admodum quadratum AG, duorum, eſt qua<lb></lb>tuor; & aggregatum AHI (ſeu PT) eſt nouem; <lb></lb>quemadmodum quadratum AI trium, eſt no<lb></lb>uem; & aggregatum AKL (ſeu PQ) eſt ſex<lb></lb>decim; quemadmodum quadratum AL qua<lb></lb>tuor, eſt ſexdecim. </s> <s id="s.000345">Poſſumus tertiò habere li<lb></lb>neam DE, pro primo gradu velocitatis acqui<lb></lb>ſitæ in fine primi temporis: quatenus, vt pri<lb></lb>mùm tempus AE non eſt indiuiduum, ſed in <lb></lb>tot inſtantia, ſeu temporula poteſt diuidi, quot <lb></lb>ſunt puncta, particulæve in ipſa AE (aut AD) <lb></lb>ita neque gradus velocitatis indiuiduus eſt, ſeu <lb></lb>vno inſtanti, acquiſitus totus; ſed ab vſque ini<lb></lb>tio per totum primum tempus increſcit, ac re<lb></lb>præſentari poteſt per tot lineas, quot poſſunt <lb></lb>parallelæ duci ipſi DE inter puncta linearum <lb></lb>AD, & AE; adeò vt quemadmodum illæ lineæ <lb></lb>continuo increſcunt à puncto A in lineam DE, ſic <lb></lb>velocitas à principio motus continuò increſcat, & re<lb></lb>præſentata, qualis eſt in interceptis primi temporis in<lb></lb>ſtantibus, per interceptas lineas, repræſentetur qualis <lb></lb>eſt in vltimo inſtanti eiuſdem primi temporis, per <lb></lb>ipſam DE inter vltima ductam puncta. </s> <s id="s.000346">Et quia ve<lb></lb>locitas deinceps increſcere pergens, repræſentari rur-<pb pagenum="8" xlink:href="028/01/048.jpg"></pb>ſus poteſt per lineas maiores, maioreſque continenter <lb></lb>ductas inter omnia puncta ſuccedentia reſiduarum <lb></lb>linearum DB, & EC, heinc efficitur, vt linea FG re<lb></lb>præſentet velocitatem acquiſitam in fine ſecundi mo<lb></lb>menti: linea HI acquiſitam in fine tertij, & linea KL <lb></lb>acquiſitam in fine quarti. </s> <s id="s.000347">Conſtat verò inde, vt ve<lb></lb>locitates ſe habeant ſicut tempora; cùm ob triangulos <lb></lb>anguli communis, & parallelarum baſium, notum ſit <lb></lb>eſſe vt DE ad EA, ita FG ad GA, HI ad IA, & KL <lb></lb>ad LA. </s> <s id="s.000348">Atque hæc quidem, vt clariùs conſtet, qua <lb></lb>de re inter nos agatur. </s> </p> <p type="main"> <s id="s.000349">V. Iam, Tu initio argumentum Diſſertationis ita <lb></lb>partiris, vt duo præſtanda tibi proponas. </s> <s id="s.000350">Vnum, <lb></lb><emph type="italics"></emph>vt Galilei hac inre errores, eorumque fonteis aperias; claré<lb></lb>que demonſtres ea, quæ ab ipſo de acceleratione Motus in na<lb></lb>turali deſcenſu grauium Libro ſecundo nouæ ſcientiæ, & <lb></lb>toto Dialogo tertio dicta ſunt, non modò ſuſpicionibus meris, <lb></lb>vixque probabilibus coniecturis niti, ſed ex principijs etiam <lb></lb>apertè falſis, euidentibuſque paralogiſmis omnia concludi; ex <lb></lb>quo conſequens ſit, nouam illam ſcientiam euaneſcere, quam <lb></lb>ingenioſo quidem, & plauſibili, ſed inani tamen, & caſſo <lb></lb>apparatu nobis<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus exhibuerit.<emph.end type="italics"></emph.end></s> <s id="s.000351"> Alterum, <emph type="italics"></emph>vt reiecta<emph.end type="italics"></emph.end><lb></lb>G<emph type="italics"></emph>alilei pſeudo-ſcientia, veram tu, ac certam in eius locum <lb></lb>ſubstituas, rationemque, modum, ac menſuram acceleratio<lb></lb>nis eiuſdem in naturali deſcenſu grauium ex euidentibus, at<lb></lb>que indubitatis experientiis demonstres.<emph.end type="italics"></emph.end></s> <s id="s.000352"> Circa priùs de<lb></lb>inde caput, duo ſunt, in quibus occuparis; nam impe<lb></lb>tis <emph type="italics"></emph>primò<emph.end type="italics"></emph.end> definitionem Motus æquabiliter accelerati à <lb></lb>Galileo traditam: & <emph type="italics"></emph>ſecundò<emph.end type="italics"></emph.end> quod idem ait de gradi<lb></lb>bus velocitatis, qui acquiruntur à mobili, dùm ſuper <pb pagenum="9" xlink:href="028/01/049.jpg"></pb>planis inclinatis mouetur. </s> <s id="s.000353">Circa poſterius exſequeris <lb></lb>tria: Nam <emph type="italics"></emph>primò<emph.end type="italics"></emph.end> declaras quod experimentum, circa <lb></lb>Bilancem excogitaſti; <emph type="italics"></emph>ſecundò<emph.end type="italics"></emph.end> deducis quam putas ex<lb></lb>inde accelerationis <expan abbr="rationẽ">rationem</expan> haberi; ac <emph type="italics"></emph>tertiò<emph.end type="italics"></emph.end> infers pro<lb></lb>greſſionem, qua ſuperantur ſpatia temporibus æqua<lb></lb>libus, imitari progreſſionem non numerorum impa<lb></lb>rium, ſed rationis continuò duplæ, quam & exprimis <lb></lb>in deſcenſu globi à Luna vſque in centrum terræ. </s> <s id="s.000354">Hæc <lb></lb>eſt igitur Diſſertationis ſumma. </s> </p> <p type="main"> <s id="s.000355"><emph type="center"></emph><emph type="italics"></emph>De Motus æquabiliter accelerati Definitione.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000356">VI. </s> <s id="s.000357">Vt ordine autem de ſingulis dicam, & à <lb></lb>Priore capite incipiam, <emph type="italics"></emph>Primum errorem, & tanquam <lb></lb>originem cæterorum<emph.end type="italics"></emph.end> dicis, quòd <emph type="italics"></emph>Galileus falſam hanc ac<lb></lb>celerati Motus definitionem inſtituerit, Motum æquabiliter <lb></lb>acceleratum dico eum, qui à quiete recedens temporibus æqua<lb></lb>libus æqualia celeritatis momenta acquirat.<emph.end type="italics"></emph.end></s> <s id="s.000358"> Rem autem <lb></lb>putas eius momenti, vt dicas <emph type="italics"></emph>te contendere huiuſmodi <lb></lb>definitionem adulterinam eſſe, ac falſam; & quicquid <lb></lb>toto illo Libro de eodem motu accelerato, ſatis alioquin <lb></lb>ingeniosè<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus commentus eſt, nibil veritatis habere.<emph.end type="italics"></emph.end><lb></lb>Improbas ſubinde, quòd <emph type="italics"></emph>definitionem non experientia <lb></lb>certa, ac euidenti confirmauerit, ſed ab eius tantum ſim<lb></lb>plicitate motibus naturalibus maximè congruente; à per<lb></lb>fecta cum demonſtratis à ſe theorematibus conſenſione; & <lb></lb>ab aperta, vt ipſe quidem fidenter aſſerat, receptæ vulgò <lb></lb>definitionis abſurditate.<emph.end type="italics"></emph.end></s> <s id="s.000359"> Tum verò circa ſimplicitatem <lb></lb>perpendere ſolùm me iubes, an non ſimplicior ſit <lb></lb>definitio, quæ à cæteris vulgò vſurpatur, dum Mo<lb></lb>tum æquabiliter acceleratum eum potiùs eſſe aſſe-<pb pagenum="10" xlink:href="028/01/050.jpg"></pb>runt, <emph type="italics"></emph>Qui æqualibus ſpatijs æqualia celeritatis augmenta <lb></lb>acquirit.<emph.end type="italics"></emph.end></s> <s id="s.000360"> Circa conſenſionem autem ſolùm, bucis, <lb></lb><emph type="italics"></emph>nouum non eſſe, ſi falſa falſis aptè quandó que, & con<lb></lb>cinnè cohæreant;<emph.end type="italics"></emph.end> ac poſtremò in eo inſiltis, vt probes <lb></lb>eſſe paralogiſmum, quo ille vulgarem, moxque re<lb></lb>latam definitionem abſurditatis apertæ damna<lb></lb>uit. </s> </p> <p type="main"> <s id="s.000361">VII Ego intereà, optime Vir, neque video De<lb></lb>ſinitionem a Galileo inſtitutam à te directè impu<lb></lb>gnari, falſitatiſve vllius conuinci; neque agnoſco quî <lb></lb>magis vera, congruaque potuerit inſtitui. </s> <s id="s.000362">Quippe <lb></lb>meminiſſe, aut potiùs adnotaſſe diligenter oportet <lb></lb>agi heic de motu æquabiliter accelerato, ſiue cuius <lb></lb>celeritas continenter, vniformiterque increſcat, ne<lb></lb>que vllum ſit momentum conſequentis temporis, in <lb></lb>quo motus non ſit velocior, quàm in quovis antece<lb></lb>dente, & in quo non eadem ratione ipſa velocitas <lb></lb>augeatur. </s> <s id="s.000363">Fieri id porrò eſt manifeſtum ex ijs, quæ <lb></lb>deducta iam ſunt; ſi æqualibus temporibus æqualia <lb></lb>celeritatis momenta, ſeu incrementa acquirantur. <lb></lb></s> <s id="s.000364">Nam vt repetamus ſuperiorem figuram, nemo dicat <lb></lb>celeritatem vniformiter increſcentem poſſe meliùs <lb></lb>repræſentari, quàm diductione crurum anguli, linea<lb></lb>rumve AB, AC, quatenus complectuntur ſpa<lb></lb>tium, quod à puncto A magis continenter, vni<lb></lb>formiterque creſcere non poſſit: ac aliunde angu<lb></lb>lus BAC apertior, aut conductior (prout finge<lb></lb>tur maior, aut minor velocitas) valet vſurpari. <lb></lb></s> <s id="s.000365">Vt autem rem magis ob oculos ponam; duco ec<lb></lb>ce lineam VX, per ipſum apicem A, quæ cum li-<pb pagenum="11" xlink:href="028/01/051.jpg"></pb>neis AB, AC, angulos conſtituat vtrimque æqua<lb></lb><figure id="id.028.01.051.1.jpg" xlink:href="028/01/051/1.jpg"></figure><lb></lb>leis, & ſeruatâ eorum<lb></lb>dem angulorum men<lb></lb>ſurâ, ita fluere conci<lb></lb>piatur, vt totum ſpa<lb></lb>tium BAC peruadat. <lb></lb></s> <s id="s.000366">Tunc enim manife<lb></lb>ſtum eſt portiones <lb></lb>huius lineæ continuò <lb></lb>veluti reſectas, inter<lb></lb>ceptaſque à lineis AB, <lb></lb>AC, creſcere ſemper, <lb></lb>ſeu maiores, maioreſ<lb></lb>que vniformiter eſſe; ac non portiones ſemel inter<lb></lb>ceptas perire, ſed ipſis permanentibus nouas, nouaf<lb></lb>que heinc inde continenter ſuper-acquiri. </s> <s id="s.000367">Cùm <lb></lb>verò etiam gradus velocitatis conſimiliter creſcant, <lb></lb>ſiue maiores, maioreſque vniformiter euadant, ac <lb></lb>ſemel acquiſiti non pereant, ſed ipſis ſuperſtitibus, <lb></lb>perſeuerantibuſque noua, atque noua momenta, ſiue <lb></lb>incrementa velocitatis ſuper-addantur; ſupereſt, vt <lb></lb>quemadmodum linearum illarum incrementa fiunt, <lb></lb>ſic fiant quoque velocitatum. </s> <s id="s.000368">Notum eſt autem. </s> <s id="s.000369">vt <lb></lb>acceptis partibus æqualibus lineæ AC, verbi cauſsâ, <lb></lb>incrementa earum portionum, ſiue linearum paralle<lb></lb>larum interceptarum, acquirantur ſemper æqualia <lb></lb>ſub æqualibus illis partibus. </s> <s id="s.000370">Nam, vt ſub AE ac<lb></lb>quiſita eſt linea DE, ita ſub EG, acquiritur æqua<lb></lb>lis alia; cùm ipſa FG ſit dupla ipſius DE; & ſub <lb></lb>GI iterum alia; cùm ipſa HI ſit eiuſdem tripla; & <pb pagenum="12" xlink:href="028/01/052.jpg"></pb>ſub IL rursùs alia, cùm ipſa KL ſit eiuſdem qua<lb></lb>drupla; atque ita porrò, ſeu vlteriùs pergas, ſeu <lb></lb>alia puncta intra eaſdem parteis lineæ AC, aliaſ<lb></lb>que parallelas commemoratis interceptas, ſingulaſ<lb></lb>que ſuis punctis reſpondenteis, accipias. </s> <s id="s.000371">Quare & <lb></lb>aſſumptis partibus æqualibus temporis per parteis <lb></lb>æqualeis lineæ AC repræſentatis, <expan abbr="notũ">notum</expan> eſt momenta, <lb></lb>ſeu incrementa velocitatis per parallelas repræſentatæ, <lb></lb>æqualia acquiri ſub huiuſmodi partibus; adeò vt <lb></lb>qualis gradus velocitatis acquiſitus eſt in fine primi <lb></lb>temporis vnus, talis alius, hoc eſt æqualis, ſit ipſi ſuper<lb></lb>acquiſitus in fine ſecundi, ac ſint iam duo; & iterum <lb></lb>æqualis alius in fine tertij, ac ſin: iam tres; & rursùs <lb></lb>alius in fine quarti, ac ſint iam quatuor; atque ita de <lb></lb>cæteris, ſiue conſequentibus, ſiue interſumptis. </s> </p> <p type="main"> <s id="s.000372">VIII. </s> <s id="s.000373">Sic itaque mihi videtur Motus æquabili<lb></lb>ter, hoc eſt continenter, vniformiterque acceleratus <lb></lb>perquàm appoſitè definiri is, <emph type="italics"></emph>Qui à quiete recedens <lb></lb>temporibus æqualibus æqualia celeritatis momenta<emph.end type="italics"></emph.end> (aug<lb></lb>mentave) <emph type="italics"></emph>acquirat;<emph.end type="italics"></emph.end> cùm præſertim non videam <lb></lb>poſſe ipſum alia ratione concipi, aut deſcribi talem. <lb></lb></s> <s id="s.000374">Nam quod ſpectat quidem ad illam à te laudatam <lb></lb>definitionem, qua motus æquabiliter acceleratus deſ<lb></lb>cribitur is, <emph type="italics"></emph>Qui æqualibus spatiis æqualia celeritatis aug<lb></lb>menta acquirit:<emph.end type="italics"></emph.end> dic amabò quanam ratione concipere <lb></lb>exinde licear acceleratum æquabiliter motum? </s> <s id="s.000375">Eſto <lb></lb>enim ſpatium percurrendum v. c. linea AB in par<lb></lb>teis æqualeis diuiſa ad puncta C, D, E, F, G, I, K. <lb></lb></s> <s id="s.000376">Decidat mobile ex A; & in C fine primæ partis ac<lb></lb>quiſierit primum velocitatis gradum; in D autem <pb pagenum="13" xlink:href="028/01/053.jpg"></pb>ſecundum, quo ad priorem perſeuerantem iunctp <lb></lb><figure id="id.028.01.053.1.jpg" xlink:href="028/01/053/1.jpg"></figure><lb></lb>duo iam ſint: in E tertium, quo <lb></lb>iuncto ad duos ſuperiores, per<lb></lb>ſeueranteiſque ſint tres; in F <lb></lb>quartum, & ita porrò, quo<lb></lb>vſque in B acquiſierit nonum, <lb></lb>quo iuncto cum octo antece<lb></lb>dentibus ſint nouem. </s> <s id="s.000377">Iam cùm <lb></lb>quilibet horum graduum la<lb></lb>titudinem quandam habeat; <lb></lb>neque enim eſt magis indiuiſi<lb></lb>bilis, aut ex indiuiſibilibus <lb></lb>conſtans, quàm pars AC, CD, <lb></lb>DE, quælibet-ve alia: ac idcir<lb></lb>cò ipſe quoque increſcat æqua<lb></lb>biliter, vnoque tenore: repræſentetur primus gradus <lb></lb>per triangulum ALC, vt pote à puncto, ſeu angulo <lb></lb>A ad baſin LC æquabiliter, vnóque tenore creſcen<lb></lb>tem. </s> <s id="s.000378">Aptentur deinde ad CD duo triangula æqua<lb></lb>lia tum inter ſe, tum cum ipſo ALC, <expan abbr="quorũ">quorum</expan> CMD <lb></lb>repræſentet illum, qui ſecundò acquiritur, LCM au<lb></lb>tem primò aquiſitum, ac perſeuerantem. </s> <s id="s.000379">Nihil eſt <lb></lb>opus, vt <expan abbr="deſude">deſudes</expan> ad oſtendendum non increuiſſe <lb></lb>velocitatem æquabiliter, eodemve tenore ex C in D, <lb></lb>quo incœperat, perrexeratque vſque in D; vt feciſſet <lb></lb>enim, oporteret deſcriptum eſſe non quadrangulum <lb></lb>LD conſtans ex duobus triangulis; ſed trapezion CN <lb></lb>conſtitutum ex tribus. </s> <s id="s.000380">Eadem autem ratione mani<lb></lb>feſtum eſt, ſi ad DE aptentur tria triangula, defutura <lb></lb>duo; ſi ad EF quatuor, defutura tria, & ita deinceps, <pb pagenum="14" xlink:href="028/01/054.jpg"></pb>quovſque, ſi ad KB aptentur nouem, ſint defutura <lb></lb>octo; vt proinde intelligamus totidem dceſſe ad acce<lb></lb>lerationis æquabilitatem velocitatis gradus, quot nu<lb></lb>merare licet triangulos ad læuam è regione cuiuſque <lb></lb>partis, complendo ſummam triangulorum APB. <lb></lb></s> <s id="s.000381">Conſtare ergo videtur Motum æquabiliter accelera<lb></lb>tum definiti non poſſe illum, <emph type="italics"></emph>Qui æquabilibus ſpatiis <lb></lb>æqualia celeritatis augmenta acquirat;<emph.end type="italics"></emph.end> ſed potiùs illum, <lb></lb><emph type="italics"></emph>Qui acquirat æqualia æqualibus temporibus:<emph.end type="italics"></emph.end> atque idcircò <lb></lb>definitionem à Galileo traditam eſſe meritò præfe<lb></lb>rendam. </s> </p> <p type="main"> <s id="s.000382"><emph type="center"></emph><emph type="italics"></emph>De Paralogiſmo, qui Galileo Definitionem ſpuriam <lb></lb>impugnanti obiicitur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000383">IX. </s> <s id="s.000384">Ac tu id quidem non fers; ſed ais, <emph type="italics"></emph>Mirari to <lb></lb>ſatis non poſſe, quomodo<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus vir alioquin perspicacis <lb></lb>ingenij receptam communi conſenſu motus accelerati defini<lb></lb>tionem non modò falſam, atque impoßibilem exiſtimauerit; <lb></lb>ſed patenti quoque, ipſiſque tyronibus obuio paralogiſmo <lb></lb>eiuſdem falſitatem palam, atque euidenter demonſtraſſe adeò <lb></lb>prafidenter aſſeruerit; & quod ampliùs eſt, etiam viru non <lb></lb>ineruditis perſuaſerit.<emph.end type="italics"></emph.end></s> <s id="s.000385"> Tum autem pergis, <emph type="italics"></emph>Audi igitur; <lb></lb>mi<emph.end type="italics"></emph.end> G<emph type="italics"></emph>aſſende, & mecum mirare tanti viri demonſtrationem. <lb></lb></s> <s id="s.000386">Si acceleratio motus,<emph.end type="italics"></emph.end> inquit, <emph type="italics"></emph>in deſcenſu grauium æquali<lb></lb>bus ſpatiis æqualia ſumeret velocitatu ineremema, eſſent <lb></lb>ſine dubio velocitates inter ſe, vt emenſa spatia: At quoiteſ. <lb></lb></s> <s id="s.000387">cúmque velocitates inter ſe ſunt vt emenſa ſpatia, debent <lb></lb>neceſſariò ea spatia aut eodem, aut æquali tempore percur<lb></lb>ri. </s> <s id="s.000388">Si igitur velocitas acquiſita per totam AC eam <lb></lb>rationem habeat ad velocitatem acquiſitam per AB, quam<emph.end type="italics"></emph.end><pb pagenum="15" xlink:href="028/01/055.jpg"></pb><emph type="italics"></emph>spatium AC ad spatium AB, neceſſe eſt, vt spatium<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.055.1.jpg" xlink:href="028/01/055/1.jpg"></figure><lb></lb><emph type="italics"></emph>totum AC eodem, aut æquali tempore decurratur, <lb></lb>quo spatium AB abſoluitur. </s> <s id="s.000389">Jmpoßibile est au<lb></lb>tem, vt corpus graue deſcendens per AC eodem, <lb></lb>aut æquali tempore percurrat totam AC, quo per<lb></lb>currit partem eius AB, niſi motus fiat in instanti. <lb></lb></s> <s id="s.000390">Tam impoßibile eſt igitur, vt velocitates in deſcenſu <lb></lb>grauium inter ſe ſint, vt emenſa ſpatia (ac proinde, <lb></lb>vt etiam æqualibus ſpatiis creſcant æqualiter) quàm <lb></lb>impoßibile eſt motum illum fieri in instanti.<emph.end type="italics"></emph.end></s> <s id="s.000391"> Pergis ſub<lb></lb>inde, <emph type="italics"></emph>Proh tuam, mi<emph.end type="italics"></emph.end> G<emph type="italics"></emph>aſſende, Philoſophorumque omnium, <lb></lb>ac Mathematicorum fidem! istudne demonſtrare eſt? </s> <s id="s.000392">Et <lb></lb>tamen mirum quantum Galileus de hac, vt putat, ſubtili, <lb></lb>clara, euidenti, ac Mathematica demonſtratione ſibi applau<lb></lb>dat, quam integra pagina mirificis laudibus exaggerat. </s> <s id="s.000393">Sed <lb></lb>illud multò adhûc mirabiùus, quod Lynceus Philoſophus, ac <lb></lb>Mathematicus, Lynceorumque princeps in tam aperta <lb></lb>luce cæcutiat, & vir eius nominis tam facilè deludatur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000394">X. </s> <s id="s.000395">Ego verò, ô optime, ac religioſſime Vir, quo <lb></lb>me cenſu putem iri habitum, qui non ſim ex viris <lb></lb>non ineruditis, & eandem tamen cum Galileo opi<lb></lb>nionem perſuaſus ſim, ac perinde cæcutiam, perinde <lb></lb>deludar? </s> <s id="s.000396">Etenim cùm meam quæſis fidem, fatcor <lb></lb>ingenüè me non videre quem in eo notas Paralogiſ<lb></lb>mum; ac videri mihi neceſſariò deduci, fore, vt ſi ve<lb></lb>locitas per totam AC acquiratur dupla illius, quæ <lb></lb>acquiritur per totam AB, ipſa AC eodem, aut æqua<lb></lb>li tempore, quo AB percurratur. </s> <s id="s.000397">Rem certe in <lb></lb>hunc modum concipio. </s> <s id="s.000398">Intelligatur AC diuiſa in <lb></lb>duodecim parteis æqualcis, ac proinde eius dimidium <pb pagenum="16" xlink:href="028/01/056.jpg"></pb>AB, ſeu ipſi æqualrs DE in ſex: ſintque primùm <lb></lb>duo mobilia, quorum vnum diſcedat ex A <lb></lb><figure id="id.028.01.056.1.jpg" xlink:href="028/01/056/1.jpg"></figure><lb></lb>verſus C, eodem momento, quo aliud ex D <lb></lb>verſus E. </s> <s id="s.000399">Notum eſt, ſi vtrumque quidem <lb></lb>ferretur non accelerato, ſed æquabili motu, <lb></lb>euenturum eſſe, vt velocitate illius exſiſtente <lb></lb>dupla ad velocitatem iſtius, illud perueniret <lb></lb>in C eodem momento, quo iſtud in E; quo<lb></lb>niam ſpatium ab illo ſuperatum foret vbi<lb></lb>que ad ſpatium ab iſto ſuperatum duplum, hoc eſt, <lb></lb>forent ab illo ſuperatæ duæ partes, cùm ab iſto vna; <lb></lb>ab illo quatuor, cùm ab hoc duæ, &c. </s> <s id="s.000400">quatenus ſpa<lb></lb>tia ſe haberent vbique vt velocitates, hoc eſt veloci<lb></lb>tas per totam AC eſſet vbique dupla velocitatis per <lb></lb>totam DE. </s> <s id="s.000401">At verò, quoniam heic agitur de motu <lb></lb>non æquabili, ſed continenter accelerato; ita deſcen<lb></lb>dant rurſus mobilia eodem tempore, vnum ab A, <lb></lb>aliud à D, vt ſuccrefcentibus continuò velocitatis gra<lb></lb>dibus, illud perueniendo in C acquiſierit duodecim, <lb></lb>hoc perueniendo in E ſex: Quæſo quid impediat, <lb></lb>quo minùs illud perueniat in C eodem tempore, quo <lb></lb>iſtud in E? </s> <s id="s.000402">Nam diſcrimen eſt quidem inter mo<lb></lb>tum acceleratum, & æquabilem, quòd in æquabili <lb></lb>partes ſpatiorum æquales percurrantur æqualibus <lb></lb>temporibus, vt ſingulæ partes lineæ DE ſingulis mi<lb></lb>nutis, & geminæ partes lineæ AC minutis item ſin<lb></lb>gulis; in accelerato non item: At in eo tamen motus <lb></lb>conueniunt, quòd vbique velocitas per totam AC <lb></lb>dupla ſit velocitatis per totam DE; & qua ratione <lb></lb>plures, plureſque ex ſingulis partibus lineæ DE <pb pagenum="17" xlink:href="028/01/057.jpg"></pb>percurruntur æqualibus temporibus, percurruntur <lb></lb>quoque plures, plureſque ex geminatis lineæ AC. <lb></lb></s> <s id="s.000403">Ex hoc autem ſit, vt quemadmodum in æquabili mo<lb></lb>tu, DE percurrebatur ſex minutis, & AC ſimiliter <lb></lb>ſex, ob geminas parteis iſtius correſpondenteis ſingu<lb></lb>lis illius, ita in accelerato, ſi DE percurratur tribus <lb></lb>minutis, AC percurratur ſimiliter tribus; quòd dum <lb></lb>primo minuto percurritur pars illius vna, percurran<lb></lb>tur iſtius duæ, ob ge minam velocitatem; & ob ean<lb></lb>dem cauſſam, dum ſecundo minuto percurruntur <lb></lb>illius duæ, percurrantur iſtius quatuor, dum tertio <lb></lb>demùm illius tres, percurrantur iſtius ſex. </s> <s id="s.000404">Nim rùm <lb></lb>non alia ratione dici poſſent habere ſe velocitates vt <lb></lb>ſpatia: neque velocitas per totam AC dupla eſſet ve<lb></lb>locitatis per totam DE Eſto deinde vnicum mobile, <lb></lb>quod decedens ab A, tendat verſus C, & ſit rursùs <lb></lb>velocitas per totam AC dupla velocitatis per totam <lb></lb>AB, patet idem prorsùs dicendum de AC, reſpectu <lb></lb>AB, quod dictum fuit de eadem reſpectu DE. </s> <s id="s.000405">Nam <lb></lb>in æquabili quidem motu oporteret mobile percur<lb></lb>rere ſimul, ſeu primo minuto primam, & ſecundam <lb></lb>parteis; ſecundo ſecundam, & quartam; ac ita porrò <lb></lb>quovſque ſexto, percurreret, ſeu attingeret ſimul <lb></lb>ſextam, atque duo ſecimam. </s> <s id="s.000406">In accelerato verò <lb></lb>eſt neceſſe, vt percurrat ſimul vnam, & duas in pri<lb></lb>mo; duas, & quatuor in ſecundo; treis, & ſex in tertio; <lb></lb>atque adeò totam AB, & totam AC tempore eo<lb></lb>dem. </s> <s id="s.000407">Atque ego quidem rem itaconcipio. </s> </p> <p type="main"> <s id="s.000408">XI Verum tu ſi mſtas, <emph type="italics"></emph>Vt prima illius Paralo<lb></lb>giſmi aſſumptio in motu vniformi, ac perpetuò ſibi æquali<emph.end type="italics"></emph.end><pb pagenum="18" xlink:href="028/01/058.jpg"></pb><emph type="italics"></emph>vera, & neceſſaria ſit; in motu tamen accelerato minime <lb></lb>neceſſaria eſt, & non vno modo tantum, ſed pluribus in<lb></lb>telligi potest, quo modo velocitates ſint inter ſe, vt emenſa <lb></lb>ſpatia: licet eadem ſpatia neque eodem, neque æquali tem<lb></lb>pore percurrantur.<emph.end type="italics"></emph.end></s> <s id="s.000409"> Pergis autem, <emph type="italics"></emph>Vt, ſi graue deſcen-<emph.end type="italics"></emph.end><lb></lb><emph type="italics"></emph>dens per AB tempus quodcumque inſumat, putà qua<lb></lb><figure id="id.028.01.058.1.jpg" xlink:href="028/01/058/1.jpg"></figure><lb></lb>drantem; ac deinde BC ipſi AB æquale, dimidio <lb></lb>quadrante percurrat; quis neget in<emph.end type="italics"></emph.end> C <emph type="italics"></emph>duplam ha<lb></lb>beri velocitatem eius, quæ fuit in B? & tamen <lb></lb>idem graue totam AC, & dimidium eius AB <lb></lb>non percurreret.<emph.end type="italics"></emph.end></s> <s id="s.000410"> Et hæc eſt quidem tota tua ad <lb></lb>conuincendum paralogiſmi Galileum proba<lb></lb>tio, ob quam continenter hæc verba ſubiun<lb></lb>gis: <emph type="italics"></emph>Aſſumptio igitur Galilei falſa eſt, & tota eius <lb></lb>ratiocinatio merus Paralogiſmus id óque nullo modo, vt ipſe <lb></lb>gloriatur communem, ſanioremque aliorum ſenſum erroris <lb></lb>reuincit, qui in naturali grauium deſcenſu volunt æqualibus <lb></lb>spatijs æqualia velocitatis momenta acquiri.<emph.end type="italics"></emph.end></s> <s id="s.000411"> An verò pa<lb></lb>tietur tua bonitas, ſi dicam poſſe cuipiam videri, eſſe <lb></lb>te potiùs, qui hoc loco incidas in paralogiſmum? </s> <s id="s.000412">Ni<lb></lb>mirum videris ſic argumentari, vt id, quod contro<lb></lb>uertitur, aſſumas pro principio, dum nihil aliud, quàm <lb></lb>ſupponis ſpatium AB, percurri duplo temporis, quo <lb></lb>ſpatium BC; & velocitatem in C, eſſe duplam eius, <lb></lb>quæ fuit in B; quæ ipſa tamen eſt controuerſia. </s> <s id="s.000413">Et <lb></lb>cùm ſoluenda eſſet ratio, qua conficitur fore, vt AC <lb></lb>percurratur eodem, aut æquali tempore, quo ſpatium <lb></lb>AB, nihil aliud, quam concluſionem negas, fore di<lb></lb>cendo, vt idem graue totam AC, & dimidium eius <lb></lb>AB eodem tempore non percurreret. </s> <s id="s.000414">Teneri certè <pb pagenum="19" xlink:href="028/01/059.jpg"></pb>videbaris ad vberiorem paralogiſmi detectionem, <lb></lb>ſolutionemque, cùm ſi iſta quidem methodus ſuffi<lb></lb>ciat, nihil eſſe videatur facilius, quàm paralogiſmi ar<lb></lb>guere vniuerſum Euclidem. </s> <s id="s.000415">Et agnoſco quidem te <lb></lb>ſupponere tanquam rem nimis euidentem, totum <lb></lb>ſpatium AC prolixiore tempore, quàm eius partem <lb></lb>AB percurri: ſed cùm Galileus non neget eſſe illud <lb></lb>tempus prolixius, imò tale eſſe reuerâ ſupponat; ab <lb></lb>incommodo tamen arguit, probando prolixius non <lb></lb>fore, ſi velocitas acquiſita per totam AC dupla defen<lb></lb>datur illius, quæ acquiritur per totam AB: vnde & <lb></lb>videtur omnmò obiecta ratio fuiſſe ſoluenda. </s> <s id="s.000416">Agnoſco <lb></lb>etiam te heinc moueri, quòd non ſatis appareat ratio, <lb></lb>cur ſi ex A in B acquiratur vnus velocitatis gradus, <lb></lb>acquiri alius ex B in C, perſeuerante primo, non <lb></lb>valeat. </s> <s id="s.000417">Sed cauſſa nimirùm intelligitur non modò <lb></lb>ex dictis in vulgarem definitionem; verùm etiam <lb></lb>maximè ex incommodo, in quod aliunde incidis, <lb></lb>dum conſequenter loquens, vis ſpatium BC percurri <lb></lb>dimidio temporis, quo AB; vt putà, quod AB vnico <lb></lb>gradu velocitatis BC, gemino percurratur. </s> </p> <p type="main"> <s id="s.000418">XII. Nam, vt illud paucis deducam, ſequitur <lb></lb>exinde, vt tempore dato, quo decurſa ſemel fuerit <lb></lb>pars AB, tempus aliud ipſi æquale attingi nulla ra<lb></lb>tione valeat, niſi ſuperato ſpatio infinito. </s> <s id="s.000419">Intelliga<lb></lb>tur enim linea AC infinitè producta, diuiſaque in <lb></lb>parteis CD, DF, EF, &c. </s> <s id="s.000420">ipſis AB & BC <lb></lb>æqualeis. </s> <s id="s.000421">Qua ratione tu vis tempus, quo percurri<lb></lb>tur AB, eſſe duplum temporis, quo percurritur BC <lb></lb>velis oportet tempus id, quo percurritur BC eſſe <pb pagenum="20" xlink:href="028/01/060.jpg"></pb>duplum temporis, quo percurritur CD, & hoc <lb></lb><figure id="id.028.01.060.1.jpg" xlink:href="028/01/060/1.jpg"></figure><lb></lb>duplum eius, quo DE, & iſtud illius, quo EF, <lb></lb>& ſic deinceps; neque enim maior vnius, <lb></lb>quàm alterius eſt ratio; ac in accelerato potiſ<lb></lb>ſimù n æquabiliter motu, de quo præſertim <lb></lb>quæſtio heic eſt. </s> <s id="s.000422">Quare & velis etiam opor<lb></lb>tet, vt cùm tempus, quo percurritur BC, ſit <lb></lb>dimidium temporis, quo percurritur AB; illud, <lb></lb>quo percurritur CD, ſit quadrans eiuſdem <lb></lb>primi temporis; illud, quo DE, octans; quo <lb></lb>EF, pars decima ſexta; quo FG, trigeſima ſe<lb></lb>cunda; quo GH ſexageſima quarta, &c. </s> <s id="s.000423">Por<lb></lb>rò hæc omnia tempora ſimul iuncta nunquam <lb></lb>æquabuntur primo tempori, quo decurſum <lb></lb>fuerit AB (quandò procedentes hoc modo <lb></lb>fractiones relinquunt ſemper ex integro, to<lb></lb>tove quidpiam inexhauſtum) niſi lineam, ſeu <lb></lb>ſpatium infinitum admiſeris, & parteis æqua<lb></lb>leis in eo infinitas, quæ infinitis analogis (ſeu <lb></lb>dimidiorum dimidiis in tempore ipſo, aut <lb></lb>æquali, quo AB percurritur) contineri intel<lb></lb>lectis, reſpondeant. </s> <s id="s.000424">Adderem heic etiam <lb></lb>incommodum aliud de ſpatijs increſcentibus, <lb></lb>& in fine cuiuſlibet æqualis temporis numerandis <lb></lb>ſecundum rationem non modò duplam, verùm etiam <lb></lb>triplam, & ampliùs: ſed res erit poſteà vberiùs dicen<lb></lb>da. </s> <s id="s.000425">Adderem rursùs alia quoque, vt Quòd ſequere<lb></lb>tur lineam proiectorum, & illam ſpeciatim, quæ deſ<lb></lb>cribitur à lapide ſurſum, & ſecundum mali altitudi<lb></lb>nem, dum nauis mouetur, proiecto, non eſſe Parabo-<pb pagenum="21" xlink:href="028/01/061.jpg"></pb>licam, neque tantum temporis, exſcendendo, quan<lb></lb>tum aſcendendo conſumi; ac proinde lapidem illum <lb></lb>neque peruenturum ad mali carcheſium, neque reca<lb></lb>ſurum in pedem eiuſdem: verùm iſta aut colliguntur <lb></lb>ex ijs, quæ ſunt dicta in Epiſtolis, aut in promptu <lb></lb>ſunt, facileque occurrunt. </s> <s id="s.000426">Et de Definitione huc<lb></lb>vſque. </s> </p> <p type="main"> <s id="s.000427"><emph type="center"></emph><emph type="italics"></emph>De Poſtulato Galilei circa Motum ſuper æquè altis, non <lb></lb>æquè inclinatis planis.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000428">XIII. </s> <s id="s.000429">Inſectaris ſecundo loco, tanquam aliam <lb></lb>erroris cauſſam, Quod Galileus ſibi dari, & gratis <lb></lb>concedi, inquis, poſtulat, <emph type="italics"></emph>Gradus velocitatis eiuſdem <lb></lb>mobilis ſuper diuerſas planorum inclinationes acquiſitos tunc <lb></lb>eſſe æqualeis, cùm eorumdem planorum eleuationes ponuntur<emph.end type="italics"></emph.end><lb></lb><emph type="italics"></emph>æquales;<emph.end type="italics"></emph.end> hoc eſt gradus velo<lb></lb><figure id="id.028.01.061.1.jpg" xlink:href="028/01/061/1.jpg"></figure><lb></lb>citatis ab eodem globo (exem<lb></lb>pli gratia) per plana CA, & <lb></lb>CD deſcendente, in punctis <lb></lb>A, & D acquiſitos, eſſe inter ſe <lb></lb>æqualeis, quòd æqualem, vel potiùs eandem eleua<lb></lb>tionem habeant, videlicet BC. <emph type="italics"></emph>Hoc enim poſtula<lb></lb>tum,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>cùm neque ex terminis notum ſit, neque vlla <lb></lb>ſufficiente experientia confirmatum; imò cùm rationes etiam <lb></lb>non deſint, quibus oppoſitum probabilius reddatur (nempe <lb></lb>gradus velocitatis per longius planum acquiſitos gradibus <lb></lb>per breuius planum acquiſitis eſſe minores) id à Galileo non <lb></lb>peti, ſed debuerat demonſtrari cùm præſertim maxima pars <lb></lb>ſubſequentium theorematum hoc vnico postulato nitantur. <lb></lb></s> <s id="s.000430">Quid enim certi ex incertis concludi poteſt. </s> <s id="s.000431">aut ex principie,<emph.end type="italics"></emph.end><pb pagenum="22" xlink:href="028/01/062.jpg"></pb><emph type="italics"></emph>vt ipſemet<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus agnoſcit, veriſimili tantum, ac probabili <lb></lb>demonstrari?<emph.end type="italics"></emph.end> Poſtmodùm autem, vbi hæc præmiſiſti, <lb></lb><emph type="italics"></emph>In ſcientiarum, ac demonſtrationum principiis euidentiam <lb></lb>exigimus, ſuſpiciones, ac veriſimilitudines nulla ratione ad<lb></lb>mittimus,<emph.end type="italics"></emph.end> ſubdis, <emph type="italics"></emph>Porrò quæ ex his conſequuntur, aut <lb></lb>inferuntur theoremata, ſuis illis principiis certiora, aut eui<lb></lb>dentiora eſſe non poſſunt, & nominatim ſolemne illud, & <lb></lb>quod totius ſcientiæ à Galileo excogitatæ firmamentum est, <lb></lb>spatia ſcilicet æqualibus temporibus emenſa eam inter ſe <lb></lb>rationem obſeruare, quæ est inter numeros omneis impareis <lb></lb>continua ſerie ab vnitate procedenteis (quamvis aliunde <lb></lb>falſum demonſtrari non poſſet) neque ex præſuppoſitis illis <lb></lb>principiis euidenter, neque aliunde ſufficienter conclude<lb></lb>retur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000432">XIV. </s> <s id="s.000433">Hoc autem loco non video primùm, quì <lb></lb>reprchendendus Galileus ſit, ſi quam propoſitionem <lb></lb>non demonſtratam, ſed veriſimilem ſolùm habuit, <lb></lb>non vt demonſtratam, ſed vt veriſimilem duntaxat <lb></lb>exhibuit. </s> <s id="s.000434">Candidè nimirùm videtur egiſſe, neque <lb></lb>exegiſſe à Lectoribus, vt maiorem, quàm ipſe Poſtu<lb></lb>lato fidem haberent; ſed illos potius quaſi monuiſſe, <lb></lb>ne ipſum concederent, niſi deinceps agnoſcerent <lb></lb>conſtabilitum variis ex eo deductis concluſionibus, <lb></lb>quæ cum experientia planè conſentirent. </s> <s id="s.000435">Deinde <lb></lb>cùm in ſcientijs, ac demonſtrationibus attinent bus <lb></lb>ad Matheſin puram, mera euidentia, non ſola ſuſpi<lb></lb>cio, aut veriſimilitudo admittenda ſit: in ſcientijs ta<lb></lb>men Phyſicis, ac miſta Matheſi, quacumque ſeſe Phy<lb></lb>ſica, hoc eſt caligo humanæ mentis in rebus natura<lb></lb>libus inueſtigandis, ingerit; fœlices ſimus, ſi non <pb pagenum="23" xlink:href="028/01/063.jpg"></pb>euidentiam, ſed veriſimilitudinem aſſequamur. </s> <s id="s.000436">Vnde <lb></lb>& videtur poſſe Poſtulatum, ſi veriſimile modò ſit, ac <lb></lb>neque ratione, neque experientia vlla oppugnetur, ad<lb></lb>mitti ad ſcientiam, quæ vtcúmque perfecta abſolutè <lb></lb>non ſit, eiuſmodi tamen ſit, cuius ſit humana imbe<lb></lb>cillitas capax. </s> <s id="s.000437">Ad hæc, addam-ne fuiſſe rem mihi <lb></lb>quodammodò ſtupendam, acceſſiſſe caſu ad me iſta <lb></lb>conſcribentem, nobiliſſimum Senatorem Petrum <lb></lb>Calcauium virum omninò promouendis bonis arti<lb></lb>bus comparatum, puræque cum-primis Matheſeos <lb></lb>ſtudioſiſſimum; ac viſa mihi præ manibus tua Diſſer<lb></lb>tatione, argumentóque cognito, innuiſſe tranſmiſ<lb></lb>ſum in hanc vrbem exemplum editi nuperrimè Libri <lb></lb>ab Euangeliſta Torricellio, qui Galilei ſucceſſor exi<lb></lb>mius demonſtrauerit in eo iſtud Poſtulatum? </s> <s id="s.000438">Præ<lb></lb>tereo autem, vt copiâ illius videndi ſtatim impetratâ, <lb></lb>deprehenderim rem confectam quinque propoſitio<lb></lb>nibus, ac Præmiſſo illo, <emph type="italics"></emph>Non poſſe duo<emph.end type="italics"></emph.end> G<emph type="italics"></emph>rauia ſimul <lb></lb>iuncta ex ſe moueri, niſi centrum commune grauitatis ipſo<lb></lb>rum deſcendat.<emph.end type="italics"></emph.end></s> <s id="s.000439"> Videlicet prima Propoſitio eſt, <lb></lb>G<emph type="italics"></emph>rauia in planis inæqualiter inclinatis, ac eandem tamen <lb></lb>eleuationem habentibus, conſtituta: ſi eandem inter ſe ratio<lb></lb>nem homologè habeant, quam habent planorum longitudi<lb></lb>nes, habere æqualia momenta.<emph.end type="italics"></emph.end></s> <s id="s.000440"> Secunda, <emph type="italics"></emph>Eadem grauia ſi <lb></lb>æqualia fuerint, habere momenta in ratione reciproca longi<lb></lb>tud num eorumdem planorum.<emph.end type="italics"></emph.end></s> <s id="s.000441"> Tertia, <emph type="italics"></emph>Illa <expan abbr="æqualiũ">æqualium</expan> grauium <lb></lb>momenta eſſe in ratione homologa cum perpendiculis par<lb></lb>tium æqualium eorumdem planorum.<emph.end type="italics"></emph.end></s> <s id="s.000442"> Quarta, <emph type="italics"></emph>Tempora <lb></lb>lationum ex quiete eſſe homologè vt longitudines eorum<lb></lb>dem planorum.<emph.end type="italics"></emph.end></s> <s id="s.000443"> Quinta autem eſt ipſum Poſtulatum <pb pagenum="24" xlink:href="028/01/064.jpg"></pb>ex ſuperioribus deductum, G<emph type="italics"></emph>radus velocitatis eiuſdem <lb></lb>mobilis ſuper diuerſas planorum inclinationes acquiſitos tunc <lb></lb>eſſe æqualeis, cùm eorumdem planorum eleuationes ęquales <lb></lb>ſunt.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000444">XV. Verùm, ne ad alia excurram, quàm quæ <lb></lb>ipſemet ex Galileo commemoras, improbas ecce ex<lb></lb>perimentum, quo ille eſt conatus fidem Poſtulato <lb></lb>aſſerere, quodque adſcripta figura ſic refers E <emph type="italics"></emph>clauo A<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.064.1.jpg" xlink:href="028/01/064/1.jpg"></figure><lb></lb><emph type="italics"></emph>parieti infixo, globus plumbeus, aut alius quilibet tenui filo, <lb></lb>tribus, aut quatuor digitis à pariete remoto ſuſpendatur, ſit<lb></lb>que AB, Deſcriptaque in pariete recta CD horizonti <lb></lb>parallela, globus B à perpendiculari eductus vſque ad alti<lb></lb>tudinem rectæ CD manu altollatur, nempe ad C; indeque <lb></lb>liberè dimittatur. </s> <s id="s.000445">Tum globus idem in uit<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus, non <lb></lb>ſolùm deſcendet ad punctum B, ſed eodem impetu vlteriùs <lb></lb>vſque ad D, aut proximè ad illud, aſcendet.<emph.end type="italics"></emph.end> S<emph type="italics"></emph>imiliter, ſi <lb></lb>globus idem è puncto E ſuspendatur, & item ad altitudinem<emph.end type="italics"></emph.end><pb pagenum="25" xlink:href="028/01/065.jpg"></pb><emph type="italics"></emph>eiuſdem rectæ<emph.end type="italics"></emph.end> C<emph type="italics"></emph>D attollatur ad<emph.end type="italics"></emph.end> G, <emph type="italics"></emph>inde liberè dimiſſus, <lb></lb>pari modo ad eandem rectam CD, aut proximè ad eam <lb></lb>conſcendet verſus H. Jmò, ſi ex F ſuſpenſus attollatur ad <lb></lb>I, inde feretur, vſque ad K. </s> <s id="s.000446">Per diuerſos igitur illos arcus <lb></lb>decidens globus, ſemper ad æqualem altitudinem conſcendit. <lb></lb></s> <s id="s.000447">Ergo è quolibet deſcenſu æqualem acquirit impetum; niſi <lb></lb>enim eſſet impetus æqualis, globum ad æqualem altitudinem <lb></lb>non attolleret. </s> <s id="s.000448">Quid ni igitur idem quoque faciat globus, <lb></lb>ſi per plana CB, GB, IB deſcendat?<emph.end type="italics"></emph.end> C<emph type="italics"></emph>redibile igitur <lb></lb>etiam eſt globum per illa, aut ſimilia plana decidentem, æqua<lb></lb>lem tali deſcenſu impetum, ac proinde æqualem quoque ve<lb></lb>locitatis gradum acquirere.<emph.end type="italics"></emph.end></s> <s id="s.000449"> Subinde autem, vt oſten<lb></lb>das quàm hæc ſint incerta, incohæcentia, &c. <emph type="italics"></emph>Impri<lb></lb>mis quidem neſcio,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>an globi ea, qua vult<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus <lb></lb>ratione ſuſpenſi, ac librati alitùs in Etruria, quàm in Gal<lb></lb>lia aſſurgant; at heic neque tam propè ad horizontalem li<lb></lb>neam, neque per diuerſos arcus ad eam æqualiter accedunt. <lb></lb></s> <s id="s.000450">Nempe filo pedum quatuor cum dimidio ſuſpenſus globus ad <lb></lb>lineam horizontalem tribus infra centum pedibus <expan abbr="deſcriptã">deſcriptam</expan>, <lb></lb>propiùs quàm duobus digitis nunquam acceßit. </s> <s id="s.000451">At centro <lb></lb>nouem tantum digitis ſupra lineam horizontalem accepto, <lb></lb>filóque duorum pedum conſtituto, iam globus ad lineam ho<lb></lb>rizontalem vno digito, quàm anteà propiùs acceßit. </s> <s id="s.000452">Vbi <lb></lb>verò centrum ſeptem infra lineam horizontalem digitis aſ<lb></lb>ſumptum est, vix ad quatuor à linea horizontali digitos <lb></lb>globus aſcendit.<emph.end type="italics"></emph.end></s> <s id="s.000453"> Concludis idcircò his verbis, <emph type="italics"></emph>Qua <lb></lb>igitur fide<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus tam aſſeueranter ait globum ita ſuſpen<lb></lb>ſum, ac per quoſcumque arcus librarum, ad æqualem ſem<lb></lb>per altitudinem aſſurgere? </s> <s id="s.000454">aut quomodo ex re adeò euiden<lb></lb>ter falſa petere auſus eſt testimonium veritatis?<emph.end type="italics"></emph.end></s> </p> <pb pagenum="26" xlink:href="028/01/066.jpg"></pb> <p type="main"> <s id="s.000455">XVI. </s> <s id="s.000456">Imprimis porrò non retices ipſe dictum <lb></lb>eſſe à Galileo demiſſum ex C globum aſcenſurum <lb></lb><emph type="italics"></emph>vſque ad D, aut proxime:<emph.end type="italics"></emph.end> vt proinde non videatur di<lb></lb>ctum ab illo aſſeueranter aſſurrecturum globum <lb></lb>ad eandem altitudinem, aut veritatis teſtimonium <lb></lb>ex re falſa ab ipſo peti; quaſi intellexerit globum aſ<lb></lb>ſequi altitudinem exquiſitè, ſeu præcisè eandem. </s> <s id="s.000457">Et <lb></lb>certè non modò dixit ipſe <emph type="italics"></emph>quaſi,<emph.end type="italics"></emph.end> ſeu <emph type="italics"></emph>ferè,<emph.end type="italics"></emph.end> ac <emph type="italics"></emph>ſuperfu<lb></lb>turum interuallum quoddam perexiguum;<emph.end type="italics"></emph.end> ſed etiam cauſ<lb></lb>ſam attigit, ob quam ita fiat; referens eam putà ad <lb></lb>impedimentum partim aëris, partim fili; de quo vtro<lb></lb>que heic dicerem, niſi iam dictum ſatis copiosè in <lb></lb>Epiſtolis memoratis foret. </s> <s id="s.000458">Deinde, quód globus ad <lb></lb>horizontalem lineam propiùs ad H, remotiùs ad <lb></lb>Kaſcendat, quàm ad ipſum D; videri poteſt cauſſa <lb></lb>perſpicua, neque infringere vim experimenti. </s> <s id="s.000459">Nam <lb></lb>quod ſpectat quidem ad H, res ideò contin git, quòd <lb></lb>quoties clauus defigitur inter A, & horizontalem <lb></lb>lineam, breuitas tum fili, tum ſpatij aërei, per quod <lb></lb>arcus deſcribitur, minùs præſtet impedimenti: vnde <lb></lb>& abfuiſſet globus adhûc propiùs, ſi fuiſſet clauus <lb></lb>infra E defixus, vti & longiùs, ſi ſupra ipſum Quod <lb></lb>verò ad K, res minùs eſt mira; quòd quoties clauus <lb></lb>defigitur infra horizontalem lineam, dimiſſus ex I <lb></lb>globus non per totum arcum IB decidat, ſed per <lb></lb>inferiorem ſolùm eius partem, in quam perpendicu<lb></lb>lariter cadit; vnde & minùs adhûc, minuſque reſi<lb></lb>liiſſet, ſi defixiſſes clauum inferiùs, quouſque globus <lb></lb>non potuiſſet ad lineam attolli; veluti & magis, ma<lb></lb>giſque, ſi ſuperiùs, quouſque clauo defixo in linea, <pb pagenum="27" xlink:href="028/01/067.jpg"></pb>ipſum reſiliendo proximè attigiſſet. </s> <s id="s.000460">Ex quo effici<lb></lb>tur, vt cùm res propriè attendenda non ſit, vbi cla<lb></lb>uus infra lineam defigitur, quòd tunc libratio ſimplex <lb></lb>non ſit, ſed miſtio duorum motuum, quorum im<lb></lb>petus ſe mutuò retundunt; ſit verò propriè atten<lb></lb>tenda, cùm clauo ſupra lineam defixo, vibrationis <lb></lb>motus ſimplex eſt; ideò non ſit exiſtimandum illam <lb></lb>qualemcumque interuallorum inæqualitatem in<lb></lb>terturbare negotium; ac potiſſimùm quidem, cùm <lb></lb>ipſa ordinata ſint, ac eandem inter ſe, quàm fili, & <lb></lb>arcus prolixitates proportionem ſeruent. </s> <s id="s.000461">Ad hæc, <lb></lb>id videtur præſertim eſſe obſeruatione dignum in <lb></lb>his pendu orum vibrationibus, quòd, Si quatuor di<lb></lb>ſtinctos g obos quatuor diſtinctis filis ſic appendas, <lb></lb>vt primi longitudo ſit vnius, v. c. pedis, ſecundi qua<lb></lb>tuor, tertij nouem, quarti ſexdecim; experturus ſis, <lb></lb>vbi omnes dimiſſi ſimul fuerint, quartum perfectu<lb></lb>rum vnam vibrationem eodem tempore, quo ter<lb></lb>tius interim perfecerit duas, ſecundus treis, & primus <lb></lb>quatuor. </s> <s id="s.000462">Scilicet exinde intelligitur, tum pendulo<lb></lb>rum vibrationes tantò ſegnius fieri, quantò earum <lb></lb>arcus planiores, ſiue inclinatiores ſunt; tum inclina<lb></lb>tiones arcuum menſuratas ſecundum varias perpen<lb></lb>diculi, ſeu fili longitudines, habere ſe perinde vt qua<lb></lb>drata temporum, ac vibrationes habere ſe reciprocè <lb></lb>vt ipſas radices; ſicque rem eximiè quadrare ad ſu<lb></lb>periùs expoſitam motus æquabilis rationem; tum <lb></lb>globum quartum non acquirere impetum ad eleua<lb></lb>tionem neceſſarium, niſi tempore duplo tertij, tri<lb></lb>plo ſecundi, quadruplo primi; ac eſſe quidem im-<pb pagenum="28" xlink:href="028/01/068.jpg"></pb>petus omnium globorum inter ſe æqualeis; ſed <expan abbr="quõ">quom</expan> <lb></lb>tempore impetus exprimitur à quarto ſemel, exprimi <lb></lb>à tertio bis, à ſecundo ter, à primo quater, &c. </s> </p> <p type="main"> <s id="s.000463">XVII. </s> <s id="s.000464">Quod attinet autem ad comparationem <lb></lb>arcuum CB, GB, IB, cum ipſis planis punctim <lb></lb>notatis inter extrema eadem; tu ſic inſtas, vt licet <lb></lb>totum id eſſe verum concederetur, quod dicitur de <lb></lb>impetu globi per diuerſos arcus librati, vrgeas <emph type="italics"></emph>aliam <lb></lb>eſſe rationem, aut meritò ſaltem videri poſſe aliam,<emph.end type="italics"></emph.end> deſ<lb></lb>cendentis globi per diuerſa plana. </s> <s id="s.000465">G<emph type="italics"></emph>lobus enim,<emph.end type="italics"></emph.end> in<lb></lb>quis, <emph type="italics"></emph>per aërem ſemper toto ſuo pondere deorsùm nititur, <lb></lb>& eatenus ſolum eius deſcenſus interturbatur, quatenus à <lb></lb>recto, & perpendiculari curſu ad circularem cogitur, at<lb></lb>que adducitur: at præter impedimentum ex varia plano<lb></lb>rum inclinatione, adhûc maius, dum globus etiam magis <lb></lb>à perpendiculari deſcenſu diſtrahitur; tantò minoribus in<lb></lb>ſuper momentis globus per planum deſcendit, quan ò mi<lb></lb>nùs accliue fuerit, vt facilè omnibus notum eſt.<emph.end type="italics"></emph.end></s> <s id="s.000466"> Verùm <lb></lb>non video quî id concludas; quatenùs non aſſumis <lb></lb>planum, quantò minùs decliue eſt, tantò eſſe quo<lb></lb>que prolixius. </s> <s id="s.000467">Etenim notum quidem eſt acquiri <lb></lb>minores velocitatis gradus in minus decliui, quod <lb></lb>ſit decliuiori æquale, at, ſi vt minùs decliue, ita etiam <lb></lb>prolixius ſit, notum quoque eſt velocitatem in fine <lb></lb>illius quæſitam eſſe poſſe æqualem velocitati in fine <lb></lb>decliuioris acquiſitæ, prolixitate nempe deſcenſus par<lb></lb>uitatem incrementorum velocitatis compenſante. <lb></lb></s> <s id="s.000468">Interim autem æqualitas impetus in B acquiſiti, ſiue <lb></lb>per arcum, ſiue per planum contingat globi delapſio, <lb></lb>ex eo videtur conſequi, quòd ſilum ſupernè globum <pb pagenum="29" xlink:href="028/01/069.jpg"></pb>cohibens aliud nihil præſtare videatur, quam præſta<lb></lb>ret infernè, & ſine filo arcus marmoreus, aut ligneus <lb></lb>perfectè politus, qui eſſet CB, ſi ſupra ipſum dela<lb></lb>beretur. </s> <s id="s.000469">Atque id quidem tantò magis, quantò idem <lb></lb>Galileus oſtendit arcum CB, & planum CB eodem, <lb></lb>ſeu æquali tempore percurri; ac pari modo arcum, <lb></lb>& planum GB, & porrò arcum quemlibet non ma<lb></lb>iorem quadrante cum plano vnà terminato. </s> <s id="s.000470">Quin<lb></lb>etiam cùm oſtenderit percurrere globum eodem, ſeu <lb></lb>æquali tempore quoduis planum inter quodlibit cir<lb></lb>cumferentiæ circuli punctum, & infimum punctum, <lb></lb>quale eſt heic B, conſtitutum, vt putà ſemper exæ<lb></lb>quato illi tempori, quo percurritur diameter circuli <lb></lb>eiuſdem perpendicularis; elicitur quoque exinde, vbi <lb></lb>ea omnia plana fuerint in eandem reducta altitudi<lb></lb>nem, diuerſa quidem tempora fore, ſed impetum <lb></lb>nihilominùs parem. </s> <s id="s.000471">Atque eadem quidem oſtendit <lb></lb>præ larus vir Ioannes Baptiſta Balianus Genuenſis, <lb></lb>edito hac dere libello, qui eodem ipſo anno, quo Ga<lb></lb>lilei Liber prodijt, argumento ſumpto ab ipſis pen<lb></lb>dulorum vibrationibus: ſed, vt præmonui, nihil eſt <lb></lb>neceſſe maiorem Galilei Poſtulato aſſerere fidem, <lb></lb>quàm ipſe aſſertam voluerit; dum eatenùs ſolùm <lb></lb>adhibendam petijt, quatenus deductæ ex eo conclu<lb></lb>ſiones cum experientia conſentirent. </s> </p> <p type="main"> <s id="s.000472">XVIII. </s> <s id="s.000473">Id prætereo, quod ſubiicis, ex aſcenſu <lb></lb>globi ad eandem altitudinem, non ſatis rectè colli<lb></lb>gi impetus æqualitatem; quoniam id aduerſaretur <lb></lb>recitandæ tuæ rationi, atque experientiæ: vti & dum <lb></lb>cauſſam petis ex eo, <emph type="italics"></emph>quòd, quò circulus minor eſt, èo<emph.end type="italics"></emph.end><pb pagenum="30" xlink:href="028/01/070.jpg"></pb><emph type="italics"></emph>deſcenſus procliuior, faciliorque, & aſcenſus difficilior vi<lb></lb>deatur:<emph.end type="italics"></emph.end> id repugnaret tum compenſationi, aduerſus <lb></lb>quam nihil obiicis, inter breuitatem, & decliuita<lb></lb>tem ſpatij; tum familiari experientiæ de rebus deor<lb></lb>sùm impactis, quæ impetu pari deiectæ tantò emer<lb></lb>gunt altiùs, quantò incidentia eſt magis perpendi<lb></lb>cularis. </s> <s id="s.000474">Attingo ergo potiùs id, quod ſupereſt, <lb></lb>dum id ſugillas, quod Galileus ſe eſſe ſæpiùs exper<lb></lb>tum ait, <emph type="italics"></emph>tum globum ferreum per aërem cadentem, tum <lb></lb>globum æneum per excauatum in longiore tigillo alueolum, <lb></lb>in quacumque tigilli ſupra horizontem eleuatione deſcenden<lb></lb>tem, perpetuò tantum præcisè temporis in deſcenſu per pri<lb></lb>mum totius percurrendi spatij quadrantem, quantum in <lb></lb>trium reliquorum decurſu inſumpſiſſe: ex quo ſine dubio con<lb></lb>ſequens eſſet, ſpatia æqualibus temporibus decurſa in ea <lb></lb>eſſe ratione, quæ reperitur inter numeros impareis ab vnita<lb></lb>te procedenteis.<emph.end type="italics"></emph.end></s> <s id="s.000475"> Nimirùm, vt oſtendas ea, quæ ex iſtis <lb></lb>quaſi principiis conſequuntur, aut inferuntur, eſſe ip<lb></lb>ſis certiora, aut cuidentiora non poſſe: <emph type="italics"></emph>Id,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>tot <lb></lb>erroribus obnoxium eſt, & exploratu adcò difficile, vt nihil <lb></lb>inde certi concludi poſſe videatur.<emph.end type="italics"></emph.end></s> <s id="s.000476"> Enimverò, vtcum<lb></lb>que experiundi modus difficilis ſit, obnoxiuſque er<lb></lb>roribus; non idcircò tamen experimentum conuin<lb></lb>citur falſum. </s> <s id="s.000477">Tuum certè illud de Libra, cui totus <lb></lb>poſteà inniteris, quot quæſo, vel te deducente, er<lb></lb>roribus obnoxium eſt? </s> <s id="s.000478">quàm exploratu difficile? </s> <s id="s.000479">& <lb></lb>ipſum tamen falſum non habes? </s> <s id="s.000480">Cùm profectò illo <lb></lb>teſtetur ſe ſaltem centies rem exploraſſe, & experi<lb></lb>mentum ſemper ita ſucceſſiſſe, vt vix vlla vnquam <lb></lb>differentiola interceſſerit; videri poteſt non eſſe tua <pb pagenum="31" xlink:href="028/01/071.jpg"></pb>ſatis idonea refutatio, niſi teſteris te eſſe rem, aliquo<lb></lb>ties ſaltem, accuratiſſimè expertum, ac ipſam falſam <lb></lb>deprehendiſſe: aut rationem certè congruam afferas, <lb></lb>qua impoſlibilem demonſtres. </s> <s id="s.000481">Et tamen, neque te <lb></lb>vel ſemel ipſam exploraſſe, falſamque comperiſſe di<lb></lb>cis, neque vllam rationem profers: ſed cauſaris ſolum<lb></lb>modo explorandi difficultatem; quam & repetis, <lb></lb>dum poſtquam retuliſti tempora ab illo notata, no<lb></lb>tatis nempe, expenſiſque ponderibus aquæ, quæ è <lb></lb>clepſydra interim fluxiſſet: <emph type="italics"></emph>Quippe nemo,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>non <lb></lb>videt, quàm hic obſeruandi modus incertus ſit, & quàm <lb></lb>difficile, ne dicam impoßibile, tempus vtriuſque illius deſ<lb></lb>cenſus ad exactam menſuram exigere, vel eo maximè no<lb></lb>mine, quòd in tanta celeritate initia, & fines horum mo<lb></lb>tuum ſatis præcisè aduerti, notarique poſſe non videantur.<emph.end type="italics"></emph.end><lb></lb>Sed nihil eſt opus inſiſtam ad arguendum id non <lb></lb>ſufficere; niſi aliunde aut resfactu impoſſibilis de<lb></lb>monſtretur; aut obſeruator probetur fuiſſe malæ fidei, <lb></lb>ac indiligens, & difficultates præcauere neſcius. </s> <s id="s.000482">Ad<lb></lb>derem quemadmodum ipſe rem explorare fuerim <lb></lb>conatus, tum dimiſſo per aërem globo, tum dela<lb></lb>bente globulo per tubulos vitreos etiam orgyiis dua<lb></lb>bus longiores, factoſque nunc magis, nunc minùs de<lb></lb>cliueis, & adnotatis partibus æquis tum ad parietem, <lb></lb>ſecundum quem globus decideret, tum ad vtram<lb></lb>que oram alueoli in tigno excauati, & tubulum quem<lb></lb>que continentis; ac ſimul adhibitis ſociis, qui adno<lb></lb>tarent ſinguli parteis ſingulas, quæ interim pertran<lb></lb>ſirentur, dum ipſe temporis momenta nunc pulſatio<lb></lb>nibus arteriæ, nunc itibus, reditibuſque penduli di-<pb pagenum="32" xlink:href="028/01/072.jpg"></pb>ſtincta, vocibus monoſyllabis cuique illorum ſigilla<lb></lb>tim aſſignatis ſigniſicarem: verùm memini rem ad te <lb></lb>perſcriptam; & circa hæc nimius iam ſum. </s> </p> <p type="main"> <s id="s.000483"><emph type="center"></emph><emph type="italics"></emph>De Experimentis circa ictum, impetumue grauium caden<lb></lb>tium, ad explorandum impetus-ne vt ſpatium increſcat.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000484">XIX. </s> <s id="s.000485">Venio igitur ad Poſterius caput, ſecun<lb></lb>damue partem tuæ Diſſertationis; in qua ſcilicet re<lb></lb>cepiſti te veram, ac certam de Motu accelerato ſcien<lb></lb>tiam falſæ, ac incertæ Galileanæ ſubſtituturum; & in <lb></lb>qua profeſſus te iterùm omnia, quæ ab illo conſcri<lb></lb>pta ſunt, falſa, ac inania eſſe demonſtraturum; prouo<lb></lb>cas me primum ad <emph type="italics"></emph>clara, facilia, indubitata experimenta:<emph.end type="italics"></emph.end><lb></lb>tametſi ego tenuitatis conſcius perſonam Arbitri, lu<lb></lb>diciſque, quam mihi humaniſſimè iteratò defers, re<lb></lb>cuſo; iteratò profeſſus nihil aliud à me, quàm rationes <lb></lb>quaſdam dubitandi exſpectari poſſe. </s> <s id="s.000486">Et <emph type="italics"></emph>prima qui<lb></lb>dem experientia petitur,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>ex impetu, quo globus, <lb></lb>aut graue aliud corpus quodcumque per aërem sponte natu<lb></lb>ræ deorsùm cadit, ac percutit. </s> <s id="s.000487">Indubitatum enim eſt,<emph.end type="italics"></emph.end><lb></lb>pergis, <emph type="italics"></emph>quod ipſemet<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus paßim agnoſcit, tantam præ<lb></lb>ciſe percutientis corporis eſſe velocitatem, quantus impetus, <lb></lb>quantaque ipſa percußio fuerit. </s> <s id="s.000488">Impetus enim omnis, & <lb></lb>percußio ex velocitate est; imò impetus ipſe velocitas est, <lb></lb>nulloque hæc abinuicem diſcrimine dirimuntur, vt meritò, pro<lb></lb>inde, qua ratione accreſcit velocitas, eadem impetus, & per<lb></lb>cußio augeantur.<emph.end type="italics"></emph.end></s> <s id="s.000489"> Hactenus nihil eſt, quod non probem. <lb></lb></s> <s id="s.000490">Proſequeris autem: <emph type="italics"></emph>At facilè experientiâ conſtat corpus <lb></lb>graue quodcumque ex qualibet altitudine per aërem cadens, <lb></lb>& percutiens, vt libet, perpetuò ex altitudine dupla duplo<emph.end type="italics"></emph.end><pb pagenum="33" xlink:href="028/01/073.jpg"></pb><emph type="italics"></emph>præcisè ampliùs, & ex tripla, quadrupláue diſtantia, triplo, <lb></lb>quadruplóue fortiùs percutere: velocitas igitur quoque ex <lb></lb>altitudine dupla, duplò maior eſt, & tripla, aut quadrupla, <lb></lb>ſi tripla, quadrupláue altitudo ſuerit: ac proinde velocitas, <lb></lb>spatiis æqualibus, non autem æqualibus temporibus, æqualia <lb></lb>momenta acquirit.<emph.end type="italics"></emph.end></s> <s id="s.000491"> Quæſo verò heic patere, religioſiſ<lb></lb>ſimè Vir, me meam teſtari hebetudinem; neque enim <lb></lb>quod tu aſſumis, <emph type="italics"></emph>facilè experientiâ conſtare,<emph.end type="italics"></emph.end> mihi vllà <lb></lb>prorsùs experientiâ conſtat; neque tu vllam ſpecia<lb></lb>lem affers, ex qua res, vt tibi, ita mihi conſtet. </s> <s id="s.000492">Ac <lb></lb>deducis quidem deinceps, quaſi ſecundam experien<lb></lb>tiam, id, quod in Libra expertus es: ſed interim circa <lb></lb>hanc primam, cæcutio planè, neque agnoſco, qui <lb></lb>rem facilè exploraris. </s> <s id="s.000493">Et exploraſſe tamen quis hæ<lb></lb>reat, quandò iſthæc ſubiicis? <emph type="italics"></emph>Experientiam hanc Ga<lb></lb>lileus, nullo (vt credibile eſt) facto ipſius periculo, tanquam <lb></lb>falſam, atque impoßibilem, eodem paralogiſmo re-<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.073.1.jpg" xlink:href="028/01/073/1.jpg"></figure><lb></lb><emph type="italics"></emph>iecit, quo definitionem motus accelerati vulgò re<lb></lb>ceptam, & ex eadem experientia ſine dubio dedu<lb></lb>ctam, conatus eſt reuellere. </s> <s id="s.000494">Si ex altitudine dupla, <lb></lb>inquit, duplò maior percußio eſt, vt puta ex A du<lb></lb>pla eius, quæ ex B, erit & velocitas dupla. </s> <s id="s.000495">At <lb></lb>velocitas dupla eſſe non poteſt, niſi graue, æquali, <lb></lb>imò eodem tempore, totum spatium AC, & di <lb></lb>midium eius AB percurrat, quod tamen eſt impoßibile. <lb></lb></s> <s id="s.000496">Nec percußio igitur, nec velocitas dupla eſt, ex altitudine <lb></lb>dupla. </s> <s id="s.000497"> Doleo equidem virum non ignobilem, in re tam <lb></lb>obvia, & facili adeò turpiter deluſum eſſe; mirorque item <lb></lb>vehementer tales, támque apertos eius errores, non modò à <lb></lb>nenune hactenus eſſe reprehenſos, ſed tanquam prima<emph.end type="italics"></emph.end><pb pagenum="34" xlink:href="028/01/074.jpg"></pb><emph type="italics"></emph>ſcientiæ principia, à viris etiam eruditis eſſe receptos.<emph.end type="italics"></emph.end><lb></lb>Quandò, inquam, hæc ſubiicis, nemo profectò fa<lb></lb>cilè hæreat, qum ipſe, expertus, illa videris, quæ <lb></lb>neque Galileus, neque alij viderunt. </s> </p> <p type="main"> <s id="s.000498">XX. </s> <s id="s.000499">Quod meattinet; cùm lapidem video ex vna, <lb></lb>ex duabus, ex tribus, ex quatuor orgyiis cadentem in <lb></lb>terram; agnoſco quidem eſſe ictum, atque idcircò <lb></lb><expan abbr="impetũ">impetum</expan>, velocitatem que maiorem ex duabus orgyiis, <lb></lb>quàm ex vna, ex tribus, quàm ex duabus, ex quatuor <lb></lb>quàm ex tribus; verùm eſſe duplò præcisè maiorem <lb></lb>ex duabus, quàm ex vna, triplò ex tribus, quadruplò <lb></lb>ex quatuor, nulla penitùs ratione agnoſco. </s> <s id="s.000500">Neque <lb></lb>enim poſſum id diſpicere ex cauitate in terram facta, <lb></lb>aut penetratione in ipſam; quoniam neque lapis du<lb></lb>plò profundiùs cauat, penetratque ex dupla altitudine, <lb></lb>aut triplò ex tripla; neque cognitus eſt aut gradus <lb></lb>reſiſtentiæ, quo talis terra obnititur; aut progreſſus, <lb></lb>quo creſcit reſiſtentia, dum quò inferiùs tenditur, <lb></lb>eò partes terræ minùs ſeu deorſum, ſeu in latera ce<lb></lb>dere, compelli, ac ſubire poſſunt: vt habita proinde <lb></lb>ratione huius reſiſtentiæ, colligere valeam id, quod <lb></lb>ad duplam penetrationem ex altitudine dupla dceſt, <lb></lb>non aliunde eſſe, quàm ex huiuſmodi reſiſtentia. </s> <s id="s.000501">Sic <lb></lb>cùm video fiſtucam in palum delapſam ex ſimplici, <lb></lb>dupla, aut tripla altitudine: quandoquidem neque <lb></lb>video palum defigi profundiùs in terram, duplo qui<lb></lb>dem ex dupla, aut triplò ex tripla altitudine; neque <lb></lb>perſpectum habeo quo gradu, in qualibet profundi<lb></lb>tatis parte ipſi vrgenti reſiſtatur; aduerto quidem <lb></lb>maiorem ictum, maioremque impetum, ac veloci-<pb pagenum="35" xlink:href="028/01/075.jpg"></pb>tatem eſſe ex altitudine dupla, quàm ex ſimplici; item<lb></lb>que ex tripla, quàm ex dupla, &c. </s> <s id="s.000502">At eſſe illam du<lb></lb>plo præcisè maiorem ex dupla, triplò ex tripla, &c. <lb></lb></s> <s id="s.000503">nulla penitùs ratione perſpicio. </s> <s id="s.000504">Sic, dum graue <lb></lb>quoduis ex dupla, triplaue altitudine decidens rem <lb></lb>ſubiectam commouet, contundit, confringit: Sic, dum <lb></lb>cadens in cuneum ſcindendo ligno accommodatum, <lb></lb>ipſum compellit, adigit, figit: Sic, dum cadens in ip<lb></lb>ſam manum, aliámue partem corporis, ipſam vrget, <lb></lb>deprimit, lædit: Sic, dum alia huiuſmodi diuerſimo<lb></lb>dè peraguntur; maiorem quidem ſemper ictum, ſine <lb></lb>impetum, ac velocitatem ex altiore caſu fieri nullus <lb></lb>hæreo; at ex caſu duplò altiore duplò maiorem fieri, <lb></lb>triplò ex triplo, &c. </s> <s id="s.000505">qui diſcernam prorsùs non habeo. <lb></lb></s> <s id="s.000506">Quocirca beaſſes me valdè, ſi experientiam, aut ſal<lb></lb>tem modum experiundi ſubindicaſſes; cùm dicas & <lb></lb>rem experientiâ in graui quocumque facilè conſtare; <lb></lb>& Galileum, cæteroſque eruditos viros coniicis ſic <lb></lb>fuiſſe ſocordeis, vt nullum ipſius periculum fecerint; <lb></lb>feciſſe autem eos, qui vulgarem definitionem accele<lb></lb>rati motus tradiderunt primi. </s> </p> <p type="main"> <s id="s.000507">XXI. </s> <s id="s.000508">Addo videri poſſe me non abſque ratio<lb></lb>ne hacce de re ambigere; & coniicere ictum, percuſ<lb></lb>ſionemque, atque idcircò impetum, velocitatemque <lb></lb>maiorem duplò non haberi, niſi ex altitudine qua<lb></lb>drupla; triplum, niſi ex nonupla; quadruplum, niſi <lb></lb>ex ſexdecupla, atque ita porrò iuxta numerorum qua<lb></lb>dratorum ſeriem. </s> <s id="s.000509">Nam Primò, ſit vas cylindricum <lb></lb>erectum, & continens aquam ad certam altitudi<lb></lb>nem, exempli cauſsâ vnius pedis: Certum eſt aquam <pb pagenum="36" xlink:href="028/01/076.jpg"></pb>in fundo ſubſtantem vrgeri, ac premi à ſuper exſtan<lb></lb>te (& ab ipſa quidem ſuperficie) vt perſpicuum fit vel <lb></lb>ex vehementia, qua exſilire deprehenditur, forami<lb></lb>ne ad baſin aperto. </s> <s id="s.000510">Aperiatur ergo foramen, & ſu<lb></lb>perfusâ leniter aquâ, ita vt contineatur ſemper ad <lb></lb>eandem altitudinem, excipiatur aqua, quæ interim <lb></lb>effluet, dato tempore, v. c. ſextantis minuti, ac ſit <lb></lb>illius menſura certa, exempli gratiâ, congius. </s> <s id="s.000511">Vt <lb></lb>deinde tempore eodem, & per idem foramen exſi<lb></lb>liant duo congij, & aqua proinde ſit duplò compreſ<lb></lb>ſior, ad quam nam vſque altitudinem adaugendus <lb></lb>erit, complenduſve cylindrus? </s> <s id="s.000512">Ad duplam-ne ſolum? <lb></lb></s> <s id="s.000513">Non ſanè, ſed omninò ad <expan abbr="quadruplã">quadruplam</expan>. </s> <s id="s.000514">Et vt exſiliant <lb></lb>tres, ad triplam-ne? </s> <s id="s.000515">Haud-quaquam profectò, ſed <lb></lb>ad nonuplam. </s> <s id="s.000516">Et vt exſiliant quatuor, ad quadru<lb></lb>plam ne? </s> <s id="s.000517">Minimè gentium, ſed ad ſexdecuplam. </s> <s id="s.000518">Quin <lb></lb>poterit etiam aliunde res facillimo negotio notari, ſi <lb></lb>repleto ſiue ad labium, ſiue ad certam vſque altitudi<lb></lb>nem cylindro, & aperto foramine, totáque aqua vno <lb></lb>tenore, nullamque refundendo effluente, notentur in <lb></lb>vaſe aquæ decrementa æqualibus temporibus facta. <lb></lb></s> <s id="s.000519">Quippe ſi interuallum vltimi decrementi fuerit vnius <lb></lb>v. c. pedis, erit interuallum penultimi trium, ante<lb></lb>penultimi quinque, antecedentis ſeptem, ac ita ſem<lb></lb>per procedendo per ſuccedenteis impareis: vnde & ſi <lb></lb>primi temporis initio fuerit altitudo pedum ſexde<lb></lb>cim, erit initio ſecundi nouem, tertij quatuor, quar<lb></lb>ti vnius. </s> <s id="s.000520">Cùm exſilitio verò aquæ continenter fiat <lb></lb>ex continente impetu, quo à ſuperſtante vigetur, & <lb></lb>impetus iſte nihil differat à continente velocitate, <pb pagenum="37" xlink:href="028/01/077.jpg"></pb>qua aqua ſuperſtans continenter incumbit, ac premit; <lb></lb>An-non planum eſt intelligere impetum, ac velocita<lb></lb>tem duplò maiorem fieri non ex altitudine dupla, <lb></lb>ſed penitùs ex quadrupla; triplo non ex tripla, ſed ex <lb></lb>nonupla, & ita deinceps? </s> <s id="s.000521">Secundò, ſi alligatus vno <lb></lb>ſui extremo ad parietem funis prælongus, altero ex<lb></lb>tremo dependeat ex fulcro, ac appenſo pondere certo, <lb></lb>v. c. vnius libræ, tenſione ſit leni inter ipſa extrema: <lb></lb>verò digitis verò, ita abducatur, vt vltro citróque horizon<lb></lb>taliter vibretur, ſeu eat, ac redeat certo tempore (erunt <lb></lb>autem itus, redituſque omnes æqui-temporanei, ſeu <lb></lb>tam primi, quam vltimi, tam longi, quàm breues <lb></lb>eiuſdem prorsù, durationis) ſitque tempus tantum, <lb></lb>quantum interſtitium ab vna artenæ pulſatione ad <lb></lb>aliam Vt fiat funis duplò intenſior, & itus, redituſ<lb></lb>que ipſius euadant duplò velociores, hoc eſt æquali <lb></lb>tempore duo; quantum, putas, erit ponderis adden<lb></lb>dum? </s> <s id="s.000522">An duplum? </s> <s id="s.000523">Non; ſed quadruplum. </s> <s id="s.000524">Et vt <lb></lb>fiat triplo, ſintque adeo itus redituſque eodem tem<lb></lb>pore triplò velociores, ſeu plures: an triplum dum<lb></lb>taxat' Nequaquam, verum nonuplum. </s> <s id="s.000525">Et vt qua<lb></lb>druplò, an quadruplum? </s> <s id="s.000526">Haud certè, ſed ſexdecu<lb></lb>plum. </s> <s id="s.000527">Cùm pondera porro æqualia primo ſuperad<lb></lb>dita ſe perinde habeant ad creandum hanc velocita<lb></lb>tem, ac partes æquales altitudinis, per quas pondus <lb></lb>demittitur: An non intelligi rursùs licet, quemadmo<lb></lb>dum velocitas non acquiritur duplò maior ex dupli<lb></lb>cato pondere, ſed planè ex quadruplicato; ita duplam <lb></lb>quoque non ex duplicata altitudine, ſed ex quadru<lb></lb>plicata acquiri? </s> </p> <pb pagenum="38" xlink:href="028/01/078.jpg"></pb> <p type="main"> <s id="s.000528">XXII. </s> <s id="s.000529">Eſt etiam Tertiò heic repetendum, quod <lb></lb>iam antè dixi de globis ad fila appenſis, & liberè ire, <lb></lb>redireque permiſſis. </s> <s id="s.000530">Videlicet globus appenſus ex <lb></lb>vno v. c. pede, dup ò quidem plureis vibrationes per<lb></lb>agit, quam appenſus ad quatuor, triplo, quàm ap<lb></lb>penſus ad nouem, quadruplo, quàm appenſus ad ſex<lb></lb>decim; ſed interim tamen ſecundus ſpatium conficit <lb></lb>dup ò maius, quàm primus, tertius triplò, quartus <lb></lb>quadruplò eodem tempore; ac velocitas interim ac<lb></lb>quiſita, impetuſque ad perpendiculum expreſſus, non <lb></lb>vt ſpatium pertranſitum, ſed vt tempus elapſum ſe <lb></lb><figure id="id.028.01.078.1.jpg" xlink:href="028/01/078/1.jpg"></figure><lb></lb>habet. </s> <s id="s.000531">Ego certè rem ſic intelligo. </s> <s id="s.000532">Sit linea per<lb></lb>pendicularis AB in pariete ducta, diuiſaque in ſex<lb></lb>decim pedes; ac ſint appenſi quatuor globi, vnus <lb></lb>ad primum, alius ad quartum, tertius ad nonum, <lb></lb>poſtremus ad decimumſextum. </s> <s id="s.000533">Siquidem tametſi <pb pagenum="39" xlink:href="028/01/079.jpg"></pb>inter experiundum applicari diuerſis ſeorſim lineis <lb></lb>debeant, ne inter mouendum ſeſe interturbent: om<lb></lb>neis tamen ſchemate vno repræſentari nihil prohibet. <lb></lb></s> <s id="s.000534">Ducantur heinc inde duæ lineæ angulum ſtatuentes <lb></lb>in A, qui à perpendiculo biſecctur, ſintque v. c. IA, <lb></lb>KA; & centro A; agantur inter illas arcus CD ad <expan abbr="pri-mũ">pri<lb></lb>mum</expan> pedem, EF ad quartum, GH ad nonum IK ad <lb></lb>ſextum-decimum; qui ſimiles proinde erunt, pares <lb></lb>videlicet portiones ſuotum cuiuſque circulorum eo<lb></lb>dem angulo menſuratæ. </s> <s id="s.000535">Ducantur & ſubtenſæ ar<lb></lb>cuum; & adnotentur quaſi ſagittæ, ſeu appellati ſinus <lb></lb>verſi, lineæ nimirùm LM, NO, PQ, RB; cùm <lb></lb>ſint altitudines, quibus globi delabuntur ex linea AI <lb></lb>(vbi ad illam abducti, ex ea dimittuntur) in ipſum <lb></lb>perpendiculum; primus putà ex C in M, ſecundus <lb></lb>ex E in O, tertius ex G in Q, quartus ex I in B. <lb></lb></s> <s id="s.000536">Abducantur proinde globi ad memoratam lineam <lb></lb>AI, vt ſuas, exinde dimiſſi, vibrationes peragant, ad <lb></lb>lineam AK, aut quam-proximè terminandas. </s> <s id="s.000537">Nam & <lb></lb>quamuis quilibet globus, ſeu longiùs, ſeu breuiùs di<lb></lb>miſſus, & ſeu moueri incipiat, ſeu deſinat, vibrationes <lb></lb>omneis æqui-temporaneas ſortiatur, temporibuſve <lb></lb>paribus perficiat; proportio tamen ſemper eſt, quoties <lb></lb>ſub æquali, eodemue angulo accipiuntur. </s> <s id="s.000538">Dimittan<lb></lb>tur & globi ſimul, ac peruenire concipiantur ad vſ<lb></lb>que perpendiculum. </s> <s id="s.000539">Quoniam tunc vt filum AO <lb></lb>quadruplum eſt fili AM, & filum AQ nonuplum, <lb></lb>filum AB ſexdecuplum; ita altitudo NO dupla eſt <lb></lb>altitudinis LM, & altitudo PQ nonupla, altitudo <lb></lb>RB ſexdecupla; quo pacto interuallum quoque per-<pb pagenum="40" xlink:href="028/01/080.jpg"></pb>tranſitum EO quadruplum eſt ſpatij CM, & ſpa<lb></lb>tium GQ nonuplum, ſpatium IB ſexdecuplum: Id<lb></lb>circò, cùm aliunde obſeruemus tempus, quo globus <lb></lb>ſecundus peruenit ad O, eſſe duplum temporis, quo <lb></lb>primus peruenit ad M, & tempus, quo tertius ad Q, <lb></lb>triplum; tempus, quo quartus ad B, quadruplum; Id<lb></lb>circò, inquam, intelligimus, impetum, ſeu velocita<lb></lb>tem, quæ acquiritur ex E, aut N in O, & ex G, aut <lb></lb>P in <expan abbr="q;">que</expan> & ex I, aut R in B, pari ratione ſe habere <lb></lb>ad velocitatem acquiſitam ex C, aut L, in M, qua <lb></lb>ſe habet impetus, ſeu velocitas, quæ acquiritur ex A <lb></lb>in O, in Q, in B, ad velocitatem acquiſitam ex A in <lb></lb>M; ſeu comparando oppoſitè, vt illam ad illam, ſic <lb></lb>iſtam ad iſtam. </s> <s id="s.000540">Hoc autem habito, quoniam im<lb></lb><figure id="id.028.01.080.1.jpg" xlink:href="028/01/080/1.jpg"></figure><lb></lb>petus, ſeu velocitas acquiſita ex E in O non eſt ac<lb></lb>quiſitæ ex C in M quadrupla, ſed dupla; & acquiſita <pb pagenum="41" xlink:href="028/01/081.jpg"></pb>ex G in Q, non nonupla eiuſdem, ſed tripla: & ac<lb></lb>quiſita ex I in B, non ſexdecupla, ſed quadrupla eſt: <lb></lb>quatenus quidem experiundo obſeruare licuit, con<lb></lb>ſtitutam pilam ſupra planum libellatum, appoſitum<lb></lb>que ad M, ad O, ad Q, ad B, dum percuteretur, pro<lb></lb>pellereturque à globis incurrentibus, aſſequi velocita<lb></lb>tem, excurrereque, non iuxta numeros quadratos, <lb></lb>quales ſunt ſpatiorum CM, EO, GQ, IB; ſed iuxta <lb></lb>radices ipſorum, qualia ſunt & tempora, vnum, duo, <lb></lb>tria, quatuor. </s> <s id="s.000541">Quamobrem & fuit iteratò procliue <lb></lb>intelligere percuſſionem quoque à re ſecundum per<lb></lb>pendiculum cadente factam, ſequi rationem non <lb></lb>quadratorum, ſeu ſpatiorum, ſed radicum, ſeu tem<lb></lb>porum; atque ita, quò cadens graue vehementiùs <lb></lb>feriat duplò, triplò, quadruplò, cadere debere ex al<lb></lb>titudine non duplò, triplò quadruplò; verùm, quadru<lb></lb>plò, nonuplò, atque ſexdecuplò maiore. </s> </p> <p type="main"> <s id="s.000542"><emph type="center"></emph><emph type="italics"></emph>De Experimento in Bilance facto ac aliud reuera probante, <lb></lb>quàm velocitates eſſe ſicut spatia.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000543">XXIII. Verumtamen, hiſce dimiſſis, acceden<lb></lb>dum eſt ad ſecundam, peculiaremve experientiam, <lb></lb>cui totam ſcientiam ſuper-exſtruis, & de qua in hunc <lb></lb>modum præfaris. <emph type="italics"></emph>Atque, vt quam tibi promiſi expe<lb></lb>rientiam, cum fœnore etiam exhibeam, adiungam & aliam, <lb></lb>à nullo mortalium hactenus obſeruatam, quæ & priorem <lb></lb>perfectißimè includat, & non rationem ſolùm, quâ celeritas <lb></lb>in naturali deſcenſu grauium augetur, ſed eiuſdem quoque <lb></lb>celeritatis pene incredibilem modum, ac menſuram, exactiſ-<emph.end type="italics"></emph.end><pb pagenum="42" xlink:href="028/01/082.jpg"></pb><emph type="italics"></emph>ſimè determinet.<emph.end type="italics"></emph.end></s> <s id="s.000544"> Pergis declarando ecqua illa ſie <lb></lb><emph type="italics"></emph>Aio igitur, ita eſſe à natura conſtitutum, vt globus quilibet, <lb></lb>tuiuſcumque materiæ, ex vnius diametri altitudine cadens, <lb></lb>duplum ſui ponderis, hoc eſt, præter pondus quod ſine im<lb></lb>petu in æquilibrio retineret, aliud ſibi æquale attollat; & <lb></lb>ex altitudine duarum diametrorum, triplum; ex tribus dia<lb></lb>metris, quadruplum; & ita deinceps: adeo vt ex quauis <lb></lb>altitudine cadens, ſemper (vltra æquilibrium) toties pro<lb></lb>prium pondus multiplieatum attollat, quot in tota, vnde <lb></lb>cadit, altitudine diametri continentur.<emph.end type="italics"></emph.end></s> <s id="s.000545"> Subiicis, rem exag<lb></lb>gerando, <emph type="italics"></emph>Mirum ſanè quòd globus, cuius figuram, vt<lb></lb>pote ſimplicißimam, capacißimàmque, natura ſingulariter <lb></lb>amare videtur, menſuram, ac modum, tam velocitatis <lb></lb>motus in deſcenſu grauium, quàm virtutis eius motricis, <lb></lb>quæ in eadem velocitate continetur, ſuâ nobis diametro exhi<lb></lb>beat: adeo vt ex decem, aut centum diametrorum altitudine <lb></lb>decidens, eum acquirat impetum, qui attollendis decem, aut <lb></lb>centum ſimilibus globis, in altera lance impoſitis, ſufficere <lb></lb>poßit, ſi materiæ conditio id patiatur.<emph.end type="italics"></emph.end></s> <s id="s.000546"> Addis & quid <lb></lb>ipſe obſeruaueris. <emph type="italics"></emph>Expertus ſum ego,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>globum plum<lb></lb>beum vnius vnciæ, ex altitudine ſex pedum, ſiue dia<lb></lb>metrorum centum quatuordecim cadentem, vncias toti<lb></lb>dem vltra æquilibrium, hoc est, libras ſeptem, & <lb></lb>vncias tres in altera lance impoſitas, ſuo impetu eleuaſſe, <lb></lb>non ſine ingenti eorum qui præſentes aderant admiratione, <lb></lb>ac stupore.<emph.end type="italics"></emph.end></s> <s id="s.000547"> Tum & hæc habes. <emph type="italics"></emph>Porrò ſi id in paucis <lb></lb>diametris experiri placuerit, non admodùm magna opus <lb></lb>erit diligentia: at ſi è maiore altitudine idem tentare pla<lb></lb>cuerit, tum in hac, vt in cæteris Phyſicis experientiis,<emph.end type="italics"></emph.end><pb pagenum="43" xlink:href="028/01/083.jpg"></pb><emph type="italics"></emph>accurata, ac ſolerti diligentia, atque industria, variis incom<lb></lb>modis occurrendum erit; vt ne fortè ex conditione materiæ <lb></lb>effectus impediatur, nóſque ex errore, aut ex ignorantia, id <lb></lb>impoßibile arbitremur, quod ſolius materiæ vitio, ac defectu, <lb></lb>in certis circumſtantiis minùs ex animi ſententia ſuccedit.<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.083.1.jpg" xlink:href="028/01/083/1.jpg"></figure><lb></lb>Paginas de<lb></lb>inceps ali<lb></lb>quot inſumis, <lb></lb>vt ea incom<lb></lb>moda deſcri<lb></lb>bas, & mo<lb></lb>dum, quo il<lb></lb>lis occurra<lb></lb>tur, tradas; <lb></lb>depicta ſcili<lb></lb>cet Bilanco, <lb></lb>quæ ipſiſſi<lb></lb>ma heic ap<lb></lb>pingitur, agi<lb></lb>na putà im<lb></lb>mobili, & al<lb></lb>tera lancium <lb></lb>ſuſpenſa in <lb></lb>aëre, altera <lb></lb>ſupra men<lb></lb>ſam CD qui<lb></lb>eſcente, cum <lb></lb>impoſito pondere, ac ſpeculatore adſtante, qui ad <lb></lb>quamque vel minimam eius elationem attendat (id<lb></lb>que dum globus manu H dimiſſus incidit in alterius <pb pagenum="44" xlink:href="028/01/084.jpg"></pb>medium, directione circuli G, cui ob æquilibrium <lb></lb>reſpondet conſimilis F) ac inſuper vtraque lance ca<lb></lb>tenulis ferreis à ſcapo AB per intermedios circulos, <lb></lb>trianguloſ-ve, dependente. </s> <s id="s.000548">Denique autem ſubiun<lb></lb>gis, <emph type="italics"></emph>Tam apertam eſſe eius rei demonſtrationem, vt nul<lb></lb>lus,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>intellectus refragari poſſe videatur; dum ſemel <lb></lb>conſtet (quod quilibet ſine tanto apparatu, tantáque diligen<lb></lb>tia facillimè experiri potest) globum quemcumque, ex vnius <lb></lb>diametri altitudine, poſſe (vltra æquilibrium) pondus ſibi <lb></lb>æquale, & ex duabus diametris duplum pondus attollere.<emph.end type="italics"></emph.end><lb></lb>Prætereo autem demonſtrationem non alio nixam <lb></lb>fundamento, quàm ipsâ experientiâ à te ſuppoſitâ; <lb></lb>prætereoque item, quod iterùm ſubdis, <emph type="italics"></emph>Illud quoque <lb></lb>pari certitudine constare, quod antè dictum eſt, nihil ad pro<lb></lb>poſitionis veritatem, atque euidentiam opus eſſe, vt ex al<lb></lb>tiore diſtantia, tantóque apparatu experientia inquiratur, <lb></lb>quæ ex aliquot diametrorum altitudine pluſquam abundè; <lb></lb>ac facillimè habeatur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000549">XXIV. </s> <s id="s.000550">Et tale eſt quidem tuum experimentum. <lb></lb></s> <s id="s.000551">Ego autem, humaniſſime Vir, gratiſſimo primùm <lb></lb>animo complector liberaliſſimum erga me affectum; <lb></lb>ac deinde etiam tibi gratulor, quod primus morta<lb></lb>lium excogitâris quemadmodum negotium viſum <lb></lb>difficile reuocari ad trutinam poſſet. </s> <s id="s.000552">Nempe quan<lb></lb>tumvis res non videatur pro tua ſtare ſententia; fuit <lb></lb>tamen tua ſolertia dignum, id in mentem inducere, <lb></lb>vnde examen improbum, quacumque ex parte huiuſ<lb></lb>modi foret, poſſet caſtigari. </s> <s id="s.000553">Ac ſi res quidem ſic ſe <lb></lb>haberet, vt enarrati abs te videtur, reputari poſſet <lb></lb>penitus confecta; nullumque eſſet dubium, quin <pb pagenum="45" xlink:href="028/01/085.jpg"></pb>Galilei ſcientiam falſitatis conuinceres, tuam tan<lb></lb>quam veram ſubſtitueres iure: at res potius ita ſe ha<lb></lb>bet, meo quidem iudicio, vt Galileanam confirmare, <lb></lb>euertere tuam omninò videatur. </s> <s id="s.000554">Ecquid-nam verò, <lb></lb>inquies, Tu igitur meus amicus mihi referenti non <lb></lb>credis; ac virum me habes malæ fidei, dum hæres, id<lb></lb>ne verum ſit, quod ipſe me fuiſſe expertum enarro? <lb></lb></s> <s id="s.000555">Abſit hoc à me, optime virorum, qui habeo te po<lb></lb>tiùs plenum fidei, & ſummo candore, finceriſſima<lb></lb>que ſinceritate viſa narrantem. </s> <s id="s.000556">Sed patietur ſanè <lb></lb>ſinceritas tua, vt, quod ſupereſt, ſi quid erroneum <lb></lb>videbitur, culpam coniiciam aut in quidpiam non <lb></lb>ſatis fortè animaduerſum, vt omnes ſumus homines; <lb></lb>aut, ſi malis, etiam in illos, quorum operâ vſus fueris, <lb></lb>quibuſve referentibus cenſueris pro tua bonitate non <lb></lb>eſſe negandum aſſenſum. </s> <s id="s.000557">Itaque cùm tua verba <lb></lb>relegens, deprehendam te nihil aliud tibi, tanquam <lb></lb>obſeruatum à te vindicare; quàm illud, quod iam re<lb></lb>tuli, <emph type="italics"></emph>Expertus ſum ego globum plumbeum vnius vnciæ ex <lb></lb>altitudine ſex pedum, ſiue diametrorum centum quatuorde<lb></lb>cim cadentem, vncias totidem vltra æquilibrium, hoc eſt li<lb></lb>bras ſeptem, & vncias treis in altera lance impoſitas ſuo <lb></lb>impetu eleuaſſe.<emph.end type="italics"></emph.end></s> <s id="s.000558"> Itemque illud, quod poſteà impedi<lb></lb>menta memorans, <emph type="italics"></emph>Propria,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>experientia ipſe <lb></lb>edoctus ſum, qui adhibita omni induſtria globum vnius vn<lb></lb>ciæ ex altitudine ſex pedum in lancem ſubiectam, viginti <lb></lb>quinque, aut triginta vicibus dimittens, ter ſolùm centrum <lb></lb>attingere, & pondus perfectè attollere potui.<emph.end type="italics"></emph.end> Cùm, in<lb></lb>quam, ita deprehendam, non cauſor tuam fidem, <lb></lb>quam cum perſuaſione aliqua non vera (re familiari <pb pagenum="46" xlink:href="028/01/086.jpg"></pb>hominibus, etiam optimis) ſtare nihil vetat. </s> <s id="s.000559">Cùm ad<lb></lb>dis autem prætereà generale eſſe, vt pro numero dia<lb></lb>metrorum, quibus idem globus dimiſſus abfuerit à <lb></lb>lance, pondera cleuet ſuo paria; quaſi cùm id præ<lb></lb>ſtiterit in certo quodam numero, non valeat citra <lb></lb>illum plureis, vltrà pauciores eleuare; hoc eſt, quod <lb></lb>peto mihi condones, vt dicere liceat, in veritatis gra<lb></lb>tiam, te aut ſatis non attendiſſe, aut alijs etiam ni<lb></lb>miùm credidiſſe. </s> </p> <p type="main"> <s id="s.000560">XXV. </s> <s id="s.000561">Vt ſaltem liceat quid-nam mihi contige<lb></lb>rit, commemorare; Tu ſæpe adeò repetiiſti non eſſe <lb></lb>magno apparatu, magnaque diligentia opus ad <lb></lb>peragendum experimentum, vt niſi argumentis ſu<lb></lb>perioribus fuiſſem oppoſitum perſuaſus, vix induxiſ<lb></lb>ſem in animum (nihil ſcilicet hæſitans, imò hæſitan<lb></lb>di pudore ſuffuſus) periculum facere vllum. </s> <s id="s.000562">Feci <lb></lb>tamen, & ipſa præſertim à te inculcata facilitate in<lb></lb>uitatus; vnde & obuiam primò Bilancen, qua numu<lb></lb>larius ſolebat nuper monetæ argenteæ ſummam ali<lb></lb>quot librarum Marcarum non-numeratam appen<lb></lb>dere, probaréque, aſſumendam duxi. </s> <s id="s.000563">Quoniam ve<lb></lb>rò tu aſſerebas <emph type="italics"></emph>ita à natura eſſe conſtitutum, vt globus <lb></lb>quilibet cuiuſcumque materiæ ex vnius diametri altitudine <lb></lb>cadens, pondus attollat ſibi æquale, præter illud, quod in ęqui<lb></lb>librio ſine impetu retineret,<emph.end type="italics"></emph.end> &c. </s> <s id="s.000564">ideo ſufficere putaui, ſi <lb></lb>globum marmoreum, quem habebam præ manibus, <lb></lb>duorum cum ſextante digitorum pedis Pariſini dia<lb></lb>metro, ac vnciarum proximè decem, Libræ itidem <lb></lb>Pariſinæ pondere, ad experiundum vſurparem. </s> <s id="s.000565">Ap<lb></lb>paratis ergo ponderibus variis, quæ ex æquo cum <pb pagenum="47" xlink:href="028/01/087.jpg"></pb>ipſo feci, appoſui ad lancem in æquilibrio ſuſtenta<lb></lb>tam (à ſuppoſita nempe tabula) duplum eiuſce pon<lb></lb>deris, hoc eſt vncias prope viginti; ac ſubinde elatum <lb></lb>globum vna ſui diametro ſupra fundum alterius lan<lb></lb>cis conſtantis in aëre, placidè in ipſam dimiſi. </s> <s id="s.000566">Tum <lb></lb>autem verum quidem fuit attolli ex ipſius caſu op<lb></lb>poſitam lancem cum ponderis duplo; at quia vidi <lb></lb>interim ipſam ſupra expectatam attolli altitudinem, <lb></lb>idcircò ſtatim duo intellexi, alterum poſſe idem pon<lb></lb>dus ex altitudine minore, alterum poſſe ex ipſa ea<lb></lb>dem, pondus adhûc maius attolli. </s> <s id="s.000567">Et aduocatis cer<lb></lb>tè amicis, qui ad lancis elationem, emotionemve à <lb></lb>tabula, me globum dimittente, attenderent, aut me <lb></lb>attendente globum ipſi dimitterent, res ita ſucceſſit, <lb></lb>vt lanx ſuſtentata cum duplo eodem pondere elata <lb></lb>fuerit dimiſſo globo non modo ex diametro vna, <lb></lb>verùm ex dimidio etiam diametri, etiam ex triente, <lb></lb>quadrante, ſextante, octante, dextante; ac vice verſa, <lb></lb>vt dimiſſo globo ex eadem vnius diametri altitudi<lb></lb>ne, elata lanx fuerit cum impoſito pondere, non <lb></lb>modo duplo, ſed etiam triplo, quadruplo, quin<lb></lb>tuplo, & ampliùs. </s> <s id="s.000568">Experiri etiam conſequenter lu<lb></lb>buit, an ſaltem globus decidens ex duplo altitudinis <lb></lb>(diametrorum ſcilicte duarum) eleuaret duplum eius <lb></lb>ponderis, quod ſummum mox extulerat; ſed longè <lb></lb>ſanè abfuit; ac magis adhûc, vt ex triplo triplum, ex <lb></lb>quadruplo quadruplum. </s> </p> <p type="main"> <s id="s.000569">XXVI. </s> <s id="s.000570">Quandoquidem verò ipſe globum plum<lb></lb>beum vnius vnciæ vſurpâras; ideò talem quoque <lb></lb>vſurpandum cenſui, plumbeum ſcilicet, ac vnius <pb pagenum="48" xlink:href="028/01/088.jpg"></pb>vnciæ Pariſini ponderis, diametro eius deprehenſa <lb></lb>continere digiti beſſem, ac idcircò partem Pariſini <lb></lb>pedis decimam-octauam. </s> <s id="s.000571">Cæterùm idem mihi eue<lb></lb>nit, quod circa globum marmorum; impoſitis enim <lb></lb>in lance ſuffulta duabus vncijs, extulit eas globus <lb></lb>ſenſibiliter non ex altitudine modo diametri vnius, <lb></lb>ſed ex dimidio etiam eiuſdem, etiam ex triente, qua<lb></lb>drante, ſextante, octante, dextante, imò, & ex vncia, <lb></lb>duodecimáve diametri parte. </s> <s id="s.000572">Ac rurſus ex eadem <lb></lb>diametri vnius altitudine, non duas modò extulit <lb></lb>vncias, verùm etiam treis, etiam quatuor, quinque, <lb></lb>ſex, ſeptem, duaſque drachmas inſuper, quadrantem<lb></lb>ve vnius vnciæ. </s> <s id="s.000573">Et cùm experiri iterum placuerit, <lb></lb>an duplum huius ponderis eleuaretur ex caſu globi <lb></lb>à duplo altitudinis, triplumque ex caſu à triplo, &c. <lb></lb></s> <s id="s.000574">deprehendi dimiſſo globo ex diametris duabus alti<lb></lb>tudinis, attolli non duplum, hoc eſt, vncias quatuor<lb></lb>decim cum ſemiſſe; ſed vncias ſolummodò nouem, <lb></lb>cum beſſe, aut dodrante duntaxat. </s> <s id="s.000575">Quo pacto de<lb></lb>inceps ex diametro tertia extulit non triplum, hoc <lb></lb>eſt viginti vnam vncias cum dodrante; ſed vncias <lb></lb>ſolummodò duodecim, ac ferè dimidium; & ex dia<lb></lb>metro quarta extulit, non quadruplum, hoc eſt vn<lb></lb>cias viginti nouem; ſed duplum ſolùm, hoc eſt vn<lb></lb>cias quatuordecim, atque ſemiſſem. </s> <s id="s.000576">Prætereo au<lb></lb>tem, quemadmodum, vt extulit dumtaxat duplum ex <lb></lb>diametris quatuor, ſic etiam deinceps extulerit ſolum<lb></lb>modò triplum ex diametris nouem, & quadruplum, <lb></lb>ex ſexdecim. </s> <s id="s.000577">Adnoto iam ſolùm, licuiſſe ex iſtis in<lb></lb>telligere, poſſe tuam hanc experientiam meritò vocari <pb pagenum="49" xlink:href="028/01/089.jpg"></pb>in dubium; nec poſſe te aſſerere quemlibet globum <lb></lb>ita eſſe à natura comparatum, vt illius diameter ſit <lb></lb>menſura præciſa velocitatis, ſeu impetus, quem inter <lb></lb>cadendum acquirit; ea ſcilicet lege, vt cadens ex dia<lb></lb>metro vna in liberam lancem, attollat ſuffultam, & <lb></lb>præter æquilibrium, ponderis tantumdem, non iti<lb></lb>dem amplius (veluti etiam neque minus, ſi minor <lb></lb>fuerit altitudo) ac deinceps ſic progredi, vt ex dua<lb></lb>bus diametris attollat præcisè duplum, ex tribus tri<lb></lb>plum, ex quatuor quadruplum, ex decem decuplum, <lb></lb>ex centum centuplum, atque ita porrò. </s> </p> <p type="main"> <s id="s.000578">XXVII. </s> <s id="s.000579">At quorſum ergo contigit, inquies, vt <lb></lb>dimiſſus vncialis globus ex altitudine diametrorum <lb></lb>centum, & quatuordecim, vncias totidem eleuârit? <lb></lb></s> <s id="s.000580">Ego profectò id præcisè diuinare non valeo; quan<lb></lb>doquidem tu nullam ſeriem obſeruationum appo<lb></lb>ſuiſti, neque expreſſiſti quid contigerit, ſi quid for<lb></lb>taſſis expertus es citra, vltrave numerum illum. </s> <s id="s.000581">Nam, <lb></lb>ſi ſaltem commemoraſſes ecquid tibi euenerit dimit<lb></lb>tenti globum ex altitudine diametrorum aut centum; <lb></lb>aut octoginta, aut quinquaginta, &c. </s> <s id="s.000582">liceret fortaſ<lb></lb>ſis rem coniicere; at tale nihil recitaſti, neque expli<lb></lb>cuiſti quali pondere, pedeve vſus fueris; cùm ſi Pa<lb></lb>riſino quidem, videri poſſis hallucinatus quinta, aut <lb></lb>ſexta ponderis parte; quatenus globi diameter fuit <lb></lb>tibi duntaxat decima-nona pedis pars, quam ego de<lb></lb>prehendi decimam-octauam. </s> <s id="s.000583">Vtcumque fuerit; ex ijs, <lb></lb>quæ ſunt à me obſeruata, deducitur, quò diametri <lb></lb>ſiunt multiplicatiores, eò ſingulas ſuper-additas at<lb></lb>tollere minus ſuper-additi ponderis; quandò ex <pb pagenum="50" xlink:href="028/01/090.jpg"></pb>ſecunda non attollitur duplum, ex tertia triplum, &c. <lb></lb></s> <s id="s.000584">ſed res ſemper ita decreſcit, vt ex tribus ſolùm pri<lb></lb>mam conſequentibus eleuetur tantumdem, ex quin<lb></lb>que aliis rursùs tantumdem, ex ſeptem aliis ſimili<lb></lb>ter, ac rutſus ex nouem, & ita deinceps. </s> <s id="s.000585">Deducitur <lb></lb>prætereà ex increſcente numero diametrorum, & de<lb></lb>creſcente numero additorum ponderum, perueniri <lb></lb>demùm ad æqualitatem; ita ſcilicet, vt ſit diametro<lb></lb>rum, ponderumque numerus par, quo ſuperato ſit <lb></lb>deinceps minor ponderum, maior diametrorum. </s> <s id="s.000586">Et <lb></lb>quia talis numerus incipiendo v. c. à duodecima vſ<lb></lb>que parte diametri, è qua fuere duæ vnciæ eleuatæ, <lb></lb>reperitur eſſe proximè quinquaginta; & incipiendo à <lb></lb>diametro integra, è qua eleuari viſæ ſunt vnciæ ſep<lb></lb>tem cum quadrante, reperitur eſſe itidem quinqua<lb></lb>ginta: idcircò videmur poſſe dicere, ſi dimittatur <lb></lb>globus vnam pendens vnciam, ex altitudine diame<lb></lb>trorum ſuarum quinquaginta, fore vt parem nume<lb></lb>rum vnciarum attollat; tametſi citra hunc numerum, <lb></lb>ſit diametrorum numerus minor, vltrà maior nu<lb></lb>mero vnciarum. </s> <s id="s.000587">Vides igitur contingere poſſe, vt <lb></lb>aliquo caſu diametrorum numerus ponderum nume<lb></lb>ro exæquetur; neque licere tamen inferre eſſe vbi<lb></lb>que diametrorum numerum numero ponderum <lb></lb>æqualem. </s> <s id="s.000588">Ac ſi res quidem tibi contigiſſet circiter <lb></lb>quinquageſimam, aut ſexageſimam diametrum, foret <lb></lb>mihi, vt vides, reſponſio in promptu; quandò verò <lb></lb>numerus iſtum ſuperat duplò circiter; ac is eſt aliunde, <lb></lb>è quo eleuari non debuerint, niſi vnciæ ſeptuaginta <lb></lb>quatuor; vnde exceſſus eſt circiter trientis: idcircò par <pb pagenum="51" xlink:href="028/01/091.jpg"></pb>eſt, vt quid id ſit rei, tibi diſcutiendum relinquam, <lb></lb>viſuro, an, ſi quid impoſuit circa vnam, pauculaſve <lb></lb>diametros, non aliquid etiam potuerit imponere cir<lb></lb>ca tam multas. </s> <s id="s.000589">Mihi certè hactenùs non licuit pe<lb></lb>riculum facere, qui Bilancem neque maiorem, neque <lb></lb>exquiſitiorem ea, de qua iam dixi, vſurpaui. </s> <s id="s.000590">Vnde <lb></lb>neque velim numeros à me deſcriptos ita habeas, <lb></lb>quaſi ſcrupulosè, præciſeve definiti fuerint; cùm ſatis <lb></lb>eſſe duxerim, ſi præter-propter veri forent, poſſem<lb></lb>que intelligere ſequi illos haud-dubiè aliam, quàm à <lb></lb>te præſcriptam rationem. </s> </p> <p type="main"> <s id="s.000591">XXVIII. </s> <s id="s.000592">Nihil verò neceſſe eſt dicam circa id, <lb></lb>quod ais, <emph type="italics"></emph>Etſi natura illud in globo peculiare, ac pro<lb></lb>prium eſſe voluit, vt eius diameter præciſa eſſet menſura <lb></lb>illius altitudinis, ex qua ſuo nutu cadens, æquale ſibi pon<lb></lb>dus attolleret; ac proinde, &c. </s> <s id="s.000593">in cæteris tamen etiam <lb></lb>corporibus idem quoque ſeruata proportione accidere; vt ſi ex <lb></lb>quacumque diſtantia æquale ſibi pondus attollant, ex eadem <lb></lb>diſtantia duplicata duplicatum, & ex triplicata <expan abbr="triplicatũ">triplicatum</expan> <lb></lb>attollant, atque ita conſequenter, ob eandem rationem; cui <lb></lb>rationi ipſa quoque experientia ſuffragetur, &c. </s> <s id="s.000594">hac ta<lb></lb>men differentia, quòd in globis, diameter altitudines præ<lb></lb>cisè definiat, vnde pondus ipſorum multiplicetur, in cæteris <lb></lb>figuris non item; ſed in illis altitudines diametris ipſarum <lb></lb>ſint minores; ratio verò poſtulet vt vniuerſim in figuris om<lb></lb>nibus tales altitudines diametro ſphæræ eiuſdem molis, ac <lb></lb>ponderis inueniantur æquales.<emph.end type="italics"></emph.end></s> <s id="s.000595"> Nihil, inquam, eſt opus <lb></lb>vt ad iſtud dicam; cùm neque ſuffragari experien<lb></lb>tiam videam, neque ipſe globus, quicum corpora <lb></lb>aliarum figurarum confers, habeat pro menſura præ-<pb pagenum="52" xlink:href="028/01/092.jpg"></pb>ciſa illius altitudinis, ex qua ſuo nutu cadens, æquale <lb></lb>ſibi pondus attollat, ſuam diametrum; ſed potiùs duo<lb></lb>decimam circiter ſuæ diametri partem; neque aliun<lb></lb>de eadem diameter præcisè definiat altitudines, vnde <lb></lb>pondus, ſeu impetus multiplicetur, euadatque tri<lb></lb>plus ex tripla, quadruplus ex quadrupla, &c. </s> <s id="s.000596">ſed id <lb></lb>potiù faciat progreſſio numerorum imparium, qua<lb></lb>dratorumve, ad quos terminantur. </s> <s id="s.000597">Addo autem <lb></lb>videri mihi rem eſſe dignam conſideratu, quæ acci<lb></lb>deret circa globos, ſi velocitatis, ſiue impetus acqui<lb></lb>ſiti gradus menſurandi eſſent penes ſingulas diame<lb></lb>tros, quæ menſurarent ſingulorum caſus. </s> <s id="s.000598">Sunto <lb></lb>enim globi, v.c. </s> <s id="s.000599">duo ex eadem materia, quorum <lb></lb>vnus ſit diametro decies maiore, quàm alius, & di<lb></lb>mittatur vterque ex eadem altitudine. </s> <s id="s.000600">Tunc, quia mi<lb></lb>nor decidet per diametros decuplò plureis, quàm ma<lb></lb>ior, fiet, vt attollat pondera ſibi æqualia decuplò <lb></lb>multipliciora, quàm attollat, maior ex ſibi æqualibus; <lb></lb>Quare & ſequetur, vt per idem ſpatium feratur de<lb></lb>cuplò citiùs, temporeve decies breuiore perueniat <lb></lb>ad lancem, quàm maior. </s> <s id="s.000601">Hoc autem conſtat, quàm <lb></lb>falſum ſit; cùm ſi globorum alteruter deberet velo<lb></lb>ciùs moueri, & peruenire citiùs, is non ſine quadam <lb></lb>veriſimilitudine deberet potiùs eſſe maior (quandò <lb></lb>& Ariſtoteles perſuaſus id fuit, & toti penè mundo <lb></lb>hactenus perſuaſit) ac doceat tamen experientia duo <lb></lb>pondera eiuſdem materiæ, inæquabiliſſima licet, ve<lb></lb>luti vnum vnius vnciæ, alterum verò librarum cen<lb></lb>tum, ex eadem cadentia altitudine, cadere eadem <lb></lb>velocitate, ac momento eodem peruenire in terram. <pb pagenum="53" xlink:href="028/01/093.jpg"></pb>Atque ex hoc quidem ratio obiter petitur, cur in <lb></lb>exemplo repetito de penſilibus, nihil referat, quod<lb></lb>cumque pondus filo appendas, vt celeritate eadem <lb></lb>vibrationes fiant; ideò enim penſile centum libra<lb></lb>rum non vibratur velociùs, quàm penſile vnius vn<lb></lb>ciæ, quoniam altitudo, ex qua vtrumque cadit, ea<lb></lb>dem eſt, menſurata nempe, eadem portione perpen<lb></lb>di uli, quemadmodum eſt ante declaratum: cùm <lb></lb>celeritas aliunde ſtatim augeatur vel minuatur, ac fi<lb></lb>lum breuius fit, vel prolixius. </s> <s id="s.000602">Et hactenus quidem <lb></lb>de tua Experientia. </s> </p> <p type="main"> <s id="s.000603"><emph type="center"></emph><emph type="italics"></emph>De Tempore, quo R. P. colligit parteis spatij ſimgulas <lb></lb>decurſum non iri.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000604">XXIX. </s> <s id="s.000605">Sequitur iam Secundum membrum Po<lb></lb>ſterioris capitis, quod tibi fuit præcipus ſcopus. <lb></lb></s> <s id="s.000606">Videlicet ita concludis. <emph type="italics"></emph>Atque ex his iam manifeſtè, at<lb></lb>que euidenter conſtat, celeritatem motus in naturali grauium <lb></lb>deſcenſu per aërem, ſecluſis externis impedimentis, vniformi <lb></lb>ſemper incremento augeri, & in spatijs æqualibus creſcere <lb></lb>æqualiter: ita ſcilicet, vt ex dupla diſtantia, celeritas dupla, <lb></lb>& ex tripla diſtantia, celeritas tripla, atque ita deinceps, <lb></lb>eadem ratione, maior ſemper celeritas habeatur: niſi fortè <lb></lb>eò vſque iam progreſſa eſſet celeritas, vt nec celeriùs <expan abbr="aẽr">aerr</expan> di<lb></lb>uidi, nec citiùs rarefieri, & accurrere ad replendum va<lb></lb>cuum naturaliter poſſet.<emph.end type="italics"></emph.end></s> <s id="s.000607"> Et poſteà: <emph type="italics"></emph>Ex quo vlteriùs il<lb></lb>lud etiam conſtat, quàm non rectè<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus, vulgò receptam <lb></lb>motus æquabiliter accelerati definitionem eam reiecerit, qua <lb></lb>motus eiuſmodi is dicitur; qui spatijs æqualibus, æqualia cele<lb></lb>ritatis augmenta acquirit; & quàm oſcitanter idem halluci-<emph.end type="italics"></emph.end><pb pagenum="54" xlink:href="028/01/094.jpg"></pb><emph type="italics"></emph>natus ſit, cùm etiam inſuper, clara, euidentíque demonſtra<lb></lb>tione, eiuſdem ſe falſitatem, impoßibilitatémque oſtendiſſe, <lb></lb>tam facilè ſibi, atque inconſuliè perſuaſit: cùm aperta iam, <lb></lb>indubitatáque experientiâ conſtet, in naturali grauium deſ<lb></lb>cenſu, æqualibus spatijs, æqualia celeritatis augmenta perpe<lb></lb>tuò acquiri, ſemperque velocitates, emenſaque ab initio mo<lb></lb>tus spatia, in eadem ratione reperiri.<emph.end type="italics"></emph.end></s> <s id="s.000608"> Ad iſta verò vides <lb></lb>profectò quid ſit iam promptum reſpondere; cùm <lb></lb>tantum abeſt, vt aperta indubitatáque experientia de<lb></lb>finitionem illam vulgarem, aut incrementa velocitatis <lb></lb>pro ipſa ſpatiorum ratione ſtabiliat, quin illam potiùs <lb></lb>planè euertat, & Galileanum ita confirmet, vt mani<lb></lb>feſtò exinde conſtet incrementa velocitatis acquiri <lb></lb>duntaxat æqualia æqualibus temporibus; acquiſita <lb></lb>verò, ſeu ſuperata ſpatia eſſe vt ipſorum temporum <lb></lb>quadrata. </s> <s id="s.000609">Ex quo fit, vt allatis illis antè argumen<lb></lb>tis, quibus permouebar, vt coniicerem percuſſionem, <lb></lb>atque idcircò impetum, velocitatémque rei deciden<lb></lb>tis maiorem duplò non haberi, niſi ex altitudine qua<lb></lb>drupla, triplum, niſi ex nonupla, quadruplum, niſi ex <lb></lb>ſexdecupla, iſtud iam nouum acceſſerit. </s> <s id="s.000610">quatenus ob<lb></lb>ſeruatum eſt duplum ponderis ex vnius diametri alti<lb></lb>tudine elati non efferri ex dupla, ſed ex quadrupla; <lb></lb>triplum non ex tripla, ſed ex nonupla; quadruplum <lb></lb>non ex quadrupla, ſed ex ſexdecupla duntaxat. </s> <s id="s.000611">Sunt <lb></lb>autem tibi habendæ gratiæ, qui pro tua ſolertia eò <lb></lb>reſpexeris, vnde argumentum adeò cuidens ducere<lb></lb>tur; ipſeque debes ex eo lætari, quòd tametſi expe<lb></lb>rimentum præconceptæ à te opinioni non faueat; <lb></lb>conferat nihilominùs ad veritatis illuſtrationem. </s> </p> <pb pagenum="55" xlink:href="028/01/095.jpg"></pb> <p type="main"> <s id="s.000612">XXX. </s> <s id="s.000613">Proſequeris deinde ſic. <emph type="italics"></emph>Porrò cùm celeritas <lb></lb>motus in naturali deſcenſu grauium, non modò ad locum, ſed <lb></lb>ad tempus quoque reſpectum includat, iamque de altero <expan abbr="dictã">dictam</expan> <lb></lb>ſit, qua videlicet ratione, celeritas ſpatijs æqualibus augea<lb></lb>tur; vt ne quid ad perfectam motus accelerati notitiam de<lb></lb>ſit, neceſſarium eſt, vt de ſpatiis quoque, quæ temporibus <lb></lb>æqualibus percurruntur, quam inter ſe rationem obſeruent, <lb></lb>reliqua diſputatione inquiramus, & ex iiſdem quoque expe<lb></lb>rientiis definiamus.<emph.end type="italics"></emph.end></s> <s id="s.000614"> Hoc iam loco, optimè Vir, agnoſ<lb></lb>cere potes originem mali. </s> <s id="s.000615">Nempe labes tota vide<lb></lb>tur ex definitione vulgari contracta, quatenus ratio<lb></lb>nem increſcentis celeritatis ita cum ſpatio comparat, <lb></lb>vt nullam interim inſtituat comparationem cum tem<lb></lb>pore, ſine quo tamen neque celeritas, neque acce<lb></lb>leratio intelligi poteſt. </s> <s id="s.000616">Non modò certè Ariſtoteles, <lb></lb>verùm etiam communis ſenſus id Velox definit, <lb></lb><emph type="italics"></emph>quod ſpatium multum tempore pauco:<emph.end type="italics"></emph.end> & Tardum, <emph type="italics"></emph>quod <lb></lb>paucum multò conficit;<emph.end type="italics"></emph.end> conſtatque aliunde, ſi velocitas <lb></lb>attendatur ſolùm penes ſpatia, debere ſemper id <lb></lb>mobile, quod decem percurrerit ſtadia, dici moueri <lb></lb>celeriter, & ſemper id, quod vnicum percurrerit, tar<lb></lb>dè; cùm contingere tamen poſſit, vt quod percurrit <lb></lb>vnicum, moueatur decuplo velocius, quàm illud, <lb></lb>quod percurrit decem. </s> <s id="s.000617">Ex quo fit, vt cùm celeri<lb></lb>tas nihil ſit aliud, quàm paſſio motus; intelligatur <lb></lb>quidem motus abſolutè ſumptus ex relatione ad ſpa<lb></lb>tium, cùm & definiatur progreſſio è loco in locum <lb></lb>(nulla mentione temporis) & duo loca ſine ſpatio <lb></lb>interiecto non accipiantur; at celeritas non intelli<lb></lb>gatur ſine relatione ad tempus, & illud quidem breue <pb pagenum="56" xlink:href="028/01/096.jpg"></pb>comparatum ad id, quo ex vno loco perueniri ad <lb></lb>alium poteſt. </s> <s id="s.000618">Fit etiam proinde, vt idem dicendum <lb></lb>de acceleratione ſit; quippe acceleratio duo ſaltem <lb></lb>tempora deſignat, in quorum vno celeriter, in alio <lb></lb>celeriùs mobile feratur; ac intelligimus aliunde tem<lb></lb>poribus illis æqualibus ſumptis, pauciores ſpatij par<lb></lb>teis priore, plureis poſteriore percurri. </s> <s id="s.000619">Et adnitere <lb></lb>facere perſpectum, quidnam acceleratio ſit, nulla men<lb></lb>tione temporis; ac pernoſces rem impoſſibilem factu <lb></lb>eſſe. </s> <s id="s.000620">Vtcumque enim plureis, plureiſque ſpatij par<lb></lb>teis memore: niſi tamen adiicias voces <emph type="italics"></emph>deinceps, conſe<lb></lb>quenter, ſucceßiuè,<emph.end type="italics"></emph.end> aut ſimileis alias, quæ ad tempus at<lb></lb>tineant, non magis accelerationem, quàm ſimplicem <lb></lb>celeritatem, aut potiuſ-quam motum ſimpliciter ſpe<lb></lb>ctatum deſcribes. </s> <s id="s.000621">Quanquam nihil eſt opus id vr<lb></lb>geam, cùm tu pro confeſſo iam habeas; profeſſus <lb></lb>nempe <emph type="italics"></emph>celeritatem in naturali deſcenſu grauium non modò <lb></lb>ad locum, ſed ad tempus quoque reſpectum includere:<emph.end type="italics"></emph.end> ac <lb></lb>mirari ſolùm quis poſſit, agnoſcere te in celeritate <lb></lb>duplicem reſpectum, & velle tamen alterum, ipſum<lb></lb>que præcipuum in tradenda definitione accelerati mo<lb></lb>tus excluſum; ac inuehi in Galileum, qui incluſum <lb></lb>voluerit. </s> <s id="s.000622">Nam & licet, veluti tu reſpectum ad tem<lb></lb>pus prætermiſſum fers, ſic ille reſpectum ad locum <lb></lb>prætermitti poſſe cenſuerit: excuſari poteſt, quòd qui <lb></lb>motum dicit, locum etiam dicat, quemadmodum <lb></lb>mox attigi; & cùm foret ſolùm de celeritate ſuperue<lb></lb>niento quæſtio, ideò nugationem deuitans, illam per <lb></lb>reſpectum ad tempus, ſine quo intelligi nequeat, pu<lb></lb>tâtit eſſe deſiniendam. </s> </p> <pb pagenum="57" xlink:href="028/01/097.jpg"></pb> <p type="main"> <s id="s.000623">XXXI. </s> <s id="s.000624">Subdis conſequenter; <emph type="italics"></emph>Quod vt certiùs <lb></lb>fiat, primùm occurrendum est errori, qui facilè obrepere <lb></lb>potest, ſi quæ de cele itatis augmento in ſpatiis æqualibus <lb></lb>antè demonstrata ſunt, minùs accuratè perpendantur. </s> <s id="s.000625">Cùm <lb></lb>enim ex ſuperioribus iam euidenter conſtet, in naturali gra<lb></lb>uium deſcenſu, ſemper ex dupla diſtantia, celeritatem ha<lb></lb>beri duplam; & ex tripla distantia, triplam; atque ita <lb></lb>deinceps, eadem ratione celeritatem augeri: nihil procliuius <lb></lb>eſſe potest, quàm vt quis exiſtimet, accelerationem illam <lb></lb>fieri per ſubdiuiſionem primi cuiuſlibet temporis, in parteis <lb></lb>ſemper minores, pro multitudine, & ratione ſpatiorum æqua<lb></lb>lium, quæ motu decurruntur; ita videlicet, vt pars ſecunda <lb></lb>spatij, abſoluatur dimidia parte temporis, quo prima pars <lb></lb>decurſa est; & tertia pars ſpatij, tertia parte eiuſdem primi <lb></lb>temporis percurratur, & ita de cæteris: maximè cùm in hac <lb></lb>etiam hypotheſi, ſpatia & velocitates in eadem eſſe ratione, <lb></lb>& quod conſequens eſt, ex impeta quoque decidentium corpo<lb></lb>rum hac ratione inuariato, iidem omnes, quos experientia <lb></lb>docet effectus haberi, primo aſpectu videantur.<emph.end type="italics"></emph.end></s> <s id="s.000626"> Heic pro<lb></lb>fectò rurſus mirari tuam ſagacitatem par eſt, qua<lb></lb>tenus eam non fugit error qui ex poſitione à te aſ<lb></lb>ſerta conſequitur; tametſi ipſe non conſequi ex iis, <lb></lb>quæ ſubiicis, contendas. </s> <s id="s.000627">Me quod attinet, is eſt <lb></lb>ipſemet, quem deduxi aliàs aduerſus Michaelem <lb></lb>Varronem, qui primus, quod ſciam, eandem poſitio<lb></lb>nem ante annos plus minùs ſexaginta defendit; de<lb></lb>clarando ex ea id incommodi inter cætera conſequi, <lb></lb>vt, quemadmodum antè inſinuaui, ſpatia acquiſita <lb></lb>in ſine æqualis cuiuſlibet temporis numeranda ſint, <lb></lb>vt difformiter, ſic in pluſquàm tripla ratione. </s> <s id="s.000628">Vt <pb pagenum="58" xlink:href="028/01/098.jpg"></pb>autem iam rem te iudice experiar; ecce aſſumptâ, diui<lb></lb>ſaque linea, quam ipſe vſurpas, AB, & ſup<lb></lb><figure id="id.028.01.098.1.jpg" xlink:href="028/01/098/1.jpg"></figure><lb></lb>poſito tempore minutorum ſex, quo ſuppo<lb></lb>nis AD primam partem percurri; Conſtat <lb></lb>omninò, ſi ſecunda æqualis pars DE per<lb></lb>curratur velocitate dupla ad illam, qua per<lb></lb>curritur AD, non inſumi plus temporis in <lb></lb>percurrenda parte ſecunda, quàm dimidium <lb></lb>eius, quod fuerit inſumptum in prima (cùm <lb></lb>hac ratione tempora velocitatum ſubmultipla <lb></lb>ſint) atque ita, ſi prima pars ſuperata fuerit mi<lb></lb>nutis ſex, percurri ſecundam dimidio, ſeu mi<lb></lb>nutis tribus. </s> <s id="s.000629">Eadem autem ratione ſi tertia <lb></lb>æqualis EF percurratur tripla, neceſſe eſt <lb></lb>percurratur temporis triente, ſeu minutis duo<lb></lb>bus; ac eodem modo quarta FG quadrante, <lb></lb>ſeu ſeſquiminuto, & quinta GH quinta par<lb></lb>te temporis, ſeu minuto vno cum ſecundis duodecim; <lb></lb>ac ſexta HB, ſextante, ſeu minuto vno, & ita deinceps. <lb></lb></s> <s id="s.000630">Atque ego quidem hûc vſque nullum video paralo<lb></lb>giſmum. </s> <s id="s.000631">Quamobrem reſtat, vt diſquiratur, quot<lb></lb>nam æqualia ſpatia, parteſve ſpatii æquales tem<lb></lb>poribus primum conſequentibus, ipſique æqualibus <lb></lb>percurrantur. </s> <s id="s.000632">Porrò cùm ad id pernoſcendum, ni<lb></lb>hil oporteat aliud, quàm iungere ſimul varia hæc <lb></lb>fragmenta primi temporis, hoc eſt dimidium, trien<lb></lb>tem, quadrantem, & porrò parteis quintam, ſextam, <lb></lb>ſeptimam, &c. </s> <s id="s.000633">deprehendimus in ipſo fine quarti <lb></lb>ſpatij, ex iunctis ſimul dimidio, triente & quadrante, <lb></lb>confectum eſſe ſecundum tempus, ſeu iteratò minuta <pb pagenum="59" xlink:href="028/01/099.jpg"></pb>ſex, cum ſuperante duodecima parte. </s> <s id="s.000634">Ac pari ratio<lb></lb>ne in fine vndecimi ſpatij, ex ſuper-adiunctis parti<lb></lb>bus quinta, ſexta, ſeptima, octaua, nona, decima, <lb></lb>vndecima, confectum eſſe tertium tempus, ſeu ite<lb></lb>rum minuta ſex, cum ſuperante vna ſexageſima par<lb></lb>te. </s> <s id="s.000635">Et in fine ſpatij trigeſimi primi, ex ſuperadiun<lb></lb>ctis duodecima, decimatertia, &c. </s> <s id="s.000636">confectum quar<lb></lb>tum, ſeu ſex minuta, cum ſuperante parte circiter <lb></lb>quadrageſima. </s> <s id="s.000637">Et in fine octogeſimi quarti, ex ſu<lb></lb>peradiunctis trigeſima ſecunda, trigeſima tertia, &c. <lb></lb></s> <s id="s.000638">confectum quintum, ſeu ſex minuta, cum ſuperante <lb></lb>vna parte proximè nonageſima, atque ita deinceps. <lb></lb></s> <s id="s.000639">Vnde licet aduertere, fore vt ſpatia ea ratione increſ<lb></lb>cant, quæ aſſumptis quibuſlibet æqualibus tempori<lb></lb>bus deprehendatur excedere, & difformiter quidem, <lb></lb>ſeu inæquabiliter, triplam; quippe procedendo per <lb></lb>hos numeros, vnum, quatuor, vndecim, triginta <expan abbr="vnũ">vnum</expan>, <lb></lb>octoginta quatuor, &c. </s> <s id="s.000640">ſicque lapide decidente pri<lb></lb>mo momento per vnam v. c. orgyiam, fore vt ſecun<lb></lb>do æquali momento decidendo per treis, in tertio <lb></lb>per ſeptem, in quarto per viginti, in quinto per quin<lb></lb>quaginta duas, deciderit in fine quinti, orgyiis octo<lb></lb>ginta quatuor, ac breui res ſit abitura in immenſum, <lb></lb>ſecuſque quàm docet ipſa experientia, iuxta quam <lb></lb>orgyiiæ in fine quinti momenti ſuperatæ, colliguntur <lb></lb>plures eſſe non debere, quàm viginti quinque. </s> </p> <p type="main"> <s id="s.000641">XXXII. </s> <s id="s.000642">Demonſtras ipſe alia ratione (ſed nimi<lb></lb>rùm aduerſum te) non fieri accelerationem pro ſub<lb></lb>diuiſione iſta temporis. <emph type="italics"></emph>Si igitur,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>accelera io <lb></lb>motus per eam primi temporis ſubdiuiſionem fieret, de qua<emph.end type="italics"></emph.end><pb pagenum="60" xlink:href="028/01/100.jpg"></pb><emph type="italics"></emph>heic ſermo eſt, pars ſecunda DE tribus minutis percurri <lb></lb>deberet, hoc eſt dimidia parte primi temporis; & pars ter<lb></lb>tia EF duobus minutis, nempe tertia parte eiuſaem primi <lb></lb>temporis, & ita de cæteris.<emph.end type="italics"></emph.end></s> <s id="s.000643"> Quamobrem verò id non <lb></lb>fieret; cùm ſuppoſito tuo illo principio de velocita<lb></lb>tibus ſeſe habentibus vt ſpatijs, & nullus ſit paralo<lb></lb>giſmus, & res ſponte ſua ſe prodat, neque videatur <lb></lb>euerti poſſe, abs te, vt mox tentas euertere, niſi tua <lb></lb>ipſius euertas principia, & falſitatem prodens conſe<lb></lb>quentis, quod tamen ex tuis principiis tam neceſſa<lb></lb>riò deducitur, videaris etiam prodere falſitatem ante<lb></lb>cedentis? </s> <s id="s.000644">Pergis itaque, <emph type="italics"></emph>At rem non ita accidere facilè <lb></lb>intelligimus, diuiſa bifariam parte AD in S, & parte <lb></lb>item DE ſimiliter in X. </s> <s id="s.000645">Tunc enim ob eandem ratio<lb></lb>nem neceſſe fuerit, vt pars SD percurratur in dimidio <lb></lb>eius temporis, quo pars AS decurritur; & DX in ter<lb></lb>tia parte, itemque XE in quarta parte eiuſdem temporis, <lb></lb>vt manifeſtum eſt.<emph.end type="italics"></emph.end></s> <s id="s.000646"> Quorſum verò id neceſſe non fue<lb></lb>rit; cùm eadem ſit ratio dimidij ad dimidium, quæ <lb></lb>totius ad totum, & nulla ſit obſeruatio, aut ratio, ex <lb></lb>qua aliud inferatur potiùs de partibus AD, DE, EF, <lb></lb>&c. </s> <s id="s.000647">quàm de partibus AS, SD, DX, &c. </s> <s id="s.000648">aut de <lb></lb>quibuſlibet minoribus, dummodò ſint omnes inter <lb></lb>ſe æquales? </s> <s id="s.000649">Pergis iterum, C<emph type="italics"></emph>ùm igitur ſupponamus <lb></lb>totam AD minutis ſex pertranſiri, neceſſe erit, vt decur<lb></lb>ſus per AS quatuor minuta, & deſcenſus per SD duo <lb></lb>tantum minuta inſumat: vt ſcilicet ea ratione tempus deſ<lb></lb>cenſus per SD ſit dimidia pars temporis in deſcenſu per AS <lb></lb>inſumpti; ideoque etiam pars DX minuti.<emph.end type="italics"></emph.end> (1 1/5)<emph type="italics"></emph>nempe tertia <lb></lb>parte temporis AS; & pars XE minuto vno, ſiue<emph.end type="italics"></emph.end><pb pagenum="61" xlink:href="028/01/101.jpg"></pb><emph type="italics"></emph>quarta parte eiuſdem temporis percurreretur; ſicque deſcen<lb></lb>ſus per totam DE minutis<emph.end type="italics"></emph.end> (2 1/3) <emph type="italics"></emph>abſolueretur.<emph.end type="italics"></emph.end></s> <s id="s.000650"> Quid ni <lb></lb>verò id quoque neceſſe non ſit, exſiſtente ſemper <lb></lb>eadem ratione dimidiorum ad dimidia, quæ toto<lb></lb>rum ad tota? </s> <s id="s.000651">At <emph type="italics"></emph>paullò antè,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>ſuppoſuimus ean<lb></lb>dem partem non niſi tribus minutis decurri.<emph.end type="italics"></emph.end></s> <s id="s.000652"> Id verò ſanè <lb></lb>non ſuppoſuiſti, vt aliquid gratis conceſſum; ſed vt <lb></lb>aliquid neceſſariò cum tuis principiis cohærens. <lb></lb></s> <s id="s.000653">Quare & fit quidem, vt euincas rem eſſe impoſſibi<lb></lb>lem, percurri partem DE dimidio eius temporis, quo <lb></lb>percurritur AD; ſed euincas tamen aduerſus teipſum; <lb></lb>cùm ex hoc rursùs efficiatur, vt motu æquabiliter ac<lb></lb>celerato ex A in E, non fuerint in E acquiſiti duo <lb></lb>celeritatis gradus, quemadmodum in D fuit acquiſi<lb></lb>tus vnus, ſi mobile quidem per totam DE non ſit <lb></lb>motum duplò velocius, quàm per totam DA; atque <lb></lb>idcircò in dimidio temporis, durationeve minuto<lb></lb>rum trium. </s> <s id="s.000654">Fit etiam, vt quando concludis, <emph type="italics"></emph>Per <lb></lb>hanc igitur primi temporis ſubdiuiſionem, accelerationem <lb></lb>motus in deſcenſu grauium ſatis exactè non explicari;<emph.end type="italics"></emph.end> adiici <lb></lb>poſſit, neque explicari per tuam illam poſitionem, <lb></lb>cum qua hæc ſubdiuiſio indiuiduè connexa eſt, & <lb></lb>à qua illam auertere, ob contradictionem conſequen<lb></lb>tem conatus, nihil aliud videris, quàm, quod vulgò <lb></lb>aiunt, incommodum per incommodum ſoluere. </s> </p> <p type="main"> <s id="s.000655">XXXIII. </s> <s id="s.000656">Prætextu ſubinde quæſito vlterioris <lb></lb><expan abbr="incõmodi">incommodi</expan>, ſubſternis quaſi fundamentum conſtituen<lb></lb>dæ poſteà à te progreſſionis motus per parteis tem<lb></lb>poris æqualeis ſecundum rationem continenter du<lb></lb>plam. </s> <s id="s.000657">Nam, <emph type="italics"></emph>Accedit,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>quòd tota DE eodem<emph.end type="italics"></emph.end><pb pagenum="62" xlink:href="028/01/102.jpg"></pb><emph type="italics"></emph>præcisè tempore, quo pars<emph.end type="italics"></emph.end> S<emph type="italics"></emph>D tranſcurreretur<emph.end type="italics"></emph.end> (tempore <lb></lb>nimirùm non trium, non duorum cum triente, vt <lb></lb>priùs, ſed minutorum præcisè duorum) id autem ſic <lb></lb>probas. <emph type="italics"></emph>Cùm enim AD dupla ponatur ipſius A<emph.end type="italics"></emph.end>S, <emph type="italics"></emph>& <lb></lb>ſimiliter AE dupla ſit ipſius AD, neceſſe eſt, vt velocitas <lb></lb>in D dupla ſit velocitatis in<emph.end type="italics"></emph.end> S; <emph type="italics"></emph>& velocitas in E eodem <lb></lb>modo dupla reperiatur velocitatis in D; imò, vt velocitas <lb></lb>etiam quæcumque in quovis puncto inter D, & E conſtitu<lb></lb>to deſignabilis perpetuò dupla ſit velocitatis alterius inter S, <lb></lb>& D etiam aßignabilis, vt facilè quilibet per ſe intelligere <lb></lb>poteſt. </s> <s id="s.000658">Sumpto enim puncto quocumque inter D, & E, <lb></lb>ex empli gratiâ T, diuiſoque bifariam interuallo AT, ſectio <lb></lb>neceſſario cadet inter D, &<emph.end type="italics"></emph.end> S, <emph type="italics"></emph>puta in V. </s> <s id="s.000659">Et quia erit <lb></lb>AT dupla ipſius AV, erit etiam velocitas in T dupla ve<lb></lb>locitatis in V, & ita in cæteris punctis, quæ deſignari poſſunt <lb></lb>inter D, & E. </s> <s id="s.000660">Quare per totum interuallum DE velocitas <lb></lb>erit dupla velocitatis per totum spatium<emph.end type="italics"></emph.end> SD, <emph type="italics"></emph>ſicut interual<lb></lb>lum DE duplum eſt interualli<emph.end type="italics"></emph.end> SD. <emph type="italics"></emph>Ambo igitur hæc in<lb></lb>terualla nempe<emph.end type="italics"></emph.end> SD, <emph type="italics"></emph>& DE æquali tempore percurruntur.<emph.end type="italics"></emph.end><lb></lb>Quo loco admitto imprimis, vt nouum incommo<lb></lb>dum, eandem partem DE, quæ probata eſt primùm <lb></lb>percurri debere ex tuo principio minutis tribus, ac <lb></lb>deinde minutis duobus cum triente, probari iam per<lb></lb>curri debere minutis duobus. </s> <s id="s.000661">Quippe nihil eſt, quod <lb></lb>magis prodat falſitatem principii, quàm tot repu<lb></lb>gnantium, atque abſurdorum capitum deductio. <lb></lb></s> <s id="s.000662">Neque verò heic adhûc finis; quandò alia innumera <lb></lb>pari ratione conſequentur. </s> <s id="s.000663">Nam ſi, v.c. </s> <s id="s.000664">AS bifa<lb></lb>riam ſecetur in P, conficietur eodem tuo ratiocinio, <lb></lb>vt PS percurratur eodem tempore, quo SD, atque <pb pagenum="63" xlink:href="028/01/103.jpg"></pb>idcirco eodem, quo DE. </s> <s id="s.000665">Et quia ſeruatâ analogià <lb></lb>PS percurri debet vno minuto cum triente, efficie<lb></lb>tur, vt non modò SD, verùm ipſa quoque DE per<lb></lb>curratur rursùs non duobus minutis, ſed vnoſolùm <lb></lb>cum triente; atque ita bifariam ſecando, diminuendo<lb></lb>que in infinitum. </s> <s id="s.000666">Adnoto deinde non tranſire te <lb></lb>vltrà comparationem partis DE cum parte SD, ne<lb></lb>que comparare ipſam cum parte PS, vt mox factum <lb></lb>eſt, & fieri poſſe nihil prohibet; cùm nulla ſit ratio, <lb></lb>ob <expan abbr="quã">quam</expan> in hac potiùs biſectione, <expan abbr="quã">quam</expan> in vlteriore vlla <lb></lb>conſiſtatur; verùm aſſumere te ſolum, id <emph type="italics"></emph>tempus, quo <lb></lb>abſoluitur interuallum<emph.end type="italics"></emph.end> SD <emph type="italics"></emph>breuius eſſe tempore, quo pars <lb></lb>ſuperior<emph.end type="italics"></emph.end> AS <emph type="italics"></emph>tranſcurritur, alioquin deſcenſus ſine accelera<lb></lb>tione vniformis eſſet;<emph.end type="italics"></emph.end> idque, vt inferas, <emph type="italics"></emph>partem primùm <lb></lb>deſignatam<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>cum eodem præcisè tempore percurratur, <lb></lb>quo interuallum<emph.end type="italics"></emph.end> SD, <emph type="italics"></emph>non in dimidio prioris temporis, ſed <lb></lb>tempore breuiore abſolui.<emph.end type="italics"></emph.end></s> <s id="s.000667"> Adnoto, inquam, vt appareat, <lb></lb>cui fundamento ſuper-exſtruas quicquid deinceps <lb></lb>ædificas, ſupponens nimirùm vt ratum principium <lb></lb>(quod obiter, & aliud agendo ſtabilieris) æqualita<lb></lb>tem temporis, quo pars SD, & ipſius dupla DE per<lb></lb>curruntur. </s> </p> <p type="main"> <s id="s.000668"><emph type="center"></emph><emph type="italics"></emph>DeTempore, quo R. P. colligit ſingulas parteis decur ſumiri.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000669">XXXIV. </s> <s id="s.000670">Etenim illicò ſic habes; <emph type="italics"></emph>Sed ex his, <lb></lb>& eadem prorſus ratione aliud demonstratur, quod ingentis, <lb></lb>atque admirabilis paradoxi loco non immeritò fortaßis habe<lb></lb>ri poßit, nempe ſi spatium, per quod corpus graue quod<lb></lb>cumque deſcendit, in parteis quotlibet æqualeis diuiſum intel<lb></lb>ligatur, & primæ, ac ſupremæ partis etiam deſignetur<emph.end type="italics"></emph.end><pb pagenum="64" xlink:href="028/01/104.jpg"></pb><emph type="italics"></emph>dimidia pars, & tertia, & quarta, ac deinceps cæteræ, inci<lb></lb>piendo diuiſiones iſtas omneis ab infimo eiuſdem primæ par<lb></lb>tis puncto, donec totidem deſignatæ ſint, quot in reliquo ſpatio <lb></lb>partes æquales acceptæ fuerint: tum ſingulæ partes huiuſmo<lb></lb>di æquales tanto præcisè tempore à corpore graui<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.104.1.jpg" xlink:href="028/01/104/1.jpg"></figure><lb></lb><emph type="italics"></emph>deſcendente percurrantur, quanto partes ipſis analo<lb></lb>gæ, ac respondentes in ſuprema parte<emph.end type="italics"></emph.end> (ſeu infe<lb></lb>riore eius dimidio) <emph type="italics"></emph>ab eodem corpore graui de<lb></lb>curſæ fuerint.<emph.end type="italics"></emph.end></s> <s id="s.000671"> Rem conſequenter ita declaras; <lb></lb>S<emph type="italics"></emph>it ſpatium<emph.end type="italics"></emph.end> AB (in ſchemate hoc) <emph type="italics"></emph>per quod <lb></lb>corpus graue deſcendat, in parteis exempli gratiâ <lb></lb>ſex æqualeis diuiſum in<emph.end type="italics"></emph.end> C, D, E, F, & G: <emph type="italics"></emph>primæ<lb></lb>que, ac ſupremæ partis<emph.end type="italics"></emph.end> AC, <emph type="italics"></emph>ex infimo eius pun<lb></lb>cto<emph.end type="italics"></emph.end> C <emph type="italics"></emph>deſignetur primùm media pars<emph.end type="italics"></emph.end> CH, <emph type="italics"></emph>dein<lb></lb>de tertia<emph.end type="italics"></emph.end> CI, <emph type="italics"></emph>& quarta<emph.end type="italics"></emph.end> CK, <emph type="italics"></emph>itemque quinta, & <lb></lb>ſexta<emph.end type="italics"></emph.end> CL, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> CM. <emph type="italics"></emph>Dico corpus graue deſcen<lb></lb>dens per<emph.end type="italics"></emph.end> AB <emph type="italics"></emph>tanto præcisè tempore pertranſire ſe<lb></lb>cundam partem<emph.end type="italics"></emph.end> CD, <emph type="italics"></emph>quanto dimidiam primæ par<lb></lb>tis<emph.end type="italics"></emph.end> HC, <emph type="italics"></emph>antè pertranſiuit; & ſimiliter pari, atque <lb></lb>æquali tempore partem<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>quæ ordine tertia est, <lb></lb>& tertiam primę partis, nempe<emph.end type="italics"></emph.end> IC <emph type="italics"></emph>ab eodem cor<lb></lb>pore deſcendente tranſcurri, & ita de cęteris.<emph.end type="italics"></emph.end></s> <s id="s.000672"> Tunc <lb></lb>autem pergis. <emph type="italics"></emph>Et quidem de ſecunda parte<emph.end type="italics"></emph.end> CD, <lb></lb><emph type="italics"></emph>eam non longiore tempore decurri, quàm quo primę <lb></lb>partis posterior dimidia pars tranſiniſſa fuerit, iam <lb></lb>paulò antè oſtenſum est, nec maiore negotio idem <lb></lb>de cęteris quoque partibus concludetur. </s> <s id="s.000673">Sumpto <lb></lb>enim<emph.end type="italics"></emph.end> CN, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000674">XXXV. </s> <s id="s.000675">Verùm priuſquàm gradus ad <lb></lb>cæteras fiat, conſiſtendum eſt in hac prima; cùm <pb pagenum="65" xlink:href="028/01/105.jpg"></pb>non ſit nequicquam, quod de ipſa admonui. </s> <s id="s.000676">Oſten<lb></lb>ſum eſſe ais tempus, quo percurritur CD, æquale eſſe <lb></lb>tempori, quo decurſum fuerit HC: ſeu, ne confun<lb></lb>damus, & rem explicemus, quaſi repetendam ex ſu<lb></lb>periore ſchemate, oſtenſum eſſe ais id tempus, quo <lb></lb>percurritur DE, æquale eſſe tempori, quo de<lb></lb><figure id="id.028.01.105.1.jpg" xlink:href="028/01/105/1.jpg"></figure><lb></lb>curſum fuerit SD. </s> <s id="s.000677">At primò, inſinuatum iam <lb></lb>eſt id eſſe impoſſibile; cùm quo iure ipſe bi<lb></lb>ſecuiſti primam partem AD in S, liceat bi<lb></lb>ſecare primum dimidium AS in P; & rursùs <lb></lb>primum horum dimidiorum in duo alia, & <lb></lb>primum iſtorum in duo, & ita porrò quoties <lb></lb>libuerit: Iuxta tuum verò ratiocinium, ſe qua<lb></lb>tur tempus, quo percurritur SD, eſſe æqua<lb></lb>le tempori, quo decurſum fuerit PS, quate<lb></lb>nus, vt velocitas per totam DE eſt dupla ve<lb></lb>locitatis per totam SD, quemadmodum in<lb></lb>teruallum duplum eſt; ita velocitas per totam <lb></lb>SD dupla eſt velocitatis per totam PS, ſicut <lb></lb>interuallum eſt itidem duplum; Hoc autem <lb></lb>poſito, vlteriùs ſequatur tempus per SD, atque <lb></lb>idcircò per DE ipſi æquale, eſſe non iam minuto<lb></lb>rum duorum, vt oſtendiſti, ſed minuti vnius cum <lb></lb>triente; vt pote coæquatum tempori per PS, quod <lb></lb>tam eſſe debet triens quatuor minutorum (quibus <lb></lb>vis AS percurri) quàm tempus per SD ſtatuitur à <lb></lb>te triens minutorum ſex (quibus percurritur AD) <lb></lb>cùm id tamen factu impoſſibile ſit, repugnantia putà <lb></lb>inuoluens, ac tantò magis, quantò ex vlterioribus <lb></lb>ſubdiuiſionibus probari poteſt eandem DE percurri <pb pagenum="66" xlink:href="028/01/106.jpg"></pb>rursùs non vno minuto, ac triente, ſed ſecundis ſolùm <lb></lb>proximè quinquaginta tribus; & rursùs proximè <lb></lb>octodecim, & rursùs ſex, &c. </s> <s id="s.000678">Deinde, cùm ad id <lb></lb>oſtendendum vſus fueris ea ratione, quòd neceſſe ſit, <lb></lb><emph type="italics"></emph>velocitatem in D duplam eſſe velocitatis in<emph.end type="italics"></emph.end> S, <emph type="italics"></emph>& veloci<lb></lb>tatem in E duplam velocitatis in D, ſicuti<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>ponitur du<lb></lb>pla ipſius<emph.end type="italics"></emph.end> AS, <emph type="italics"></emph>& ſimiliter<emph.end type="italics"></emph.end> AE <emph type="italics"></emph>dupla eſt ipſius<emph.end type="italics"></emph.end> AD; ſe<lb></lb>quitur exinde, vt tam tota DE, quàm tota SD per<lb></lb>curratur non triente, ſed dimidio temporis, quo tota <lb></lb>AD: cùm vbicumque eſt velocitatis duplum, vbi ſit <lb></lb>dimidium temporis duntaxat, neque tu id infregeris, <lb></lb>ſed incommodum ſolùm attuleris, quod cùm euertat <lb></lb>conſequutionem de ſubdiuiſione primi temporis, ſup<lb></lb>poſitionem quoque euertit de velocitate dupla in du<lb></lb>plo ſpatii, tripla in triplo, &c. </s> <s id="s.000679">vt aliquoties eſt incul<lb></lb>catum. </s> <s id="s.000680">Nam & quod poſteà aſſumis tempus per <lb></lb>SD, atque adeò DE eſſe breuius, quàm dimidium <lb></lb>eius, quo tranſcurritur AD, id facis quidem rectè, <lb></lb>verumtamen iure non tuo; quippe id facis ſolùm me<lb></lb>tu eius incommodi, quod præſenſiti poſſe vrgeri de <lb></lb>motus acceleratione vniformiter, continenterque in<lb></lb>creſcente: cùm id alioquin & repugnet tuæ ſuppoſi<lb></lb>tioni de velocitate dupla in duplo ſpatio, tripla in <lb></lb>triplo, &c. </s> <s id="s.000681">& euertat demonſtrationem ipſam, ad <lb></lb>quam iam recurris, cùm oſtenſum ais tempus, quo <lb></lb>percurritur ſecunda pars, æquale eſſe tempori, quo <lb></lb>tranſmittitur dimidium poſterius, ſeu inferius primæ: <lb></lb>neque enim id fuit oſtenſum alio ratiocinio, quam <lb></lb>quod ipſemet ſtatim pernegaſti. </s> </p> <p type="main"> <s id="s.000682">XXXVI. </s> <s id="s.000683">Attamen ſupponatur etiam tua huiuſ-<pb pagenum="67" xlink:href="028/01/107.jpg"></pb>modi de monſtratio; Sequitur ecce rursùs, vt tempus, <lb></lb>quo percurritur DE ſeſquialterum ſit, non verò æqua<lb></lb>le illi tempori, quo percurritur SD. </s> <s id="s.000684">Cum velocita<lb></lb>tes enim ſint per te, vt ſpatia; ac aliunde ſit manife<lb></lb>ſtum, vbi eſt duplum velocitatis, ibi dimidium eſſe <lb></lb>temporis, vbi triplum trientem, atque itaſemper in ra<lb></lb>tione ſubmultipla; ſi ſit primò vt AE ad AD, ita <lb></lb>AD ad AS; erit igitur diuidendo vt AS ad SD, ita <lb></lb>AD, ad DE; ac deinde, ſi ſit AS tempus minuto<lb></lb>rum quatuor, & SD minutorum duorum; Erit igitur <lb></lb>tempus AD quidem minutorum ſex, & DE minuto<lb></lb>rum trium, atque adeò ſeſqui-alterum, non æquale <lb></lb>tempori SD. </s> <s id="s.000685">Sequitur iterùm, vt non ſecùs, quàm <lb></lb>Galileus ratiocineris, dum Paralogiſmi illum arguis. <lb></lb></s> <s id="s.000686">Siquidem ex tuo quoque ratiocinio euineitur, vt to<lb></lb>ta AE eodem tempore, quo ipſa AD, quæ pars eius <lb></lb>eſt, percurratur. </s> <s id="s.000687">Nam ſi vt AE ad AD, ita DE ad <lb></lb>SD; ergo vt DE tempus ad SC tempus, ita AE tem<lb></lb>pus ad AD tempus: Atqui DE tempus per te eſt <lb></lb>æquale tempori SD; igitur AE tempus æquale erit <lb></lb>AD tempori; hoc eſt totum, & pars percurrentur <lb></lb>tempore æquali, aut eodem. </s> <s id="s.000688">Sequitur prætereà, vt <lb></lb>quia quælibet magnitudo etiam ipſa diameter Mundi <lb></lb>tam eſt dupla ſui dimidij, quàm AE eſt ipſius AD, & <lb></lb>tam in fine dupli eſt velocitas dupla, quam in fine <lb></lb>dimidij dimidia; ideò etiam diameter Mundi ita ſe <lb></lb>ad ſemidiametrum habeat, vt DE ad SD; quare & <lb></lb>quemadmodum DE percurritur eodem tempore, quo <lb></lb>SD, duobus videlicet minutis; ita etiam Mundi ſemi<lb></lb>diameter debeat eodem tempore, ſeu duobus minutis <pb pagenum="68" xlink:href="028/01/108.jpg"></pb>percurri. </s> <s id="s.000689">Quippe & tametſi partes ſint incompara<lb></lb>biliter plures in ſemidiametro Mundi, quàm in ſpa<lb></lb>tiolo DE, ſunt tamen gradus velocitatis incompara<lb></lb>biliter etiam plures, ac proportione totidem; vt tem<lb></lb>pora ſubmultipla illis ſuperandis ſufficere valeant. </s> <s id="s.000690">Vt <lb></lb>breue faciam, erroris origo ex eo profluxiſſe videtur, <lb></lb>quòd merè gratis conſtiteris in parte AD, eiuſque <lb></lb>dimidio inferiore SD; & rem perinde habueris, ac ſi <lb></lb>dimidium ſuperius AS diuidi perinde non poſſet, ne<lb></lb>que haberet ſpeciatim dimidium eadem ratione, qua <lb></lb>habet AD. </s> <s id="s.000691">Proptereà enim accepiſti ſolùm omnia <lb></lb>deſignabilia punctaper totam DE, in quibus veloci<lb></lb>tas eſſet dupla velocitatis in totidem punctis per to<lb></lb>tam SD; neque reputaſti pergendum, vt haberes <lb></lb>eodem tenore puncta deſignabilia per totam SD, in <lb></lb>quibus velocitas eſſet dupla velocitatis in totidem <lb></lb>punctis deſignabilibus per totam PS, atque ita in in<lb></lb>finitum; vt prorsùs neceſſarium eſt ex tua ipſius ſup<lb></lb>poſitione. </s> <s id="s.000692">Quanquam res vberiùs cognoſcenda eſt <lb></lb>circa cæteras, quas deſcribis parteis. </s> </p> <p type="main"> <s id="s.000693">XXXVII. </s> <s id="s.000694">Vt enim probes (reſumpto iam recen<lb></lb>tiore ſchemate) tempus per tertiam partem DE æqua<lb></lb>le eſſe tempori per trientem primæ partis IC, <emph type="italics"></emph>Sumpto,<emph.end type="italics"></emph.end><lb></lb>inquis, CN <emph type="italics"></emph>æquali ipſi<emph.end type="italics"></emph.end> CE, <emph type="italics"></emph>erit tota<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>diuiſa in <lb></lb>treis parteis æqualeis<emph.end type="italics"></emph.end> AI, IN, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> ND; <emph type="italics"></emph>eritque veloci<lb></lb>tas in<emph.end type="italics"></emph.end> D <emph type="italics"></emph>ad velocitatem in<emph.end type="italics"></emph.end> I, <emph type="italics"></emph>vt tota<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>ad ipſam<emph.end type="italics"></emph.end> AI, <emph type="italics"></emph>hoc <lb></lb>eſt tripla. </s> <s id="s.000695">Cumque ob eandem cauſſam velocitas quoque in<emph.end type="italics"></emph.end> E <lb></lb><emph type="italics"></emph>tripla etiam ſit velocitatis in<emph.end type="italics"></emph.end> C, <emph type="italics"></emph>erit velocitas per totam<emph.end type="italics"></emph.end> DE <lb></lb><emph type="italics"></emph>tripla velocitatis per totam<emph.end type="italics"></emph.end> IC, <emph type="italics"></emph>ſicut tota<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>tripla eſt ipſius<emph.end type="italics"></emph.end><lb></lb>IC; <emph type="italics"></emph>ac proinde percurrentur<emph.end type="italics"></emph.end> IC, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>æquali tempore.<emph.end type="italics"></emph.end><pb pagenum="69" xlink:href="028/01/109.jpg"></pb>Et conſequenter, vt pergas probate tempus per <lb></lb><figure id="id.028.01.109.1.jpg" xlink:href="028/01/109/1.jpg"></figure><lb></lb>quartam partem EF æquale eſſe tempori per <lb></lb>KC quadrantem primæ, <emph type="italics"></emph>Similiter,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>di<lb></lb>uiſa bifariàm<emph.end type="italics"></emph.end> CD <emph type="italics"></emph>in<emph.end type="italics"></emph.end> O, <emph type="italics"></emph>ſumptoque quadr inte<emph.end type="italics"></emph.end><lb></lb>DP <emph type="italics"></emph>æquali ipſi<emph.end type="italics"></emph.end> KC, <emph type="italics"></emph>tota<emph.end type="italics"></emph.end> AE <emph type="italics"></emph>diuiſa erit in par<lb></lb>teis quatuor æqualeis<emph.end type="italics"></emph.end> AK KO, OP, PE; <emph type="italics"></emph>ideó <lb></lb>que velocitas in<emph.end type="italics"></emph.end> E <emph type="italics"></emph>erit quadrupla velocitatis in<emph.end type="italics"></emph.end> K, <emph type="italics"></emph>vt <lb></lb>tota<emph.end type="italics"></emph.end> AE <emph type="italics"></emph>quadrupla eſt ipſius<emph.end type="italics"></emph.end> AK. <emph type="italics"></emph>At velocitas <lb></lb>quoque in<emph.end type="italics"></emph.end> F <emph type="italics"></emph>ob eandem rationem quadrupla etiam eſt <lb></lb>velocitatis in<emph.end type="italics"></emph.end> C; <emph type="italics"></emph>velocitas igitur per totam<emph.end type="italics"></emph.end> EF <lb></lb><emph type="italics"></emph>quadrupla eſt velocitatis per totam<emph.end type="italics"></emph.end> KC, <emph type="italics"></emph>ſicut tota<emph.end type="italics"></emph.end><lb></lb>EF <emph type="italics"></emph>quadrupla eſt ipſius<emph.end type="italics"></emph.end> KC. <emph type="italics"></emph>Percurrentur igitur<emph.end type="italics"></emph.end><lb></lb>KC, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> EF <emph type="italics"></emph>æquali tempore.<emph.end type="italics"></emph.end></s> <s id="s.000696"> Sequitur, <emph type="italics"></emph>Ea <lb></lb>dem autem etiam ratio eſt cæterarum omnium par<lb></lb>tium, vt facilè quilibet ex iſtis per ſe intelliget.<emph.end type="italics"></emph.end></s> <s id="s.000697"> Con<lb></lb>cludis, <emph type="italics"></emph>Si ſpatium igitur, per quod corpus quodcum<lb></lb>que graue deſcendit, ea, qua dictum eſt, ratione diui<lb></lb>ſum intelligatur, ſingulæ partes huiuſmodi æquales tanto <lb></lb>præcisè tempore à corpore graui deſcendente percur<lb></lb>rentur, quantò partes ipſis analogæ ac reſpondentes <lb></lb>in ſuprema parte<emph.end type="italics"></emph.end> (aut inferiore eius dimidio) <emph type="italics"></emph>deſi <lb></lb>gnatæ ab eodem corpore graui decurſæ fuerint, vt est <lb></lb>propoſitum.<emph.end type="italics"></emph.end></s> <s id="s.000698"> Prætereo autem, quod ſubinde de<lb></lb>claras te adſcripſiſſe fini cuiuſque ſex partium <lb></lb>numerum integrum, incipiendo ab vnitate, <lb></lb>ad deſignandum velocitatis gradus illeic acquiſitos, & <lb></lb>ex æquo factos cum decurſis partibus; adſcripſiſſe au<lb></lb>tem mediis interuallis ſecundæ, & ſequentium partium <lb></lb>fractos numeros, ad deſignandum tempora, ſiue fra<lb></lb>ctiones temporis primi, quibus vnumquodque ſpa-<pb pagenum="70" xlink:href="028/01/110.jpg"></pb>tiorum primum conſequentium percurritur. </s> </p> <p type="main"> <s id="s.000699">XXXVIII. </s> <s id="s.000700">Videris itaque imprimis haud abs re <lb></lb>dixiſſe <emph type="italics"></emph>admirabile Paradoxum:<emph.end type="italics"></emph.end> cùm habuiſti videlicet <lb></lb>poſterius primæ partis dimidium, vt ſcalam Prototy<lb></lb>picam, cuius gradibus coæquetur, exquiſitéque men<lb></lb>ſuretur cæterarum omnium conſequentium duratio; <lb></lb>tametſi illud eſſe poſſit parte digiti milleſima minus, <lb></lb>& iſtarum aggeries, quanta eſt tota ſemidiameter <lb></lb>mundi. </s> <s id="s.000701">Non ſanè, quod negem dari lineas, aliaſque <lb></lb>magnitudines, in quibus arcana prorsùs admiranda, <lb></lb>& quæ nemo vnquam ſuſpicatus fuiſſet, detegantur à <lb></lb>Geometris: ſed quod videri iure poſſit penitus incre<lb></lb>dibile alligaſſe potius naturam ipſa quaſi fatȧ cætera<lb></lb>rum partiumipſi poſteriori, quàm prioridimidio; imò <lb></lb>& non tam toti ipſi dimidio, quàm infimo illius pun<lb></lb>cto, à quo triens, quadrans, cæteræ fractiones debeant <lb></lb>ſupputari. </s> <s id="s.000702">Ecquod-nam eſſe enim poteſt illius pri<lb></lb>uilegium; aut quid-nam admiſſum à priore dimidio <lb></lb>eſt, vt eo excidiſſe, & pro nihilo reputari iure cenſea<lb></lb>tur? </s> <s id="s.000703">Quid habere <expan abbr="cõmune">commune</expan> poteſt centeſima, milleſima <lb></lb>decieſque, & centies milleſima pars <expan abbr="cũ">cum</expan> poſteriore hoc <lb></lb>dimidio; non habere autem cum illo priore, à quo to<lb></lb>tus motus dependet; non cùm cæteris partibus perinde <lb></lb>ſuccedentibus; non ſaltem cum vicinis, quibuſcum <lb></lb>proximè cohæret? </s> <s id="s.000704">Deinde, ne hac in re hæream, ea<lb></lb>dem prorsùs incommoda ex triente pro tertia parte, <lb></lb>ex quadrante pro quarta, atque ita de cæteris, quæ ex <lb></lb>ipſo dimidio pro ſecunda conſequuntur. </s> <s id="s.000705">Nam, vt <lb></lb>rem circa ipſum trientem, partemque tertiam ſolùm <lb></lb>atringam, Sicuti primùm totam AC in treis diuiſiſti <pb pagenum="71" xlink:href="028/01/111.jpg"></pb>trienteis quorum poſtremus ſit IC; ſic tota AH diui<lb></lb>di poteſt in trienteis treis, quorum poſtremus ſit QH; <lb></lb>& vt facis tempus per IC minuti vnius cum triente; <lb></lb>cùm ſit nempe triens minutorum quatuor, ſiue duo<lb></lb>rum bes; ita facere licet tempus per QH quadragin<lb></lb>ta ſecundorum, cùm ſit triens minutorum duorum, <lb></lb>ſiue bes vnius minuti. </s> <s id="s.000706">Cùm autem hoc modo QH <lb></lb>ſe habeat ad IC, vt IC, ad ND; & CA non minùs ſit <lb></lb>tripla ipſius AQ, quàm DA ipſius AI, vtráque nem<lb></lb>pe pari modo, quo EA ipſius AC; adeò vt velocitati<lb></lb>bus ob rationem triplam exæquatis, ſic ego poſſim <lb></lb>concludere QH ſe habere ad IC, vt tu concludis IC <lb></lb>ſe habere ad DE, ſequitur, vt, quia concludis tempora <lb></lb>per IC, & DE eſſe æqualia; tempora quoque per QH, <lb></lb>& IC æqualia ſint, ac proinde tempus per IC ſit iam <lb></lb>non vnius minuti cum beſſe, ſed dimidium minuti <lb></lb>cum ſextante; & qua ratione hoc ſequitur, ſequetur vt <lb></lb>aſſumpto dimidio ipſius AH, ac ita ſumptis in infini<lb></lb>tum dimidiorum dimidiis, quæ per trienteis diuidan<lb></lb>tur, futurum, vt ipſa IC minore ſemper, ac minore in <lb></lb>inſinitum tempore, quàm ipſe admiſeris, cenſeatur per<lb></lb>curri. </s> <s id="s.000707">Sic ex eo, quod vis velocitatem in E eſſe tri<lb></lb>plam velocitatis in C; & velocitatem in D triplam <lb></lb>velocitatis in I, pro ratione nempe ſpatiorum, Sequi<lb></lb>tur vt tam tota DE, quàm tota IC percurrantur non <lb></lb>iam vno minuto cum triente, ſed omninò duobus <lb></lb>minutis, trienteve minutorum ſex, quibus percurritur <lb></lb>AC: cùm vbicumque eſt velocitatis triplum, ibi ma<lb></lb>nifeſtò non ſit nec ampliùs nec minùs, quàm tempo<lb></lb>ris triens. </s> <s id="s.000708">Sic incidis rursùs in eum, quem eſſe cauſ-<pb pagenum="72" xlink:href="028/01/112.jpg"></pb>ſatus es in Galileo Paralogiſmum. </s> <s id="s.000709">Nam ſi vt AE ad; <lb></lb>AC ita DE ad IC; ergo vt DE tempus ad IC tempus, <lb></lb>ita AE tempus ad AC tempus; atqui tempus DE per <lb></lb>te eſt æquale tempori IC; ergo AE tempus tempori <lb></lb>AC æquale erit; hoc eſt pars, & totum æquali tempo<lb></lb>re percurrentur. </s> <s id="s.000710">Sic quia totum quodlibet ita ſe habet <lb></lb>ad ſui trientem, & velocitas in fine totius ad velocita<lb></lb>tem in fine trientis, vt ſe habet magnitudo, & veloci<lb></lb>tas AE comparata ad AC: ſequitur, vt etiam pari mo<lb></lb>do ſe habeat, quo DE comparata ad IC; quare & <lb></lb>quemadmodum DE triens ipſius AE eodem tempo<lb></lb>re percurritur, quo IC: ita diametri mundi triens eo<lb></lb>dem tempore percurratur. </s> <s id="s.000711">Neque enim dicas maio<lb></lb>rem eſſe connexionem ipſius DE, quàm trientis dia<lb></lb>metri mundi cum ipſa IC; nam vis ratiocinij eſt ſo<lb></lb>lùm in comparatione totius ad trientem; & aliunde <lb></lb>quot ſunt plures partes in triente diametri mundi, <lb></lb>quàm in triente ſpatij DE: totidem ſunt etiam veloci<lb></lb>tates plures, quibus tempore eodem ſuperetur, atque <lb></lb>ita de cæteris. </s> </p> <p type="main"> <s id="s.000712"><emph type="center"></emph><emph type="italics"></emph>De Ratione continuò dupla, qua ſpatia decurri temporibus <lb></lb>æqualibus R. P. concludit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000713">XXXIX. </s> <s id="s.000714">Supereſt poſtremum, ſiue tertium mem<lb></lb>brum, de Ratione continuò dupla, qua pertranſiri <lb></lb>ſpatia temporibus continuò æqualibus infers. </s> <s id="s.000715">Primùm <lb></lb>autem, vbi adnotaſti non poſſe quidem ex deductio<lb></lb>ne à te mox facta, <emph type="italics"></emph>abſolutè colligi quantum præcisè tem<lb></lb>poris graue ex aßignata altitudine deſcendens in toto deſ<lb></lb>cenſu inſumat, niſi diſtinctè etiam cognoſeatur tempus deſ-<emph.end type="italics"></emph.end><pb pagenum="73" xlink:href="028/01/113.jpg"></pb><emph type="italics"></emph>cenſus non tantum per totam primam partem<emph.end type="italics"></emph.end> AC (in nu<lb></lb>pero ſchemate) <emph type="italics"></emph>ſed etiam ſeorſum per<emph.end type="italics"></emph.end> AH, <emph type="italics"></emph>& per<emph.end type="italics"></emph.end> HC; <lb></lb><emph type="italics"></emph>quod multò difficilius eſſe arbitreris, quàm<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileo videatur; <lb></lb>at cognitis, aut præſuppoſitis temporibus illis, facilè deinceps <lb></lb>totum tempus totius deſcenſus per quamcumque deſignatam <lb></lb>altitudinem determinari:<emph.end type="italics"></emph.end> id quod <emph type="italics"></emph>postmodum te ostenſu<lb></lb>rum recipis.<emph.end type="italics"></emph.end></s> <s id="s.000716"> Tum ſupponens me exſpectare <lb></lb><figure id="id.028.01.113.1.jpg" xlink:href="028/01/113/1.jpg"></figure><lb></lb>diutiùs, quid ſis dicturus de <emph type="italics"></emph>Ratione, qua ſe ha<lb></lb>bent ſpatia æquali tempore emenſa,<emph.end type="italics"></emph.end> ſic infis, <emph type="italics"></emph>Aio <lb></lb>verò æqualibus temporibus ſpatia decurri maiora <lb></lb>ſemper, ac maiora in Ratione dupla. </s> <s id="s.000717">Diuiſo enim <lb></lb>spatio<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>per quod ſupponitur fieri deſcenſus, in <lb></lb>parteis quotcumque æqualeis in<emph.end type="italics"></emph.end> C, D, E, F, <emph type="italics"></emph>&c. </s> <s id="s.000718">iam <lb></lb>ostenſum est partem ſecundam<emph.end type="italics"></emph.end> CD, <emph type="italics"></emph>& primæ par<lb></lb>tis dimidiam partem inferiorem<emph.end type="italics"></emph.end> NC <emph type="italics"></emph>æquali tempore <lb></lb>percurri; & ob eam quidem cauſſam, quòd, vt pars<emph.end type="italics"></emph.end><lb></lb>CD <emph type="italics"></emph>dupla eſt partis<emph.end type="italics"></emph.end> NC, <emph type="italics"></emph>ita velocitas quoque per <lb></lb>totam<emph.end type="italics"></emph.end> CD <emph type="italics"></emph>dupla ſit velocitatis per totam<emph.end type="italics"></emph.end> NC. <emph type="italics"></emph>At <lb></lb>ſimili ratione etiam efficitur, velocitatem per totam<emph.end type="italics"></emph.end><lb></lb>DF <emph type="italics"></emph>duplam eſſe velocitatis eius, quæ habetur per <lb></lb>totam<emph.end type="italics"></emph.end> CD; <emph type="italics"></emph>ſicut tota<emph.end type="italics"></emph.end> DF <emph type="italics"></emph>dupla eſt ipſius<emph.end type="italics"></emph.end> CD. <lb></lb>Æ<emph type="italics"></emph>quali igitur tempore<emph.end type="italics"></emph.end> CD, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> DF <emph type="italics"></emph>decurruntur; <lb></lb>eademque omninò ratio eſt ipſarum<emph.end type="italics"></emph.end> DF, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> FK, <lb></lb><emph type="italics"></emph>cæterarumque omnium ſe pariter in ratione dupla ſu <lb></lb>perantium; vt ſatis manifeſtum eſt.<emph.end type="italics"></emph.end> S<emph type="italics"></emph>patia igitur <lb></lb>æqualibus temporibus emenſa, & velocitates iiſdem <lb></lb>temporibus æqualibus acquiſitæ ſemper augentur in <lb></lb>continua ratione dupla.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000719">XL. Cæterùm, cùm iſte habeatur quaſi <lb></lb>prouentus quidam eximius totius tuæ Diſſertationis; <pb pagenum="74" xlink:href="028/01/114.jpg"></pb>Patietur tua bonitas adm rari imprimis me, quid eſſe <lb></lb>agendum cogitaueris de primo dimidio AN. </s> <s id="s.000720">Vide<lb></lb>licet rationem duplam, progreſſionemque à puncto <lb></lb>N ita inchoas, vt ſi motus inciperer, ac vniformiter <lb></lb>quidem, non à puncto A, ſed à puncto N. </s> <s id="s.000721">An dices <lb></lb>fortè poſſe AN ita biſecari, vt motus, & ratio, pro<lb></lb>greſſioque illius incipiat à puncto inter A, & N me<lb></lb>dio? </s> <s id="s.000722">Sed biſeca, vt voles, eadem erit ruina. </s> <s id="s.000723">Biſeca <lb></lb>rursùs, iterumque, & porrò vſque in infinitum; atta<lb></lb>men ſemper ſupererit pars, à cuius medio, non autem <lb></lb>ab A fieri incœptio cogitetur; adeò vt prorsùs perinde <lb></lb>ſit conſiſtere in dimidio AN. </s> <s id="s.000724">Cùm autem dicturus <lb></lb>prætereà non ſis fieri ſolùm quoddam quaſi tyroci<lb></lb>nium, ſeu præludium ex A in N, ac motum deinde, <lb></lb>& rationem, progreſſionemque incipere ſeriò ab N; <lb></lb>cùm non ſis, in quam, id dicturus, vt pote, qui motum <lb></lb>admittas à primo vſque ſui momento accelerari vni<lb></lb>formiter; ac ſupponas etiam, vbi tempus per AC mi<lb></lb>nutorum ſex fuerit, tempus per AN futurum minuto<lb></lb>rum quatuor; quæſo te, ecquis modus eſt progreſſio<lb></lb>nis ex A in N? </s> <s id="s.000725">Nam ab A quidem incipiens motus <lb></lb>acceleratur continuò, & progreſſu accelerationis in<lb></lb>alterato tranſit per N, ac pergit vlterius, nec dicere <lb></lb>licet quid illi ſpeciale contingat in N, quod in alio <lb></lb>quovis puncto non contingat. </s> <s id="s.000726">An non ergo, ſi tem<lb></lb>poribus æqualibus ſpatia decurruntur in ratione du<lb></lb>pla; debet omninò ſpatium AN percurti tempore <lb></lb>æquali cum ſpatio conſequente duplo, vt putà ipſo <lb></lb>NS? </s> <s id="s.000727">Id autem cùm prorſus ita eſſe debeat, qui fit, vt <lb></lb>per te etiam triplum percurratur ſpatium, putà ND? <pb pagenum="75" xlink:href="028/01/115.jpg"></pb>Quippe, vt tempus per AN eſt <expan abbr="minutorũ">minutorum</expan> quatuor; ita <lb></lb>tempus per NC, & CD, vtrumque, ex te, minutorum <lb></lb>duorum, ſtatuitur coniunctim minutorum quatuor. <lb></lb></s> <s id="s.000728">Ecquo ergo modo ſanari id putas? </s> <s id="s.000729">Patere rursùs mi<lb></lb>rari me, quorſum ablegandam cenſueris progreſſio<lb></lb>nem illam arithmeticam, qua velocitates ſe, vt ſpatia <lb></lb>habent, & quam ſternendam, vt fundamentum ædifi<lb></lb>cij totius cenſuiſti? </s> <s id="s.000730">Ecce enim, cùm velles gradus ce<lb></lb>leritatis ita diſtribui, vt in D eſſent duo gradus, quo<lb></lb>rum vnus eſſet acquiſitus ab A in C, & alius ipſi æqua<lb></lb>lis acquiſitus à C in D; vis iam à C in D talem gra<lb></lb>dum acquiri, qualis acquiritur ab N in C; quando<lb></lb>quidem CD tanto tempore, quanto NC, cuius eſt <lb></lb>dupla, percurritur. </s> <s id="s.000731">Ex quo rurſus conſequitur, vt ve<lb></lb>locitates per AC, & NC acquiſitæ ſint prorsùs æqua<lb></lb>les; ac proinde, vt AC, & NC hoc eſt totum, & pars <lb></lb>eodem tempore percurrantur; ac ſpatium CD non <lb></lb>percurratur modò eodem tempore, quo NC, ſed <lb></lb>etiam eodem, quo AC; quæ iterùm neſcio ſanari quá <lb></lb>valeant. </s> </p> <p type="main"> <s id="s.000732">XLI. </s> <s id="s.000733">Patere inſuper, vt requiram, ſubſit-ne tibi <lb></lb>ratio, quamobrem diuisâ lineâ AB in parteis æqua<lb></lb>leis, deligere poſſis dimidium NC, &i pergendo pro<lb></lb>portione dupla dicere, vt NC ad CD, ita CD ad <lb></lb>DF, & DF ad FK, &c. </s> <s id="s.000734">dicere autem perinde non <lb></lb>liceat, vt AC ad CE, ita CE ad EI, & EI ad ſui du<lb></lb>plam? </s> <s id="s.000735">Dicere certè accipiendum eſſe poſterius pri<lb></lb>mæ partis dimidium, quòd contineatur in eo men<lb></lb>ſura cæterarum partium conſequentium, videtur eſſe <lb></lb>dicere gratis, ipſamque petere quæſtionem; ac aliunde <pb pagenum="76" xlink:href="028/01/116.jpg"></pb>agitur ſolùm de progreſſione Geometrica, quam ge<lb></lb>neralem cùm ſtatuas, incipere vndelibet licet, & nullo <lb></lb>quidem ex puncto magis ſecundum naturam, quàm <lb></lb>ex puncto A. </s> <s id="s.000736">Dic enim, amabò, ſi quiſpiam pernoſſe <lb></lb>rationem exoptet, qua decidens graue progrediatur <lb></lb>ab A in B, & tu oſtenſurus ita exordiaris, Vt NC ad <lb></lb>CD, ita CD ad DF, &c. </s> <s id="s.000737">putas te illi facturum <lb></lb>ſatis, ac tibi obiectum non iri quæſtionem eſſe, non <lb></lb>de progreſſu ab N ſolùm, ſed de progreſſu ab vſque <lb></lb>A, de quo ſi nolles dicere, nihil dicere foret præſtabi<lb></lb>lius? </s> <s id="s.000738">Patere quin etiam, vt rogitem te, quî ea expedi<lb></lb>re, quæ à te deinceps ſubiunguntur, valeas? </s> <s id="s.000739">Compa<lb></lb>rans enim tempora, quibus partes omnes primum ſe<lb></lb>quentes percurruntur, cum temporibus, quibus vis <lb></lb>fragmenta poſterioris illius dimidij ſigillatim ſumpta <lb></lb>percurri, iſthæc habes verba, <emph type="italics"></emph>Sic tempus, quo primi in<lb></lb>terualli media pars inferior abſoluitur, & quo duæ ſequen<lb></lb>tes partes, nempe<emph.end type="italics"></emph.end> 3, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 4, <emph type="italics"></emph>ſigillatim tranſcurrerentur; <lb></lb>itemque illud, quo quatuor ſequentes<emph.end type="italics"></emph.end> 5, 6, 7, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 8, <emph type="italics"></emph>vel <lb></lb>ſequentes octo<emph.end type="italics"></emph.end> 9, 10, 11, 12, 13, 14, 15, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> 16, <emph type="italics"></emph>aut cæ<lb></lb>teræ conſequenter, ſeorſim tamen, & ſucceßiuè abſolueren<lb></lb>tur.<emph.end type="italics"></emph.end></s> <s id="s.000740"> Quæſo te verò, quî id fieri, quod hac ratione <lb></lb>deducis valeat? </s> <s id="s.000741">Aſſume enim integrum tempus, quod<lb></lb>cúmque volueris, vt ad illud referas quaſcúmque heic <lb></lb>enumeras parteis, & peruidebis ratio-ne dupla id ip<lb></lb>ſum, quod moliris, abſoluat. </s> <s id="s.000742">Eſto v. c. tempus per <lb></lb>AC triginta ſex, vt triens, ſeu tempus, quod tribuis <lb></lb>poſteriori dimidio, quodque primum facis, ſit duode<lb></lb>cim; cùm ſubinde ſpatium æquale dimidio, cui debi<lb></lb>tum ſit tempus 6. ideò duplices, vt pro ſecundo ſpatio <pb pagenum="77" xlink:href="028/01/117.jpg"></pb>habeas iterum duodecim; compone deinde in vnum <lb></lb>duo tempora duorum ſequentium interuallorum, vi<lb></lb>delicet trientem 4, & quadrantem 3, ac habebis non <lb></lb>duodecim, hoc eſt tempus æquale primo, ſed ſeptem <lb></lb>illius duodecimas dumtaxat; aut ſi duplices, etiam duo<lb></lb>decimas quatuordecim. </s> <s id="s.000743">Adde pari modo quatuor <lb></lb>tempora quatuor aliorum interuallorum, hoc eſt par<lb></lb>teis 5, 6, 7, 8, & habebis iterùm non duodecim, ſed <lb></lb>vix ampliùs quàm duodecimas ſeptem, cum ſemiſſe; <lb></lb>aut ſi duplices, etiam quidpiam amplius, quàm duode<lb></lb>cimas quin lecim. </s> <s id="s.000744">Adde & quæ octo ſequuntur inter<lb></lb>uallorum conſequentium; & habebis rursùs non duo<lb></lb>decim, ſed duodecimas non omninò octo: aut ſi <lb></lb>duplices, etiam duodecimas ferè ſexdecim. </s> <s id="s.000745">Imò & <lb></lb>adde ſexdecim, quæ interuallorum ſuccedentium ſunt, <lb></lb>& vix habebis ampliùs, quàm duodecimas octo: <lb></lb>aut ſi duplices, etiam aliquid amplius quàm duodeci<lb></lb>mas ſexdecim. </s> <s id="s.000746">Adde & quæ ſunt triginta duorum <lb></lb>proximorum, & habebis ſolùm duodecimas non om<lb></lb>ninò octo cum triente: aut ſi duplices, etiam duodeci<lb></lb>mas ſexdecim cum proximè beſſe, atque ita de cæteris. <lb></lb></s> <s id="s.000747">Ex quo profecto ſit, vt videas nulla ratione cohærere, <lb></lb>quam ſubeſſe exiſtimaſti, æqualitatem temporum cum <lb></lb>ratione dupla ſpatiorum. </s> </p> <p type="main"> <s id="s.000748">XLII. Denique, vt alia præteream, quæ tuo ex ra<lb></lb>tiocinio, dum rationem duplam ſtabilire conaris, con<lb></lb>ſequuntur incommoda; Sequitur ecce vt ſtabilias <lb></lb>non modò duplam, ſed etiam triplam, quadruplam, <lb></lb>decuplam, & quamlibet aliam. </s> <s id="s.000749">Nam vt de tripla ſo<lb></lb>lùm dicam (cùm in cæteris idem iuris ſit) ac non <pb pagenum="78" xlink:href="028/01/118.jpg"></pb>repetam, quod iam inſinuaui, velle te AN, & ND, <lb></lb>quod ſpatium eſt triplum, æquali tempore percurri, ac <lb></lb>ita rationem incipere triplam, deberéque eodem pro<lb></lb>gredi tenore ex D in T ipſius ND triplam, & ita <lb></lb>deinceps; ne id, inquam, repetam: accipiatur non NC, <lb></lb>ſed XC infimus triens primæ partis. </s> <s id="s.000750">Vis tu tempora <lb></lb>XC, & DE eſſe æqualia, quoniam XC eſt triens ip<lb></lb>ſius DE, eo modo, quo vis tempora per NC, & CD, <lb></lb>eſſe æqualia; quoniam NC eſt dimidium ipſius CD: <lb></lb>Quare, vt, aſſumendo partem analogam ipſi NC, vt <lb></lb>putà CD, progrederis deinceps in ratione dupla CD, <lb></lb>DF, FK, &c. </s> <s id="s.000751">ita aſſumendo partem analogam ipſi <lb></lb>XC, progredi deinceps licebit in ratione tripla DE, <lb></lb>EH, HB, &c. </s> <s id="s.000752">Sequitur quoque te recidiſſe in illud <lb></lb>ipſum incommodum, quod deduxi antè aduerſus <lb></lb>eandem rationem duplam: nempe, vt debeas admit<lb></lb>tere, peracto primo tempore in percurrendo aliquo <lb></lb>ſpatio, percurri deinceps debere ſpatia omninò infini<lb></lb>ta, priuſquam finis temporis alterius æqualis adueniat. <lb></lb></s> <s id="s.000753">Quippe, ſi vt tu biſecuiſti partem primam AC in N, <lb></lb>ita cæteræ biſcentur in S, V, &c. </s> <s id="s.000754">Quemadmodum <lb></lb>tempus NC fit per te dimidium temporis AN, ita <lb></lb>tempus CS erit dimidium temporis NC, & tempus <lb></lb>SD dimidium temporis CS, &c. </s> <s id="s.000755">Et vtcumque con<lb></lb>tendas iam, incipiendum eſſe non à puncto A, ſed à <lb></lb>puncto N: idem nihilominùs ſequetur. </s> <s id="s.000756">Nam rema<lb></lb>nente eadem biſectiore partium, ac habentibus, ſe <lb></lb>dimidiis eadem ratione, qua habent tota; cùm ſi ex <lb></lb>N in C certus velocitatis gradus acquiratur, is ſit dein<lb></lb>de in S duplus, ac pari ratione eſſe debeat in D qua-<pb pagenum="79" xlink:href="028/01/119.jpg"></pb>druplus, in V octuplus, &c. </s> <s id="s.000757">quòd vt geminatur à pri<lb></lb>mo interuallo in ſecundum, ſic geminati debeat à ſe<lb></lb>cundo in tertium, à tertio in quartum, &c. </s> <s id="s.000758">ideò tem<lb></lb>pora fient ſemper dimidiorum dimidia. </s> <s id="s.000759">Vnde eueniet, <lb></lb>vt peracto tempore primo, procedatur ſolùm conſe<lb></lb>quenter per eiuſdem dimidium, quadrantem, octan<lb></lb>tem, & fractiones cæteras nunquam ipſi toti, niſi <lb></lb>tranſactis ſpatiis infinitis, exæquandas. </s> </p> <p type="main"> <s id="s.000760"><emph type="center"></emph><emph type="italics"></emph>De Tempore, quo<emph.end type="italics"></emph.end> G<emph type="italics"></emph>lobum ferreum caſurum ex Luna in <lb></lb>Terram contendit.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000761">XLIII. </s> <s id="s.000762">Cùm tibi ſubinde in animo eſſet ſpecimen <lb></lb>quoddam inſigne dare huiuſce tuæ rationis duplæ, <lb></lb>caſum delegiſti globi ferrei ex Luna vſque in centrum <lb></lb>Terræ. </s> <s id="s.000763">Ac primùm quidem adnotas ſequi ex tua illa <lb></lb>ratione, G<emph type="italics"></emph>rauia omnia longè celeriùs deorſum moueri, <lb></lb>quàm à<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileo conſtituatur; quoniam cùm ex eius principiis <lb></lb>corpus graue quodcumque ſex temporibus, exempli gratiâ, <lb></lb>inter ſe æqualibus deſcendens, non niſi triginta ſex interualla <lb></lb>æqualia percurrat; poſita aliunde acceleratione motus <lb></lb>æqualibus temporibus in ratione dupla, demonſtratum<emph.end type="italics"></emph.end> à te <lb></lb>dicis <emph type="italics"></emph>neceſſe omninò eſſe, vt idem corpus graue ſex iiſdem <lb></lb>temporibus deſcendens in terualla non tantum triginta ſex, <lb></lb>ſed ſexaginta tria decurrat.<emph.end type="italics"></emph.end></s> <s id="s.000764">Verùm hac in re non eſt <lb></lb>immorandum, neque exaggeranda eſt exorbitatio, <lb></lb>qua facta progreſſio in ratione dupla, vtcumque initio <lb></lb>moderata ſit, & progreſſionem ſecundum ſeriem nu<lb></lb>merorum imparium proximè circumſtet; illicò tamen <lb></lb>omneis metas probabilitatis prætergreditur, cùm res <lb></lb>ſtatim pateat in ipſo de caſu ex Luna exemplo. </s> <s id="s.000765">Ecce <pb pagenum="80" xlink:href="028/01/120.jpg"></pb>enim quia Galileus, ſupponendo eſſe à Luna in cen<lb></lb>trum terræ milliaria 196000. ratiocinatur globum <lb></lb>ferreum è Luna dimiſſum peruenturum ad centrum <lb></lb>Terræ intra horas 3. & minuta 22. cum ſecundis 4. <lb></lb>quatenus ex obſeruatione ab eo peracta decidit ini<lb></lb>tio, intra ſecunda quinque, centum cubitis; ac perre<lb></lb>cturus eſt deinceps iuxta progreſſionem ab eo aſſi<lb></lb>gnatam: idcircò tu illa milliaria diuidens in pedes <lb></lb>980000000 (quanquam Galileus non pedes vſurpa<lb></lb>uit, ſed cubitos, quorum numerus foret 588000000) <lb></lb>& numerum reducens in pedum centena 9800000, <lb></lb>aſſumis 100 pedes (aſſumpſit ille ex obſeruatione 100 <lb></lb>cubitos, qui continent pedes (166 2/3)) pro ſpatio, quod <lb></lb>percurritur quinque ſecundis, ſeu tempore vno, qua<lb></lb>lia ſunt duodecim in vno minuto, & 24 in duobus mi<lb></lb>nutis: ac tum extendendo 24. hæc tempora, tribuis <lb></lb>primo 100, ſecundo 200, tertio 400, quarto 800, at<lb></lb>que ita ingeminando, quovſque vigeſimo quarto tri<lb></lb>buas 838860800: & colligis poſtea omnium ſum<lb></lb>mam 1677721500, numerum videlicet pedum, qui <lb></lb>percurruntur intra duo minuta. </s> <s id="s.000766">Et quia illi ſunt pedes <lb></lb>longè plures, quàm in prædicto ſpatio à Luna ad cen<lb></lb>trum teriæ aſſignentur, concludis fore, vt <emph type="italics"></emph>prædictus glo<lb></lb>bus in eo deſcenſu à Luna vſque ad <expan abbr="centrũ">centrum</expan> Terræ, duo prima <lb></lb>horæ minuta, ſiue trigeſimam vnius horæ partem non inſu<lb></lb>meret:<emph.end type="italics"></emph.end> ac iubes me <emph type="italics"></emph>videre, quàm dispar celeritatis ratio in<lb></lb>ter vtrumque calculum inueniatur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000767">XLIIII. </s> <s id="s.000768">Ego autem & video ſanè, & quantum <lb></lb>aſſequor, debet globus ferreus cadere per te à Luna in <lb></lb>centrum aut vno minuto, & quinquaginta ſeptem <pb pagenum="81" xlink:href="028/01/121.jpg"></pb>ſecundis, quatenus vſurpas pedes; aut minuto vno, ſe<lb></lb>cudis quinquaginta quatuor, quatenus videris debuiſ<lb></lb>ſe vſurpare cubitos. </s> <s id="s.000769">Verum neque video, neque aſſe<lb></lb>quor pernicitatem vllam tantam, qua decidens graue <lb></lb>tempore tam breui percurrat tam immane ſpatium, <lb></lb>quale continere admittis ducenta milliarium, prope<lb></lb>modum millia. </s> <s id="s.000770">Certè, cùm attendo globum tormen<lb></lb>tarium è machina quapiam maiore exploſum vertica<lb></lb>liter, vno circiter pòſt minuto repetitam terram attin<lb></lb>gere, & vix tamen, ex ſupputatis obſeruationibus variis, <lb></lb>pertigiſſe ad vnum milliare altitudinis, ex qua vſque <lb></lb>recidens dimidium eius temporis, ſeu ſemi-minutum <lb></lb>inſumpſerit: (ſæpe enim ſæpiùs obſeruauimus eſſe re<lb></lb>rum grauium ſurſum proiectarum deſcenſum æqui<lb></lb>temporaneum aſcenſui) cùm ad iſtud, inquam, at<lb></lb>tendo, conſideróque ſimul globum per hoc milliare <lb></lb>decidere eadem illa velocitate, qua inciperet cadere à <lb></lb>Luna; aſſequor quidem euenturum, vt ex Luna deci<lb></lb>dens, & iuxta progreſſionem Arithmeticam numero<lb></lb>rum ab vnitate imparium incedens, decideret altero <lb></lb>ſemi-minuto milliaribus tribus, tertio quinque, & <lb></lb>quarto ſeptem; adeò vt, ſub finem ſecundi minuti de<lb></lb>prehenderetur decidiſſe milliaribus ſexdecim, ſeu <lb></lb>iuxta Galileum, nouemdecim, cum vna quinta millia<lb></lb>ris parte: At quid-nam hoc eſt ad milliarium ducenta <lb></lb>millia comparatum? </s> <s id="s.000771">Quanquam & iuxta illam tuam, <lb></lb>Geometricamve rationem duplam, poſſet res prope <lb></lb>verum haberi, quod ad milliaria illa prima, ac minuta <lb></lb>duo prima attinet, ſi diceremus eundem globum de<lb></lb>curſurum primo ſemi-minuto milliare vnum, ſecundo <pb pagenum="82" xlink:href="028/01/122.jpg"></pb>duo, tertio quatuor, quarto octo: ex quo futurum <lb></lb>vides, vt duobus minutis milliaria non decideret pluſ<lb></lb>quam quindecim; cùm alias mirà incohærentiâ de<lb></lb>ducatur, vt primo ſemi-minuto decidere velis globum <lb></lb>milliaribus ſex cum fere triente; ſecundo milliaribus <lb></lb>quadringentis, ac tribus, & vna quinta milliaris parte, <lb></lb>tertio vicies quinquies mille octingentis quatuor, cum <lb></lb>dodrante; & quarto totis milliarium myriadibus cem<lb></lb>tum ſextaginta quinque; ac inſuper mille quingentis <lb></lb>ſeptem, cum vna quinta; totidem enim ex tua ſerie, ac <lb></lb>ſumma pedum colliguntur. </s> <s id="s.000772">Quæ admonere ſanè po<lb></lb>tuiſſe videntur, quàm incredibilem admitteres rem, <lb></lb>dum concluderes, & ad marginem exprimeres <emph type="italics"></emph>fore, vt <lb></lb>globus ferreus à Lunæ concauo ad centrum deſcendens, ſer<lb></lb>uata temporibus æqualibus acceleratione in ratione dupla, in <lb></lb>toto deſcenſu duo vnius horæ minuta prima integre non in<lb></lb>ſumeret.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000773"><emph type="center"></emph><emph type="italics"></emph>De Tempore per primas parteis obſeruatione determinandos <lb></lb>pauca de cauſſa Phyſica, deque lapſu circa eam admiſſo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000774">XLV. </s> <s id="s.000775">Videris deinde fidem liberare circa id, <lb></lb>quod facturum te receperas de tempore determinan<lb></lb>do, quo duo illa primæ partis percurruntur dimidia; <lb></lb>vt quo habito diſtinctè deinde præ iſum tempus cog<lb></lb>noſceremus, quo decidens graue deſignatum ſpatium <lb></lb>ſuo deſcenſu percurteret. </s> <s id="s.000776">Dicis autem primò, G<emph type="italics"></emph>alileum <lb></lb>quidem id fidenter promittere, dum ait ſe iteratis ſæpiùs ac <lb></lb>diligenter experient is obſeruaſſe globum ferreum ex altitud ne <lb></lb>cubitorum centum decidentem quinque ſecundis horæ minutis <lb></lb>totum illud ſpatium decurriſſe: verùm, cùm idem non minùs<emph.end type="italics"></emph.end><pb pagenum="83" xlink:href="028/01/123.jpg"></pb><emph type="italics"></emph>audacter etiam affirmet ſe item eadem methodo expertum <lb></lb>eſſe spatia ęqualibus temporibus emenſa eam inter ſe ratio<lb></lb>nem obſeruare, quæ inter numeros omneis impareis ab vni<lb></lb>tate continua ſerie procedenteis inuenitur; & in hac tamen <lb></lb>poſteriore obſeruatione vehementer errauerit, magnoperè <lb></lb>verendum eſſe, ne in priore quoque non minùs hallucinatus <lb></lb>ſit.<emph.end type="italics"></emph.end></s> <s id="s.000777"> Dicis deinde, <emph type="italics"></emph>Satis non eſſe, ſi tempus habeatur, quo <lb></lb>prima quælibet pars deſignati spatij tranſmittitur, niſi tem<lb></lb>pus quoque cognoſcatur, quo pars ſequens priori æqualis, vel <lb></lb>duæ medietates primę ſeorſim decurruntur; quod tamen <lb></lb>exactè determinare,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>per quam difficile arbitror, ob <lb></lb>cauſſas iam ſæpiùs adductas.<emph.end type="italics"></emph.end></s> <s id="s.000778"> Et quænam quidem fue<lb></lb>rint huiuſmodi cauſſæ non commemini; ſed interim <lb></lb>tamen candorem commendo, quo dicis Tertiò, <emph type="italics"></emph>te qua<lb></lb>cúmque diligentia adhibita nihil habere potuiſſe, in quo in<lb></lb>tellectus conquieſceret:<emph.end type="italics"></emph.end> ac author es; vt ſi aliquis ſe id <lb></lb>fœliciùs aſſequi poſſe confidat, <emph type="italics"></emph>turrim ſatis excelſam <lb></lb>eligat, puta<emph.end type="italics"></emph.end> 200 <emph type="italics"></emph>pedum; ac deinde aliam altitudinem duplò <lb></lb>præcisè minorem, pedum videlicet centum; & ex vtraque <lb></lb>altitudine, tempus deſcenſus exactißimè inquirat; tum mino<lb></lb>re tempore, ex maiore ſubducto, reſiduum daturum tempus <lb></lb>deſcenſus per turris maioris centum pedes infimos: tempus <lb></lb>verò illud minus, quo idem corpus ex ſola centum pedum al<lb></lb>titudine deſcendet, ęquale tempori futurum, quo ex maiori <lb></lb>quoque altitudine, per centum pedes ſuperiores deſcenderit.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000779">XLVI. </s> <s id="s.000780">Ad primum porrò quod attinet; videtur <lb></lb>ſanè non ſatis idonea refutatio experimenti, quod <lb></lb>ille teſtatur ſe ſæpiùs, ac diligenter peregiſſe, niſi teſte<lb></lb>ris temetipſum idem tentaſſe, peregiſſeque, ac fuiſſe <lb></lb>rem ſecùs à te obſeruatam, falſitatiſque adeò con-<pb pagenum="84" xlink:href="028/01/124.jpg"></pb>uictam. </s> <s id="s.000781">Quod enim eſſe verendum ais, ne halluci<lb></lb>natus fuerit, hoc ſatis profectò non eſt; & quòd argu<lb></lb>mento eſt tibi error vehemens, quem admiſiſſe illum <lb></lb>ais, circa progreſſionem iuxta ſeriem numerorum im<lb></lb>parium; declaratum iam antè eſt, vt ea quoque ipſa in <lb></lb>re non fuerit erroris conuictus; imò & ſuffragium <lb></lb>etiam tulerit cùm ex aliis experimentis, tum etiam ex <lb></lb>tuo, hoc eſt in Bilance peracto. </s> <s id="s.000782">Ad ſecundum quod <lb></lb>ſpectat, determinauit ille, quo præcisè tempore ſecun<lb></lb>da ſpatij pars, ac dimidium primæ, & quævis alia per<lb></lb>curreretur, ex aſſignato tempore, quo pars prima de<lb></lb>curritur. </s> <s id="s.000783">Oſtendit nimirum ex ſuis principijs, <emph type="italics"></emph>Si à <lb></lb>lationis principio duo quælibet spatia ſumantur, tempora <lb></lb>ipſorum fore inter ſe, vt alterum eorum ad spatium medium <lb></lb>proportionale inter ipſa.<emph.end type="italics"></emph.end></s> <s id="s.000784"> Adeò vt, ſi inter AB pri<lb></lb>mam partem, & AC aggregatum primæ cum <lb></lb><figure id="id.028.01.124.1.jpg" xlink:href="028/01/124/1.jpg"></figure><lb></lb>ſecunda inuenias mediam proportionalem AD, <lb></lb>tempus caſus per AB, ad tempus caſus per AC, <lb></lb>futurum ſit vt AB, ad AD. </s> <s id="s.000785">Nimirùm id <lb></lb>conſequitur ex eo, quòd ſpatia ſint inter ſe <lb></lb>in duplicata temporum ratione; ſeu vt quadra<lb></lb>ta temporum; quódque ſit perſpicuum ratio<lb></lb>nem ſpatij AC ad ſpatium AB eſſe duplam <lb></lb>rationis AC, ad AD, ſeu eandem, quam ha<lb></lb>bent quadrata AC, & AD. </s> <s id="s.000786">Ex quo fiet, vt cùm AB <lb></lb>ſupponas eſſe ſex minutorum, AC compobetur mi<lb></lb>nutorum octo, & 29. ſecundorum proximè; ac proin<lb></lb>de tempus per BC ſit minutorum duorum, & viginti <lb></lb>nouem proximè ſecundorum. </s> <s id="s.000787">Eadem autem ratione <lb></lb>diuiſa bifariam prima parte in E, & accepta AF media <pb pagenum="85" xlink:href="028/01/125.jpg"></pb>proportionali inter AB, & AE, reperietur tempus <lb></lb>per primum dimidium AE minutorum 4, & ſe cun<lb></lb>dorum (14 1/2) ac relinquetur proinde tempus per poſte<lb></lb>rius dimidium FB minuti 1, at ſecundorum 45. Ad <lb></lb>Tertium nihil eſt, quod dicam, quandò nihil determi<lb></lb>nas, ſed prouocas <expan abbr="ſolũ">ſolum</expan> ad experimentum, quod fieri ab <lb></lb>alio exoptes. </s> <s id="s.000788">Ac videbatur quidem id <expan abbr="experimentũ">experimentum</expan> abs <lb></lb>te præſertim exſpectandum, cùm profitereris <emph type="italics"></emph>nouam <lb></lb>ſcientiam,<emph.end type="italics"></emph.end> ſeu <emph type="italics"></emph>demonſtrationem, qua ratio, menſura, modus, <lb></lb>ac potentia accelerationis motus in naturali deſcenſu grauium <lb></lb>determinaretur:<emph.end type="italics"></emph.end> idque aduerſus eam, quam <emph type="italics"></emph>excogitatam à <lb></lb>Galileo pſeudo-ſcientiam<emph.end type="italics"></emph.end> appellitares; ſed nolo tamen <lb></lb>hac in re eſſe importunus; addoque ſolùm, vbi id ex<lb></lb>perimentum peractum fuerit, ſucceſſeritque, certum <lb></lb>me propemodum eſſe, ex ijs, quæ hactenus peregi ipſi <lb></lb>valdè affinibus, elicitum exinde iri, quod opinionem <lb></lb>fulciar, non tuam, ſed ex Galileo hactenus expreſſam. </s> </p> <p type="main"> <s id="s.000789">XLVII. </s> <s id="s.000790">Iam ad finem properans, <emph type="italics"></emph>omittere<emph.end type="italics"></emph.end> te dicis, <lb></lb><emph type="italics"></emph>quæ etiam de Motu accelerato examinari poſſent, vt, quę, qua<lb></lb>liſque ſit cauſſa accelerationis in naturali deſcenſu grauium: <lb></lb>cur corpora, ſaltem, quæ eiuſdem figuræ, & homogenea ſint, <lb></lb>cuiuſcumque, & quantumlibet inęqualis ponderis illa fuerint, <lb></lb>deorsùm nihilominùs ęquali celeritate deſcendant: aliàque <lb></lb>eiuſmo li, quę tibi quidem in promptu ſint, & alio loco, ac <lb></lb>tempore opportuniùs fortaſſe proferenda in publicum: ſed in<lb></lb>terim hęc pręlibanda putaſſe, quę non mo ò ad reuincendos<emph.end type="italics"></emph.end><lb></lb>G<emph type="italics"></emph>alilei errores opportuna, ſed ad veram quoque, ac germa<lb></lb>nam accelerati motus naturam aperiendam neceſſaria vide<lb></lb>rentur.<emph.end type="italics"></emph.end></s> <s id="s.000791"> Quo rursùs loco, nihil eſt, quod addam, neque <lb></lb>cur importunè rogem, quamobrem non cenſueris <pb pagenum="86" xlink:href="028/01/126.jpg"></pb><expan abbr="ſubiiciendũ">ſubiiciendum</expan> aliquid eſſe de quæſtionibus illis Phyſicis <lb></lb>ac duabus præſertim heic commemoratis; cùm id fe<lb></lb>cerit maximè ſperandum, qui titulus eſt <emph type="italics"></emph>Phyſica demon<lb></lb>ſtratio<emph.end type="italics"></emph.end> præſcriptus. </s> <s id="s.000792">Scilicet tibi liberum fuit exſpecta<lb></lb>re tempus, quoddam opportunius; ac mihi ſanè op<lb></lb>pidò nimiùm pro tua comitate tribuiſti, cùm faciens <lb></lb>editionis ſpem, id futurum interſeruiſti, <emph type="italics"></emph>maximè, ſi <lb></lb>cognoueris iſta viris eruditis, mihique imprimis minimè diſ<lb></lb>plicuiſſe.<emph.end type="italics"></emph.end></s> <s id="s.000793"> Ac intelligo quidem non fuiſſe cur tibi pla<lb></lb>cerent, quæ de iiſdem quæſtionibus in priore mearum <lb></lb>illarum Epiſtolarum commentus ſum, ac cætera inter, <lb></lb>quod adnixus fui explicare Phyſicam cauſſam, ob <lb></lb>quam cadens graue primo momento per vnam or<lb></lb>gyiam, cadit in ſecundo per treis, in tertio per quin<lb></lb>que, &c. </s> <s id="s.000794">Verùm ratio iam nulla ſubeſt, quorsùm aut <lb></lb>quicquam repetam, aut obiectionem, ſi quampiam es <lb></lb>propoſiturus præoccupem; cùm paratus aliunde ſim <lb></lb>& manus dare, & habere gratiam, quam maximam <lb></lb>voueo, meliora docenti. </s> <s id="s.000795">Agnoſco interim, me inſigni <lb></lb>quadam incuria illa confcripſiſſe, quæ leguntur potiſ<lb></lb>ſimùm à calce paginæ ſeptuageſimæ ad caput ſexage<lb></lb>ſimæ tertiæ, vbi figuram explicans, quam ab initio hûc <lb></lb>retuli, ipſos velocitatis gradus ſic feci ex pari cum par<lb></lb>tibus ſpatij, vt per eoſdem triangulos repræſentatos <lb></lb>aſſumpſerim; cùm debuerim potiùs per ipſas triangu<lb></lb>lorum veluti baſeis parallelas repræſentare. </s> </p> <p type="main"> <s id="s.000796">XLVIII. </s> <s id="s.000797">Poſtremò anacephalæoſi concludens; <lb></lb><emph type="italics"></emph>Ex his enim,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>niſi vehementer fallor, manifestè iam <lb></lb>vides, & euidenter agnoſcis, quàm non rectè<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus mo<lb></lb>tum æquabiliter acceleratum eum eſſe definierit, qui æqualibus<emph.end type="italics"></emph.end><pb pagenum="87" xlink:href="028/01/127.jpg"></pb><emph type="italics"></emph>temporibus, æqualia celeritatis augmenta acquirat: cùm Sole <lb></lb>clarius iam tibi ſit, eumdem motum, æqualibus temporibus, non <lb></lb>ęqualia, ſed maiora ſemper, ac maiora recipere celeritatis aug<lb></lb>menta, in continua ratione dupla. </s> <s id="s.000798">Vides item, & pari eui<lb></lb>dentiâ perſpicis, non minus erraſſe<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileum, cùm ſpatia <lb></lb>ęqualibus temporibus emenſa, eam inter ſe rationem ob<lb></lb>ſeruare voluit, quæ inter numeros omnis imparis ab vnitate <lb></lb>procedenteis reperitur; cùm eadem quoque spatia, clarè ac <lb></lb>manifeſtè ignoueris, ęqualibus temporibus, maiora ſemper <lb></lb>ac maiora percurri, in eadem continua ratione dupla. </s> <s id="s.000799">Vides <lb></lb>porrò, ac penè palpas, quàm vana, atque inanis ſit noua illa, <lb></lb>& tantopere ab ipſomet auctore laudata, de Motu accelerato <lb></lb>pſeudo ſcientia: cùm non niſi falſis, atque erroneis principiis <lb></lb>innitatur; & quam non immeritò ante annos duos mihi diſ<lb></lb>plicuerit, quòd tu quoque iiſdem illis principiis nonnullam fi<lb></lb>dem adhiberes.<emph.end type="italics"></emph.end> C<emph type="italics"></emph>ertiora nunc habes, & quibus intrepidé <lb></lb>aſſenſum prębeas, reſtitutam ſcilicet motus accelerati defini<lb></lb>tionem & ab iniuſta Galilei oppugnatione vindicatam. </s> <s id="s.000800">Ha<lb></lb>bes & veram, germanàmque in naturali deſcenſu grauium <lb></lb>accelerationis rationem, tam in temporibus, quàm in ſpatijs <lb></lb>ęqualibus conſideratam. </s> <s id="s.000801">Habes denique eam quoque ratio<lb></lb>nem, quę inter spatia ęqualibus temporibus emenſa reperi<lb></lb>tur, indubitatis experientiis, certis, euidentibúſque rationibus <lb></lb>demonſtratam. </s> <s id="s.000802">Quę ſi, vt ſpero, tibi accepta, probataque fue<lb></lb>rint, non exiguum huius operę pretium me conſecutum eſſe <lb></lb>arbitrabor.<emph.end type="italics"></emph.end></s> <s id="s.000803"> Ad hæc verò omnia, Optime virorum, <lb></lb>nihil regerere in animo eſt: cùm illa ſatis, ſuperque <lb></lb>ſint, quæ circa ſingula ediſſerui. </s> <s id="s.000804">Eſt ſolùm, quòd <lb></lb>gratias agam vberes, pro inſigni illo affectu, quem <lb></lb>ante duos annos in me teſtari dignatus es, quemque <pb pagenum="88" xlink:href="028/01/128.jpg"></pb>expreſſiſti nunc etiam, pretium collocans operæ, <lb></lb>quam meam ſperaſti comprobationem. </s> <s id="s.000805">Quòd ſi <lb></lb>videaris ſpe excidiſſe, dum reprobantem potiùs, quàm <lb></lb>approbantem habes me: at non excidiſti profectò, <lb></lb>cùm & ſperaſtia ffarite tui reuerent <lb></lb>amantiſſimum virum; & me eum voluiſti, vt interpre<lb></lb>tor, qui aliunde ius amicitiæ ſeruans illibatiſſimum, <lb></lb>tibi, in veritatis gratiam, non erubeſcerem repugnare. <lb></lb></s> <s id="s.000806">Et quàm, putas, ſæpe expetij poſſe tibi ſubſcribere, vt <lb></lb>foret non affectum magis, quàm opinionum conſpi<lb></lb>ratio; verùm ipſemet iudex eris, vbi meas nugas per<lb></lb>volveris, an-non ſaltem diſſenſerim cum aliqua ſpecie <lb></lb>probabilitatis. </s> <s id="s.000807">Sic certe habe, fore me ſemper com<lb></lb>paratiſſimum aſſentiendo, ſi quandò maior mihi ex <lb></lb>te ſimilitudo veri affulgeat, qui ſum interim, ſi quis <lb></lb>alius, comparatiſſimus obſequendo. </s> <s id="s.000808">Vale, Pariſijs, <lb></lb>Eidib. Mart. M. DC. XLV. <lb></lb><figure id="id.028.01.128.1.jpg" xlink:href="028/01/128/1.jpg"></figure></s> </p> <pb pagenum="89" xlink:href="028/01/129.jpg"></pb> <figure id="id.028.01.129.1.jpg" xlink:href="028/01/129/1.jpg"></figure> <p type="main"> <s id="s.000809"><emph type="center"></emph>DE PROPORTIONE,<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000810"><emph type="center"></emph>QVA GRAVIA DECIDENTIA<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000811"><emph type="center"></emph>accelerantur.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000812"><emph type="center"></emph>EPISTOLA SECVNDA.<emph.end type="center"></emph.end><lb></lb></s> </p> <p type="main"> <s id="s.000813"><emph type="center"></emph><emph type="italics"></emph>EIDEM.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000814">QVOD non improbâris, oprimè CASRÆE, <lb></lb>mandari typis meam Reſponſionem, ſeu <lb></lb>qualecumque Iudicium de tua illa Demon<lb></lb>ſtratione, circa accelerationem grauium <lb></lb>decidentium, cuius autographum ad te miſi, ſi modo <lb></lb>Vindicias, quas intercedente eodem nobili Senatore, <lb></lb>& amico ſingulari, Franciſco Luillerio, dediſti ad me, <lb></lb>iuberem attexi: Ecce non alia conditione Typogra<lb></lb>pho annui, dum meam opellam exigeret, quàm vt <lb></lb>tuam ſimul accipiens, tuo deſiderio faceret ſatis. </s> <s id="s.000815">Vſus <lb></lb>ſum autem ea licentia, quam abs te factam memini, <lb></lb>committendi etiam Reſponſionem ad Epiſtolam il<lb></lb>lam tuam, cuius aliquoties à te facta mentio; idque <lb></lb>tam in tuo, quàm in meo contextu, pro tuo arbitratu, <lb></lb>variatis perpaucis: & quod Vindicias attinet, omi-<pb pagenum="90" xlink:href="028/01/130.jpg"></pb>natus ſum, vt pro tuo candore, tuaque æquitate, lici<lb></lb>tum cenſeres Exceptione vti (Notis ſcilicet interpoſitis, <lb></lb>quibus controuerſia fieret explicatior (ac tum inte<lb></lb>gram facere Lectori adiudicationem. </s> <s id="s.000816">Cùm certè, quòd <lb></lb>ſpectat ad me, tuæ Demonſtrationis vim non per<lb></lb>ſentiſcam, ac tu, tametſi iam agnoſcas id Experimen<lb></lb>tum, cui, vt fundamento, innixam fecoras, collabi, <lb></lb>conſcribis tamen, petiſque Vindicias, aiens <emph type="italics"></emph>te ignotam <lb></lb>mihi veritatem maiori iam luce illuſtratam aperire, & <lb></lb>quam quæſiui, optauique, ab errore vindicatam exhibere:<emph.end type="italics"></emph.end><lb></lb>incumbit ſanè neceſſitas, inquirendi quid illud ſit, <lb></lb>quod obſtet mihi tantoperè, ne tua Demonſtratione <lb></lb>mouear; quove modo ſim adeò hebes, vt ne in tanta <lb></lb>quidem luce poſitam à te veritatem videam. </s> <s id="s.000817">Quin<lb></lb>etiam, cùm à capite ad calcem, quod aiunt, queraris, <lb></lb>ſupponere me extuis principiis, quæ ex illis non de<lb></lb>ducantur, ac affingere tibi quædam, quæ te imperitiæ <lb></lb>coarguant; teneor vel ex hoc maximè ad intertexen<lb></lb>dum velut Apologiam; vt cùm nihil habeam veritate, <lb></lb>ſinceritatéque antiquius, ac nihil minùs volüerim, <expan abbr="quã">quam</expan> <lb></lb>aut admittere quidpiam falſum, aut tibi quicquam <lb></lb>imponere; deuoueam, ſi quid tale mihi imprudenti <lb></lb>exciderit, aut ſaltem declarem quid potuerit me ad id <lb></lb>efferendum mouere. </s> <s id="s.000818">Nam vides alioquin habitum <lb></lb>me iri malæ fidei, improbumque virum, qualem non <lb></lb>haberi (Deum immortalem) quantum magis mea <lb></lb>intereſt, quàm imperitum non reputari! Quanquam <lb></lb>ego ſanè longè ſemper abfui, vt imperitiam in te <lb></lb>cauſarer, cuius magnam potiùs peritiam, virtutem<lb></lb>que reuereor; ſed animo ſolùm præconcepi, fore, vt <pb pagenum="91" xlink:href="028/01/131.jpg"></pb>pro eo, quo te habui erga veritatem affectu, minimè <lb></lb>impatienter ferres, ſi in iſta tanta caligine rerum, di<lb></lb>cereris non inſpexiſſe attentè ſatis aliquid, enuncians <lb></lb>videlicet ea, ex quibus quæpiam incommoda conſe<lb></lb>qui deprehenderentur. </s> <s id="s.000819">Noſti etiam, quantum ſudâ<lb></lb>rim, vt inſinuatione lenire id poſſem; ac ſpeciatim <lb></lb>quantum laboris inter cætera ſuſtinuerim, cùm articu<lb></lb>lo xxiv. </s> <s id="s.000820">oſtendenda tibi fuit falſitas tui illius Experi<lb></lb>menti. </s> <s id="s.000821">Quin-etiam tametſi in hiſce Vindiciis conti<lb></lb>nuo veluti inſultu dicas paſſim <emph type="italics"></emph>me grauiter errare; pec<lb></lb>care, decipi, ſuppoſitionibus tantum falſis vti; præoccupato <lb></lb>animo, & non intelligentem eſſe; non eſſe in buius controuer<lb></lb>ſiæ ingreſſum penetralia; non penitiùs dicta à te, ipſamque <lb></lb>naturam rei inspexiſſe,<emph.end type="italics"></emph.end> & quæ id genus ſimilia ſunt; om<lb></lb>nia tibi lubens condono, partim conſcius meæ imbe<lb></lb>cillitatis, partim contentus libertatem Lectoribus per<lb></lb>mittere, vt diiudicent quicquid id eſt rei. </s> <s id="s.000822">Quod atti<lb></lb>net autem ad ea, quæ toties tibi à me affingi, impo<lb></lb>nique exaggeras, æquum eſt profectò, vt eam inficias, <lb></lb>ac eam labem, qua ſentio me adſpergi, pro viribus <lb></lb>eluam. </s> <s id="s.000823">Facio verò id etiam vel eo nomine maximè <lb></lb>inuitus, quòd ea mouenda iterùm ſint, quæ diſplicuiſ<lb></lb>ſe tibi videntur; ſed neceſſitatem ipſe hanc feciſti, niſi <lb></lb>contendiſti, vt me proderem, non rudem quidem, ac <lb></lb>ineptum, quorum nominum non puderet me; ſed pro<lb></lb>fligatæ conſcientiæ, & nullius candoris virum, qualis, <lb></lb>Deo propitio, neque ſim, neque vt habear, pati poſſim. <lb></lb></s> <s id="s.000824">Sed ecce demùm tuas Vindicias, cum ne minimo qui<lb></lb>dem vllo ſenſus, vocumque detrimento; vtcum que ſe<lb></lb>ponerem volens hoſce titulos, quibus me exornas, <pb pagenum="92" xlink:href="028/01/132.jpg"></pb>quoſque non promereri me, quemadmodum ſentio, <lb></lb>ſic ingenuè profiteor. </s> </p> <p type="main"> <s id="s.000825"><emph type="center"></emph><emph type="italics"></emph>VINDICI<emph.end type="italics"></emph.end>Æ <emph type="italics"></emph>DEM<emph.end type="italics"></emph.end>O<emph type="italics"></emph>NSTRATI<emph.end type="italics"></emph.end>O<emph type="italics"></emph>NIS<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000826"><emph type="center"></emph><emph type="italics"></emph>PHYSICÆ.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000827"><emph type="center"></emph><emph type="italics"></emph>De Proportione, qua grauia decidentia accelerantur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000828"><emph type="center"></emph><emph type="italics"></emph>Ad clarißimum Virum D. Petrum<emph.end type="italics"></emph.end> G<emph type="italics"></emph>aſſendum Cathedra<lb></lb>dralis Eccleſiæ Dinienſis Præpoſitum dignißimum.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000829"><emph type="italics"></emph>Vidi,<emph.end type="italics"></emph.end> C<emph type="italics"></emph>larißime Gaſſende, ad eam Epiſtolam, quam <lb></lb>de Motu accelerato ante paucas hebdomadas ad te direxi, <lb></lb>Responſionem tuam, eamque accuratè, ac diligenter per<lb></lb>legi. </s> <s id="s.000830">In qua ſanè non poſſum non probare quam-maximè <lb></lb>diligentiam, ac ſagacitatem tuam, in eius Experientiæ exa<lb></lb>mine, quæ totius Epistolæ fundamentum, & occaſio etiam <lb></lb>fuit: ea quippe fœlicitate rem perfeciſti, vt meritò tibi gra<lb></lb>tiæ habendæ ſint, quòd ea demùm perſpexeris, ex quibus mul<lb></lb>tò certiùs tota de motu accelerato controuerſia dirimatur. <lb></lb></s> <s id="s.000831">Qua in re, cùm partem mihi quoque nonnullam fœlicitatis <lb></lb>huius facis, vt qui viam, ac methodum nouam ad illuſtra<lb></lb>tionem tandiù deſideratæ veritatis certißimam, clarißimam<lb></lb>que exhibuerim, id pro ingenita tibi humanitate, conſueta<lb></lb>que vrbanitate facis.<emph.end type="italics"></emph.end> C<emph type="italics"></emph>æterùm, cùm in hoc præcipuo tuæ, <lb></lb>ac meæ Epistolæ argumento ſolertiam tuam, atque induſtriam <lb></lb>pro innata animi mei ingenuitate vehementer probem, & <lb></lb>amicè deoſculer, in cæteris tamen capitibus nec à me, nec <lb></lb>(opinor) à cæteris, obtinere poteris approbationem; in ijs <lb></lb>maxime, in quibus postrema parte Reſponſionis tuæ ea <lb></lb>mihi affingis, quæ nec mea ſint, nec ex meis legitimè de<lb></lb>duci poßint: vt ſcilicet ex iis, tanquam datis, abſurdam de<lb></lb>cretorum meorum omnium pugnam, & tanquam diſſenſio-<emph.end type="italics"></emph.end><pb pagenum="93" xlink:href="028/01/133.jpg"></pb><emph type="italics"></emph>nem, eamque inter ſeſe diſcordiam, contrarietatemque con<lb></lb>cludas, quam ne rudioribus quidem harum rerum tyronibus <lb></lb>obuceres; & in iis tamentam pertinaci inſtas induſtria, tan<lb></lb>taque vehementia depugnas, imò toties eadem multis pa<lb></lb>ginis, & maiore tuæ Epiſtolæ parte inculcas, vt apud minùs <lb></lb>harum rerum peritos qui tuaplurimùm authoritate mouebun<lb></lb>tur, videri poßim mortalium omnium imperitißimus. </s> <s id="s.000832">Et <lb></lb>ſanè, ſi id iure faceres, & ea dicerem, quæ mihi affingis, <lb></lb>aut eadem ex meis ceu verbis, ceu principiis legitima illatio<lb></lb>ne concluderes; haberes quidem pro mea ingenuitate confi<lb></lb>tenrem reum; ſed ęterno quoque me ſilentio addicerem, qui <lb></lb>etiam num hac ætate tam pueriliter balbutirem. </s> <s id="s.000833">Sed cùm <lb></lb>euidens, perspectumque mihi ſit, nihil à me dictum, quod <lb></lb>ſibi omni ex parte perfectißimè non cohæreat; patieris pro <lb></lb>tua humanitate, Vir prudentißime, vt qua potero breuitate <lb></lb>tibi primùm, ac deinde cæteris, in iis pręſertim rebus ſatis<lb></lb>faciam, quę minus ſibi cohęrere putaueris; vbi primùm pau<lb></lb>ca quædam etiam examinauero, quæ pro<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei defenſione <lb></lb>adducis.<emph.end type="italics"></emph.end> </s> </p> <p type="main"> <s id="s.000834">Hæc tua eſt Præfatio, ob quam dicendorum quic<lb></lb>quam præoccupare nihil eſt neceſſe; cùm repetiturus <lb></lb>eadem omnia ſis. </s> <s id="s.000835">Quia verò deinceps Articulos ſingu<lb></lb>los Epiſtolæ meæ, ſiue Reſponſionis, ad Demonſtratio<lb></lb>nem tuam, numeris diſcretos percurris; age incipiamus <lb></lb>à primis. </s> </p> <p type="main"> <s id="s.000836"><emph type="center"></emph>IN ARTICVLOS II. III. IV. V. </s> <s id="s.000837">De Statu Controuerſiæ.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000838"><emph type="italics"></emph>Atque imprimis, cùm initium Reſponſionis tuæ, vſque ad <lb></lb>numerum<emph.end type="italics"></emph.end> VI. <emph type="italics"></emph>in explicando Controuerſiæ<emph.end type="italics"></emph.end> S<emph type="italics"></emph>tatu penè totum <lb></lb>occupetur, nihil adhùc eſt, in quo diſſentiamus.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="94" xlink:href="028/01/134.jpg"></pb> <p type="main"> <s id="s.000839">Dicere vis ſanè circa explicandum vtriuſque opi<lb></lb>nionis modum quatenus etiam opinionem, quam tu <lb></lb>defendis ita expoſui, vt ipſe cam exponeres (tametſi <lb></lb>poſteà me non ingreſſum in penetralia controuerſiæ <lb></lb>dicas) alioquin enim circa rem ipſam planum eſt, <lb></lb>quantum diſſentiamus; cùm tu gradus velocitatis in <lb></lb>acceleratione grauium decidentium acquiſitæ habere <lb></lb>ſe velis vt tranſacta ſpatia, non vt tempora; ego vnà <lb></lb>cum Galileo ſe vt tranſacta tempora, non verò vt <lb></lb>ſpatia habere opiner: ac tu defendas ſpatia æqualibus <lb></lb>temporibus in dupla continuò ratione percurri; ego <lb></lb>ſpatia decurri cenſeam æqualibus temporibus iuxta <lb></lb>progreſſionem numerorum imparium ab vnitate in<lb></lb>cœptorum. </s> <s id="s.000840">Porrò quia ad illuſtrationem totius <lb></lb>controuerſiæ deſiderari adhùc videtur ratio illius Ti<lb></lb>tuli, quo fuit libellus à te inſcriptus, <emph type="italics"></emph>Phyſica Demonstra<lb></lb>tio, qua ratio, menſura, modus, ac potentia accelerationis mo<lb></lb>tus in naturali deſcenſu grauium determinantur, Aduerſus <lb></lb>nuper excogitatam à Galileo<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei Florentino Philoſopho, <lb></lb>ac Mathematico de eodem motu Pſeudo ſcientiam<emph.end type="italics"></emph.end> (ſiqui<lb></lb>dem non pauci tuo libro <emph type="italics"></emph>lege<emph.end type="italics"></emph.end> pellicto quæſierunt ex me, <lb></lb>quamobrem tu illum Demonſtrationem indigitaſſes, <lb></lb>quod non ſatis perſpicerent, qua forma conſtare De<lb></lb>monſtratio poſſet) ideò videtur operæ-pretium rem <lb></lb>heic ſupplere; ac tantò magis, quantò iam etiam titu<lb></lb>lus eſt tuus, <emph type="italics"></emph>Vindicię Phyſicę Demonſtrationis.<emph.end type="italics"></emph.end></s> <s id="s.000841"> Itaque, <lb></lb>vt Demonſtrationem, quantum quidem aſſequor, toto <lb></lb>ex opere eliciam, ea videtur huiuſmodi. </s> </p> <p type="main"> <s id="s.000842"><emph type="italics"></emph>Si in motu accelerato grauium decidentium velocitates <lb></lb>acquiſitę ſe habent, vt emenſa ſpatia, neceſſe eſt spatia<emph.end type="italics"></emph.end><pb pagenum="95" xlink:href="028/01/135.jpg"></pb><emph type="italics"></emph>decurri temporibus æqualibus in ratione continuò dupla:<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000843"><emph type="italics"></emph>Atqui in motu accelerato grauium decidentium velocitates <lb></lb>acquiſitę ſe habent vt emenſa spatia:<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000844"><emph type="italics"></emph>Igitur in motu accelerato grauium decidentium neceſſe eſt <lb></lb>spatia decurri æqualibus temporibus in ratione continuò du<lb></lb>pla.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000845">Propoſitionis conſequutio probatur. </s> </p> <p type="main"> <s id="s.000846"><emph type="italics"></emph>Diuiſo ſpatio in quotcumque æqualeis parteis lubuerit, ſi <lb></lb>in fine primæ partis vnus velocitatis gradus acquiſitus ſit, in <lb></lb>fine ſecundi acquiſiti ſint duo, in fine tertij tres, & ita dein<lb></lb>ceps; oportet tempus, quo percurritur ſecunda pars, æquale eſſe <lb></lb>tempori, quo percurritur dimidium inferius primæ partis, <lb></lb>quòd velocitas per illam acquiſita ſit dupla velocitatis acqui<lb></lb>ſitæ per hoc, vti & spatium duplum eſt; ac deinde tempus, <lb></lb>quo percurruntur tertia, & quarta (tempus, inquam, aliun<lb></lb>de æquale tempori, quo ſigillatim percurrerentur triens, <lb></lb>& quadrans infimi eiuſdem primæ partis) eſſe ſimiliter <lb></lb>æquale, quòd vt ambarum ſpatium duplum eſt ſpatij ſecun<lb></lb>dæ, ita dupla velocitas acquiſita per illas ſit: & iterùm tem<lb></lb>pus, quo percurruntur quinta, ſexta, ſeptima, octaua, pari <lb></lb>ratione eſſe æquale, quod vt ſpatium illarum iunctim spatij <lb></lb>ſecundæ, & tertiæ eſt duplum, ſic dupla velocitas ſit; atque ita <lb></lb>de cæteris:<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000847"><emph type="italics"></emph>Igitur, ſi in motu accelerato grauium decidentium veloci<lb></lb>tates acquiſitæ ſe habent vt emenſa ſpatia; neceſſe eſt spatia <lb></lb>decurri temporibus æqualibus in ratione continuò dupla.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000848">Aſſumptio autem ita probatur. </s> </p> <p type="main"> <s id="s.000849"><emph type="italics"></emph>Conſtat experientia clara, facili, & indubitata, ſi globus <lb></lb>quilibet aſſumatur, & Bilanx ita ſuspendatut, vt lance al<lb></lb>tera ſuſtentata cum impoſito tanto pondere, quantum ipſius<emph.end type="italics"></emph.end><pb pagenum="96" xlink:href="028/01/136.jpg"></pb><emph type="italics"></emph>globi eſt (quantumque eſt, ſatis vt cum globo in altera lance <lb></lb>per aërem libera impoſito æquilibrium faciat) globus dein<lb></lb>ceps dimittatur in ipſam lancem liberam: fore, vt dimiſſus <lb></lb>ex ſuæ vnius diametri altitudine globus attollat ſuo impetu <lb></lb>non modò lancem ſuſtentatam cum æqualibrij pondere, ſed <lb></lb>vnum pondus prætereà, ſuo itidem ponderi æquale, præcisè: <lb></lb>& dimiſſus ex duarum diametrorum altitudine, duo attollat <lb></lb>pondera, hoc eſt duplum ſui ponderis præcisè, & ex trium <lb></lb>altitudine, treis, ſeu triplum, &c.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000850"><emph type="italics"></emph>Igitur, cùm tanta ſit velocitas cuiuſque rei, quantus impe<lb></lb>tus, imò impetus velocitas ſit; habent ſe velocitates in motu <lb></lb>accelerato grauium decidentium acquiſitæ vt emenſa ſpa<lb></lb>tia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000851">Confirmatur Aſſumptio aduerſus Galileum. </s> </p> <p type="main"> <s id="s.000852"><emph type="italics"></emph>Quia<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus falsò definit motum æquabiliter accelera<lb></lb>tum illum, qui à quiete recedens æqualibus temporibus æqua<lb></lb>lia celeritatis momenta acquirit; & paralogiſticè probat mo<lb></lb>tum æquabiliter acceleratum non eſſe eum, qui æqualibus ſpa<lb></lb>tiis æqualia celeritatis augmenta acquirit (quandò id arguit <lb></lb>ex eo, quod totum, & pars eodem, aut æquali tempore per<lb></lb>currerentur: cùm tamen conſtet dimidium tempore breuiore <lb></lb>percurri, quàm duplum) ac tum gratis ſibi poſtulat concedi <lb></lb>gradus velocitatis eiuſdem mobilis ſuper diuerſas planorum <lb></lb>inclinationes acquiſitos tunc eſſe æqualeis, cùm eorumdem pla<lb></lb>norum eleuationes ponuntur æquales: tum ad id probandum <lb></lb>falsò aſſumit globum filo nunc longiore, nunc breuiore ſuſpen<lb></lb>ſum, & ex eadem altitudine per inæqualeis arcus vibratum, <lb></lb>aſſurgere ſemper ad eandem altitudinem.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000853">Ac talis quidem formari poteſt, vt mihi videtur, <lb></lb>tua Demonſtratio, quantum, vt dixi, elicitur ex operis <pb pagenum="97" xlink:href="028/01/137.jpg"></pb>tui totius contextu; cuius & hæc poteſt eſſe quaſi Sum<lb></lb>ma; ordine licet retrogrado, ob analyſin, qua fuit re<lb></lb>texendus. </s> <s id="s.000854">Videlicet initium facis ab Aſſumptionis <lb></lb>Confirmatione, dum prima parte operisin refutando <lb></lb>Galileo es totus; proſequeris deinde probando ean<lb></lb>dem Aſſumptionem tuo Experimento, dum ipſum <lb></lb>copiosè deducis, & exaggeras; ae tandem probas, vt <lb></lb>conſequens Propoſitionis deducatur ex poſito ante<lb></lb>cedente, dum ſtabilire fusè conaris illam ſpatiorum <lb></lb>Rationem duplam; quæ etiam Concluſio eſt De<lb></lb>monſtrationis. </s> <s id="s.000855">Nihil verò neceſſe heic eſt adnotare <lb></lb>quemadmodum non modò Aſſumptio ſit falſa; ſed <lb></lb>etiam Propoſitionis conſequutio ſit nulla: cùm hoc ſit <lb></lb>totius controuerſiæ opus. </s> <s id="s.000856">Itaque hac luce præmiſſa, <lb></lb>& tuum contextum, vt inſequamur, initium facia<lb></lb>mus ab ipſa Aſſumptionis confirmatione. </s> </p> <p type="main"> <s id="s.000857"><emph type="center"></emph>IN ARTICVLOS VI. VII. VIII. </s> <s id="s.000858">De Motus <lb></lb>æquabiliter accelerari Definitione.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000859"><emph type="italics"></emph>At numero<emph.end type="italics"></emph.end> VI. <emph type="italics"></emph>iam reprehendis primùm, quòd aßigna<lb></lb>tam à<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileo motus accelerati definitionem minùs probem; <lb></lb>tum quòd eam quoque rationem, <expan abbr="quã">quam</expan> idem<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus vulgò <lb></lb>receptam accelerati motus definitionem abſurditatis arguit, <lb></lb>paralogiſmum eſſe contendam. </s> <s id="s.000860">Jdeoque numero<emph.end type="italics"></emph.end> VII. G<emph type="italics"></emph>a<lb></lb>lilei definitionem inde numeris omnibus perfectam eſſe conclu<lb></lb>dis, quòd eà ſeruatâ rectè vniformis acceleratio intelligatur. <lb></lb></s> <s id="s.000861">At imprimis istud non reprehendo; ſed quòd ſuam illam <lb></lb>definitionem nouam nec ſufficienter, nec ea, qua par eſſet, <lb></lb>ratione confirmauerit.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000862">Niſi tu illud reprehendis; non videbaris ergo dicere <pb pagenum="98" xlink:href="028/01/138.jpg"></pb><emph type="italics"></emph>debere fuiſſe ab eo falſam accelerati motus definitionem <lb></lb>institutam.<emph.end type="italics"></emph.end></s> <s id="s.000863">Quòd fueris autem cauſatus ipſum <emph type="italics"></emph>ſuam <lb></lb>illam Definitionem experientia certa, ac euidenti non con<lb></lb>firmaſſe;<emph.end type="italics"></emph.end> agnoſce quæſo tu-ne certiore, ac euiden<lb></lb>tiore <emph type="italics"></emph>tuam<emph.end type="italics"></emph.end> confirmâris. <emph type="italics"></emph> Tuam,<emph.end type="italics"></emph.end> inquam; namlicet eam <lb></lb>ſemper eſſe repetas <emph type="italics"></emph>vulgò receptam communemque;<emph.end type="italics"></emph.end> ec<lb></lb>qui <expan abbr="nã">nam</expan> tamen illi ſunt, qui eodem <expan abbr="tecũ">tecum</expan> modo definiunt? <lb></lb></s> <s id="s.000864">Galileus certè eam non vt receptam, communemque <lb></lb>impugnauit, ſed vt eam, quæ poſſet fortè ab aliquo ex<lb></lb>cogitari. </s> <s id="s.000865">Verumtamen id obiter. </s> </p> <p type="main"> <s id="s.000866"><emph type="italics"></emph>Deinde, non minùs rectè aliter quoque vniformis accele<lb></lb>ratio haberi poteſt, vt ſtatim conſtabit: Satis-ne igitur Gali<lb></lb>lei definitio inde perfecta concluditur, quòd eà ſeruatâ vnifor<lb></lb>mis acceleratio habeatur?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000867">Ita profectò, ſi per eam conſtet, quid ſit motum <lb></lb>accelerari, & accelerari æquabiliter; neque id vulgari, <lb></lb>ſiue potiùs tua, de qua dicis mox conſtiturum, perinde <lb></lb>præſtetur. </s> </p> <p type="main"> <s id="s.000868"><emph type="italics"></emph>Vt autem probes,<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.138.1.jpg" xlink:href="028/01/138/1.jpg"></figure><lb></lb><emph type="italics"></emph>quàm rectè iuxta Galilei <lb></lb>mentem, acceleratio illa <lb></lb>motus habeatur, iu<lb></lb>bes concipere duas li<lb></lb>neas<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> AC, <lb></lb><emph type="italics"></emph>angulum conſtituentes in<emph.end type="italics"></emph.end><lb></lb>A, <emph type="italics"></emph>& tertiam<emph.end type="italics"></emph.end> VX <emph type="italics"></emph>per <lb></lb>anguli apicem<emph.end type="italics"></emph.end> A <emph type="italics"></emph><expan abbr="ince-dentẽ">ince<lb></lb>dentem</expan>, & cùm prioribus <lb></lb>duabus angulos vtrim<lb></lb>que æqualeis conſtituentem: hanc, ſeruatâ ſemper eadem<emph.end type="italics"></emph.end><pb pagenum="99" xlink:href="028/01/139.jpg"></pb><emph type="italics"></emph>angulorum æqualitate, ita fluentem, ac deſcenden<lb></lb>tem concipi postulas, vt etiam intelligamus partem inter <lb></lb>lineas<emph.end type="italics"></emph.end> AB, AC, <emph type="italics"></emph>interceptam continuò ea ratione augeri, <lb></lb>vt notatis in<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> AC, <emph type="italics"></emph>partibus æqualibus<emph.end type="italics"></emph.end> AE, EG, <lb></lb>GI, IL, <emph type="italics"></emph>ſemper interceptarum parallelarum incrementa <lb></lb>haberi æqualia aduertamus. </s> <s id="s.000869">Nempe vt<emph.end type="italics"></emph.end> AG <emph type="italics"></emph>dupla est <lb></lb>ipſius<emph.end type="italics"></emph.end> AE, <emph type="italics"></emph>ſic<emph.end type="italics"></emph.end> GF <emph type="italics"></emph>dupla est ipſius<emph.end type="italics"></emph.end> ED: <emph type="italics"></emph>& eadem ratione<emph.end type="italics"></emph.end><lb></lb>IH <emph type="italics"></emph>eiuſdem<emph.end type="italics"></emph.end> ED <emph type="italics"></emph>eſt tripla, &<emph.end type="italics"></emph.end> LK <emph type="italics"></emph>quadrupla, atque <lb></lb>ita deinceps. </s> <s id="s.000870">Ex quibus ita concludis:<emph.end type="italics"></emph.end> Quare aſſumptis <lb></lb>partibus æqualibus temporis per parteis æqualeis lineæ <lb></lb>AC repræſentatis, notum eſt momenta, ſeu incremen<lb></lb>ta velocitatis per parallelas repræſentatæ æqualia ac<lb></lb>quiri ſub huiuſmodi partibus. <emph type="italics"></emph>Hæc ſanè vera ſunt; <lb></lb>ſed recordare verißimè quoque à te dictum numero<emph.end type="italics"></emph.end> IV. <emph type="italics"></emph>pun<lb></lb>ctum<emph.end type="italics"></emph.end> A <emph type="italics"></emph>poſſe non tantum pro initio temporis haberi, ſed etiam <lb></lb>pro initio spatij, & (vt item addis) pro initio velocitatis.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000871">Recordor; ſed adnoto ſimul habuiſſe me punctum <lb></lb>A, pro initio temporis quidem æquabiliter ſluentis, <lb></lb>prout comparatur ad lineam AC (aut AB) in parteis <lb></lb>æqualeis diuiſam; pro initio verò ſpatij in longum de<lb></lb>currendi, prout comparatur ad aream AKL in trian<lb></lb>gulos æqualeis diſtinctam; ac pro initio velocitatis <lb></lb>continenter acquirendæ, prout comparatur cum linea <lb></lb>parteis æqualeis continuò adſciſcente, quovſque cœ<lb></lb>pta à puncto A, euadat KL. </s> </p> <p type="main"> <s id="s.000872"><emph type="italics"></emph>Vt igitur punctum<emph.end type="italics"></emph.end> A, <emph type="italics"></emph>nunc habes pro initio temporis, <lb></lb>& parteis æqualeis<emph.end type="italics"></emph.end> AE, EG, GI, IL, <emph type="italics"></emph>pro partibus <lb></lb>æqualibus temporis; concipe etiam vicißim idem punctum<emph.end type="italics"></emph.end> A <lb></lb><emph type="italics"></emph>initium eſſe ſpatij, cuius parteis æqualeis æqualia item ſeg<lb></lb>menta<emph.end type="italics"></emph.end> AE, EG, GI, IL, <emph type="italics"></emph>deſignent. </s> <s id="s.000873">Quo poſito, tam<emph.end type="italics"></emph.end><pb pagenum="100" xlink:href="028/01/140.jpg"></pb><emph type="italics"></emph>notum erit, quàm anteà momenta, ſeu incrementa velocitatis <lb></lb>per parallelas<emph.end type="italics"></emph.end> ED, GE, IH <emph type="italics"></emph>&<emph.end type="italics"></emph.end> LK <emph type="italics"></emph>repræ|entatæ. </s> <s id="s.000874">æqualia <lb></lb>ſub huiuſmodi partibus acquiri. </s> <s id="s.000875">Cùm igitur in vtraque <lb></lb>hypotheſi eadem omninò velocitatis acceleratio habeatur, cur <lb></lb>prior à te constituta perfectam omnibus numeris<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei de<lb></lb>finitionem oſtendat; vulgatam autem defi utionem poſterior <lb></lb>hypotheſis pari ratione perfectam non euincat?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000876">Cauſſam inſinuaui tum mox, tum verbis illis, quæ <lb></lb>præmiſeram, <emph type="italics"></emph>Quippe meminiſſe, aut potiùs adnotaſſe dili<lb></lb>genter oportet agi heic de motu æquabiliter accelerato, ſiue <lb></lb>cuius celeritas continenter, vniformiterque increſcat, neque <lb></lb>vllum ſit momentum conſequentis temporis, in quo motus non <lb></lb>ſit velocior, quàm in quouis antecedente, & in quo non eadem <lb></lb>ratione ipſa velocitas augeatur.<emph.end type="italics"></emph.end></s> <s id="s.000877"> Nempe memini <emph type="italics"></emph>Tempo<lb></lb>ris,<emph.end type="italics"></emph.end> ob rationem poſteà deductam, vbi tu primùm de <lb></lb>eo egiſti, admonendo fuiſſe originem mali, quòd in <lb></lb>definitione vulgari, ſeu tua nulla eſſet facta <expan abbr="mẽtio">mentio</expan> tem<lb></lb>poris, ſine quo tamen neque celeritas, neque accele<lb></lb>ratio (& maximè quidem vniformis) intelligi poſſit. <lb></lb></s> <s id="s.000878">Obieci illeic, <emph type="italics"></emph>Si velocitas attendatur ſolùm penes ſpatia, <lb></lb>debere ſemper id mobile, quod decem percurrerit ſtadia, dici <lb></lb>moueri celeriter, & ſemper id, quod vnicum percurrerit, tar<lb></lb>dè, cum contingere tamen poßit, vt quod percurrit vnicum, <lb></lb>moueatur decuplò velociùs, quàm illud, quod percurrit decem.<emph.end type="italics"></emph.end><lb></lb> Addo heic ſolùm; ſi AC ſit ſpatium, & mobile diſce<lb></lb>dens ab A acceleretur vſque ad E per parteis integri <lb></lb>minuti; & motu non interrupto accelerari pergat ab <lb></lb>E in G, ſed per parteis integræ horæ; ac rursùs motu <lb></lb>non interrupto accelerari pergat à G in I, ſed per par<lb></lb>teis integri ſecundi; rurſuſque etiam non interrupto <pb pagenum="101" xlink:href="028/01/141.jpg"></pb>motu, accelerari pergat ab I, in L, ſed per parteis in<lb></lb>tegri diei: quæſo, dices ne huiuſmodi accelerationem <lb></lb>eſſe vn formem? </s> <s id="s.000879">Et ecce ea tamen futura eſt continens; <lb></lb>ac ipſi gradus velocitatis repræſentati iuxta te paralle<lb></lb>lis ED, GF, IH, LK, cum interceptis omnibus, ha<lb></lb>bituri ſunt inter ſe, eandem rationem, quam ipſæ par<lb></lb>tes ſpati, repræ entatæ iuxta te partibus lineæ AC. <lb></lb></s> <s id="s.000880">Quòd ſi id reputes abſurdum; abſurdum quoque vi<lb></lb>deri debet metiri accelerationem, ac vniformem po<lb></lb>tiſſimùm, penes ſpatium, non penes tempus: atque <lb></lb>idcircò lineam AC comparatam ad eas parallelas pro <lb></lb>velocitatibus habitas, non pro tempore, ſed pro ſpatio <lb></lb>habere. </s> </p> <p type="main"> <s id="s.000881">Enim verò, vt expreſſiùs dicam quamobrem lineæ <lb></lb>DE, FG, & parallelæ cæteræ accipi non poſſint pro <lb></lb>gradibus velocitatis, ſi partes lineæ AC accipiantur pro <lb></lb>ſpatij, non pro temporis partibus, ac ſimul inſinuem <lb></lb>quid diſcriminis circa repræſentationem per eandem <lb></lb>figuram, inter vtramque hypotheſin ſit, rem ecce <lb></lb>paucis ita deduco. </s> <s id="s.000882">Si DE ſit velocitatis gradus, qui per <lb></lb>additamenta continua à puncto A ſecundum trian<lb></lb>gulum ADC, acquiſitus ſit, dum mobile AE percur<lb></lb>rit; quæro quî euadat hic gradus, vbi deinceps mobi<lb></lb>le pergendo decurrit EG? </s> <s id="s.000883">An peniſſe illum dicemus? <lb></lb></s> <s id="s.000884">Non ſane: quoniam alioquin mobili perueniente ex <lb></lb>A in G non reperiretur acquiſitus in G, niſi vnus velo<lb></lb>citatis gradus; quatenus etiam per te, ſeu ex vulgari de<lb></lb>finitione, additamenta ex E in G æqualia ſunt addita<lb></lb>mentis ex A in E, nec poteſt proinde ab vſque E ac<lb></lb>quiſitus eſſe, niſi gradus vnus, v. c. FP æqualis ipſi DE <pb pagenum="102" xlink:href="028/01/142.jpg"></pb>acquiſito ab vſque A. </s> <s id="s.000885">Et quamvis tu ſis inferiùs di<lb></lb>cturus velocitatem acquiſitam ex E in G duplam eſſe <lb></lb>acquiſitæ in E (nempe dum ſtatuis primum gradum <lb></lb>acquiri à ſolo medio ipſius AE) & ſic velle debeas <lb></lb>gradum acquiſitum in E, ſeu DE perire; quoniam re<lb></lb>periri in G, niſi duos gradus non vis: cùm ſi acquiſitus <lb></lb>in E remaneret, futuri eſſent tres: vide nihilominùs <lb></lb>quid hoc loco ſequatur. </s> <s id="s.000886">Nam ſi pereunte gradu DE, <lb></lb>duo gradus, quos vis reperiri in G, vt puta FP, & <lb></lb>PG, acquirendi ſint per ſolum ſpatium EG, factis vi<lb></lb>delicet augmentis ſecundum triangulum, qui ducta <lb></lb>linea ex E in F ſit EFG, neceſſe eſt, accelerationis <lb></lb>æquabilitas interrumpatur prorſus in E; & cùm ibi <lb></lb>acceleratio ad ſuum redierit principium, non ſit dein<lb></lb>ceps futura tanta, quanta fuerit in E, niſi in medio <lb></lb>ſpatij EG. </s> <s id="s.000887">Itaque gradus velocitatis DE acquiſitus <lb></lb>ex A in E non perit, ſed manet; & cum mobile pro<lb></lb>inde peruenit ad G, talis gradus euadit PG, ac illi ad<lb></lb>iunctus reperitur FP acquiſitus interim per augmen<lb></lb>ta facta ſecundum triangulum DFP. </s> </p> <p type="main"> <s id="s.000888">Quæro deinde, an gradus velocitatis DE manens, <lb></lb>dum mobile percurrit EG, otioſus ſit, an aliquid agat? <lb></lb></s> <s id="s.000889">Non dices ſanè otioſum eſſe; alioquin enim mobile <lb></lb>tempore nihilo breuiore perueniret ex E in G, quàm <lb></lb>ex A in E, vt putà tranſlatum æquali ſolùm velocita<lb></lb>te. </s> <s id="s.000890">Igitur agit aliquid. </s> <s id="s.000891">Requiro, quantum? </s> <s id="s.000892">hoc eſt, <lb></lb>Si concipiamus mobile, poſtquàm peruenit ad E, non <lb></lb>accipere amplius vlla augmenta, qualia acquiri dixi<lb></lb>mus ſecundum triangulum DFP, ſed moueri ſolùm <lb></lb>æquabiliter velocitate acquiſita DE: requiro quanto <pb pagenum="103" xlink:href="028/01/143.jpg"></pb>tempore mobile ſit peruenturum ad G? </s> <s id="s.000893">An dices <lb></lb>ſolùm quanto tempore peruenerit ex A in E? Atqui, <lb></lb>vt faceret, oporteret velocitatem non totam permane<lb></lb>re, ſed ſenſim deminur, vt ſi deminutio fieret ſecun<lb></lb>dum triangulum DPE: quippe hoc ſolùm modo <lb></lb>tempus poſſet æquale fieri, dum nimirum velocitas ſie <lb></lb>decreſceret ad vſque P, vt ab vſque A reciprotè incre<lb></lb>uiſſet. </s> <s id="s.000894">Quo caſu neque mobile æquabiliter moue<lb></lb>retur; neque peruenienti in G ſupereſſet ampliùs vlla <lb></lb>velocitas: neque proinde, ſi velocitate hac decreſcente <lb></lb>intelligamus acquiri velocitatem ſecundum triangu<lb></lb>lum DFP, acquiſita erit in G velocitas alia, quàm FP <lb></lb>ipſius DE æqualis, non dupla. </s> <s id="s.000895">Igitur mobile percur<lb></lb>rens EG velocitate ſola DE percurreret ipſum tem<lb></lb>pore breuiore, quàm percurriſſet AE. </s> <s id="s.000896">Quanto igitur? <lb></lb></s> <s id="s.000897">Omninò dimidio. </s> <s id="s.000898">Siquidem cùm velocitas DE non <lb></lb>foret deminuta, ſed mobili perueniente ad G, reperi<lb></lb>retur adhùc integra, vt puta effecta PG, ideò vim <lb></lb>ſuam exprimeret ſecundum totum quadrangulum <lb></lb>DG, hoc eſt ſecundum duos triangulos triangulo <lb></lb>ADE ſigillatim æqualeis; ſicque velocitas bis illud poſ<lb></lb>ſet ſecundum quadrangulum DG, quod poſſet ſemel <lb></lb><expan abbr="ſecundũ">ſecundum</expan> <expan abbr="triangulũ">triangulum</expan> ADE: atque adeò mobile perueni<lb></lb>ret duplò citius (quod eſt dimidium temporis) ex E in <lb></lb>G velocitate DE manente eadem, quam ex A in E, <lb></lb>velocitate eadem DE increſcente à nihilo ſui. </s> <s id="s.000899">Atque <lb></lb>ex hoc eſt, quare adnotem, gradum, qui acquiritur, & <lb></lb>gradum, qui manet, eſſe inæqualeis; ac manentem di<lb></lb>ci poſſe duplò maiorem, quatenùs eſt duplò poten<lb></lb>tior, ſeu duplo fortiùs ampliúſque agens. </s> </p> <pb pagenum="104" xlink:href="028/01/144.jpg"></pb> <p type="main"> <s id="s.000900">Intelligamus iam, dum mobile percutrit EG, & <lb></lb>velocitas DE manens promouetur ſecundum qua<lb></lb>drangulum DG, quovſque euadat PG, nouum in<lb></lb>terim velocitatis gradum acquiri ſecundum triangu<lb></lb>lum DFP, quovſque euadat FP: neceſſe eſt prorsùs <lb></lb>ob nouam velocitatem additam percurri EG tempore. <lb></lb></s> <s id="s.000901">breuiore, quàm ſit dimidium temporis, quo decurſum. <lb></lb></s> <s id="s.000902">fuerit AE. Quanto-nam ergo? </s> <s id="s.000903">Sanètriente. </s> <s id="s.000904">Nam vt <lb></lb>velocitas ſecundum quadrangulum DG, dupla ve<lb></lb>locitatis ſecundum triangulum ADE diminuit tem<lb></lb>pus ad dimidium; ita velocitas ſecundum trapezion <lb></lb>DFGE, triplum eiuſdem trianguli, diminuit ad vſ<lb></lb>que trientem: Adeò vt, ſi tempus, quo decurſum <lb></lb>fuerit AE, ſupponatur, vt à te fit, minutorum v. c. ſex, <lb></lb>tempus, quo decurretur EG, futurum ſit minutorum <lb></lb>duorum. </s> <s id="s.000905">Cæterùm præter iam obiecta alibi incom<lb></lb>moda, tum illud quoque heinc ſequitur, Quòd ſi <lb></lb>EG ſecunda pars ſpatij percurratur triente eius tem<lb></lb>poris, quo decurſa fuerit prima AE, futurum ſit, vt <lb></lb>tempore ſecundo percurrantur partes non modò ſe<lb></lb>cunda, ſed etiam tertia, quarta, quinta, ſexta, ſeptima, <lb></lb>& penè octaua; quandò qua ratione ſecundum ſpa<lb></lb>tium percurritur triente, eadem tertium percurretur <lb></lb>quinta eiuſdem temporis parte; quartum ſeptima, <lb></lb>quintum nona, ſextum vndecima, ſeptimum decima<lb></lb>tertia, octauum quintadecima, & hæc fragmenta ſi<lb></lb>mùl iuncta vnum integrum proximè conficient. <lb></lb></s> <s id="s.000906">Hoc autem falſum qu dem eſt, & tu ipſe longè abes, <lb></lb>vt fatearis ſed vides tamen, vt fuerit ex ea poſitione <lb></lb>deductam, qua vis parteis lineæ AC eſſe parteis ſpatij, <pb pagenum="105" xlink:href="028/01/145.jpg"></pb>& parallelas DE, FG eſſe gradus velocitatis. </s> </p> <p type="main"> <s id="s.000907">Vides ergo quantum repugnet poſitio huiuſmodi; <lb></lb>ac peruidere ſimul potes, quantum interſit diſeriminis <lb></lb>inter hypotheſin vtramque. </s> <s id="s.000908">Nam in ea quidem, <lb></lb>quam ſequor, cùm partes lineæ AC, fiant partes <lb></lb>temporis, linea DE optimè repræſentat velocitatem <lb></lb>aquiſitam in nfie primi, & ſimul triangulum ADE op<lb></lb>timè repræſentat vnum ſpatium, dum ea acquiritur, <lb></lb>tranſactum: FG verò optimè repræſentat velocita<lb></lb>tem acquiſitam in fine ſecundi; & ſimul trapezion <lb></lb>DFGE optimè repræſentat tribus triangulis tria ſpa<lb></lb>tia peracta, quorum vnum debeatur gradui FP, prout <lb></lb>interim acquiſito, & alij duo gradui PG, prout per<lb></lb>ſeueranti ab vſque puncto E. </s> <s id="s.000909">At in ea, quam tu fe<lb></lb>queris, neque habes, quò referas tempus, cuius etiam <lb></lb>tua definitio non meminit: neque cùm plures ſpatij <lb></lb>partes æquali tempore percurrantur, illarum diſtin<lb></lb>ctionem habes, vt ad eas referas gradus inæqualeis ve<lb></lb>locitatis. </s> <s id="s.000910">Addo autem, quædam præclarè ex mea <lb></lb>hypotheſi intelligi, quibus nihil ſimile ex tua. </s> <s id="s.000911">Veluti <lb></lb>Primò, Quemadmodum omnes velocitatis gradus <lb></lb>ſemel acquiſiti inuariati maneant, & ſingulis tempo<lb></lb>ribus æquipolleant conſtanter duobus gradibus, hoc <lb></lb>eſt duobus ſpatijs æqualibus primo percurrendis ſuf<lb></lb>ficiant; vt deſignatur continua ſerie quadrangulo<lb></lb>rum æqualium, DG, PI, QL, itemque FQ, <lb></lb>RM, &c. </s> <s id="s.000912">Deinde, Quemadmodum primo tempore <lb></lb>vnicum ſpatium percurratur, quatenus vnicus eſt gra<lb></lb>dus, qui acquiritur, & nullus interim, qui permaneat: <lb></lb>In ſecundo autem ſint tria, quorum vnum quidem per <pb pagenum="106" xlink:href="028/01/146.jpg"></pb>recens acquiſitum percurratur, & alij duo per primum <lb></lb>perſeuerantem: In tertio quinque, quorum vnum per <lb></lb>tunc acquiſitum, & ex alijs quatuor, duo per primum, <lb></lb>duo per ſecundum perſeueranteis: In quarto ſeptem, <lb></lb>quorum vnum itidem per tunc acquiſitum, & ex alijs, <lb></lb>duo per primum, duo per ſecundum, duo per tertium <lb></lb>perſeueranteis, atque ita de cæteris. </s> <s id="s.000913">Ad hæc, Quem<lb></lb>admodum proinde æqualibus temporibus æqualia <lb></lb>fiant additamenta, ſeu æquales gradus velocitatis ac<lb></lb>quirantur, & interim tamen decurſus ſpatiorum ſecun<lb></lb>dum ſeriem numerorum ab vnitate incœptorum <lb></lb>fiat. </s> </p> <p type="main"> <s id="s.000914"><emph type="italics"></emph>Adde quòd ad vniformen motus accelerationem minimè <lb></lb>neceſſarium eſt, vt acquiſita æqualibus temporibus velocitatis <lb></lb>incrementa æqualia ſint (vt paßim ſupponere videris) ſed <lb></lb>ſatis eſt, ſi continuò maiora in quacumque ratione<emph.end type="italics"></emph.end> G<emph type="italics"></emph>eome<lb></lb>trica acquirantur: cùm notum ſit omnibus progreßiones <lb></lb>Geometricas non minùs vniformeis eſſe, quàm Arithmeticas. <lb></lb></s> <s id="s.000915">Ex quibus planè efficitur, definitionem accelerati motus <lb></lb>quamcúmque inde veram, perfectamque non probari, quòd <lb></lb>ea ratione concepta ſit, qua vniformis acceleratio exprima<lb></lb>tur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000916">Id, quod dicis videri me ſupponere, reuerâ ſuppo<lb></lb>no: & quod ais <emph type="italics"></emph>notum omnibus progreßiones Geometricas <lb></lb>non minùs eſſe vniformeis, quàm Arithmeticas,<emph.end type="italics"></emph.end> mihi ſal<lb></lb>tem notum non eſt (<emph type="italics"></emph>qualemcumque me habiturus ſis<emph.end type="italics"></emph.end>) vt <lb></lb>neque capio id, quod ais, <emph type="italics"></emph>ad vniformem motus acceleratio<lb></lb>nem ſatis eſſe, ſi incrementa velocitatis continuò maiora in <lb></lb>quacumque ratione Geometrica acquirantur.<emph.end type="italics"></emph.end></s> <s id="s.000917"> Sed nempe <lb></lb>videris tu mihi <emph type="italics"></emph>vniformitatem<emph.end type="italics"></emph.end> cum <emph type="italics"></emph>conformitate<emph.end type="italics"></emph.end> confun-<pb pagenum="107" xlink:href="028/01/147.jpg"></pb>dere; & quia videtur <emph type="italics"></emph>conformitas<emph.end type="italics"></emph.end> idem ſonare, quod <lb></lb><emph type="italics"></emph>proportio,<emph.end type="italics"></emph.end> confundere quoque cum <emph type="italics"></emph>proportione vnifor<lb></lb>mitatem:<emph.end type="italics"></emph.end> cùm videatur tamen <emph type="italics"></emph>Vniformitas<emph.end type="italics"></emph.end> relatio eſſe <lb></lb>identitatis, ob vnum, eundemque tenorem, in vna, <lb></lb>atque eademre; <emph type="italics"></emph>Proportio<emph.end type="italics"></emph.end> autem eſſe potiùs ſimilitu<lb></lb>dinis relatio, quæ in rebus alioquin diuerſis, ſiue diſſi<lb></lb>tis reperiatur. </s> <s id="s.000918">Ex hoc quippe eſt, cur dicatur inter <lb></lb>fontem, & radicem, non <emph type="italics"></emph>vniformitas,<emph.end type="italics"></emph.end> ſed <emph type="italics"></emph>proportio<emph.end type="italics"></emph.end> eſ<lb></lb>ſe: & in colore pennarum cycni, non <emph type="italics"></emph>proportio,<emph.end type="italics"></emph.end> ſed <lb></lb><emph type="italics"></emph>vniformitas:<emph.end type="italics"></emph.end> ac eodem ex capite eſt, cur in progreſſio<lb></lb>ne Geometrica rationem vnius ad quàtuor, quatuor ad <lb></lb>ſexdecim, ſexdecim ad ſexaginta quatuor, dicamus <lb></lb>eſſe <emph type="italics"></emph>proportionem,<emph.end type="italics"></emph.end> non verò vniformitatem; & in pro<lb></lb>greſſione Arithmetica vnius duorum, trium, quatuor, <lb></lb>vel duorum, quatuor, ſex, octo; vel trium ſex, nouem, <lb></lb>duodecim, &c. <emph type="italics"></emph>vniformitatem<emph.end type="italics"></emph.end> eſſe, & non <emph type="italics"></emph>proportionem<emph.end type="italics"></emph.end><lb></lb>dicamus. </s> <s id="s.000919">Heinc igitur eſt, quorsùm videar non iniu<lb></lb>riâ ſupponere accelerationem motus, vt <emph type="italics"></emph>vniformis,<emph.end type="italics"></emph.end> ſeu <lb></lb>æquabilis ſit, debere Arithmetica progreſſione ince<lb></lb>dere, & ea quidem ſecundum impareis ab vnitate nu<lb></lb>meros, putà vnum, tria, quinque, ſeptem, &c. </s> <s id="s.000920">aſſum<lb></lb>pta; cùm tu, licet Geometricarum ſim pliciſſimam, du<lb></lb>plam nempe, elegeris reperire in ea vniformitatem, <lb></lb>ſeu æquabilitatem non poſſis: &, ſi reperire velis ali<lb></lb>quam, Arithmeticam vſurpare cogaris, eam nempe, <lb></lb>quæ ſecundum vnitates eſt, veluti dum ais gradus ve<lb></lb>locitatis ſic acquiri, vt ſint in fine primi ſpatij vnus, in <lb></lb>ſine ſecundi duo, in fine tertij tres, &c. </s> <s id="s.000921">Quamobrem <lb></lb>autem dicas definitionem, de qua agitur, <emph type="italics"></emph>veram, per<lb></lb>fectamque non probari, quòd ea ratione concepta ſit, qua<emph.end type="italics"></emph.end><pb pagenum="108" xlink:href="028/01/148.jpg"></pb><emph type="italics"></emph>vniformis acceleratio exprimatur:<emph.end type="italics"></emph.end> non video quorsùm <lb></lb>reſpexeris; cùm videam heic agi de motu, cuius vni<lb></lb>formis ſit acceleratio. </s> </p> <p type="main"> <s id="s.000922"><emph type="italics"></emph>Sed ex his porrò etiam vides, quàm non rectè vulgatam <lb></lb>accelerati motus definitionem inde numero<emph.end type="italics"></emph.end> VIII. <emph type="italics"></emph>reprehen<lb></lb>das, quòd ea ratione concepta ſit, qua vniformis acceleratio <lb></lb>non exprimatur. </s> <s id="s.000923">Modò enim vtdisti puncto<emph.end type="italics"></emph.end> A <emph type="italics"></emph>pro initio <lb></lb>ſpatij conſtituto, cuius partes æquales æqualibus ſegmentis<emph.end type="italics"></emph.end><lb></lb>EG, GI, IL <emph type="italics"></emph>deſignentur, non tantum recti vniformem <lb></lb>quampiam, ſed eandem planè velocitatis accelerationem ha<lb></lb>beri: vt iam ampliùs inquirere tibi non liceat, quomodo ex <lb></lb>vulgata motus accelerati definitione, qua<emph.end type="italics"></emph.end> is dicitur, qui <lb></lb>æqualibus ſpatijs æqualia velocitatis augmenta acqui<lb></lb>rat, <emph type="italics"></emph>motum concipere liceat æquabiliter acceleratum. </s> <s id="s.000924">Iam <lb></lb>enim habes concipi prorſus eodem modo, quo tu illum con-<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.148.1.jpg" xlink:href="028/01/148/1.jpg"></figure><lb></lb><emph type="italics"></emph>cipis, atque exprimis ex data<emph.end type="italics"></emph.end> G<emph type="italics"></emph>a<lb></lb>lilei definitione. </s> <s id="s.000925">Nam quòd eodem <lb></lb>numero<emph.end type="italics"></emph.end> VIII. <emph type="italics"></emph>deſcripto nouo trian<lb></lb>gulo<emph.end type="italics"></emph.end> APB <emph type="italics"></emph>accelerationis augmen<lb></lb>tum minoribus triangulis inter pa<lb></lb>rallelas<emph.end type="italics"></emph.end> CL, DM, EO, <emph type="italics"></emph>&c. <lb></lb></s> <s id="s.000926">conſtitutis metiendum putas, non <lb></lb>rectè id facis. </s> <s id="s.000927">Vt enim velocitas <lb></lb>acquiſita per ſpatium<emph.end type="italics"></emph.end> AC <emph type="italics"></emph>deſigna<lb></lb>tur per lineam<emph.end type="italics"></emph.end> CL, <emph type="italics"></emph>velocitas ac<lb></lb>quiſita in<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>exprimitur linea<emph.end type="italics"></emph.end><lb></lb>DN: <emph type="italics"></emph>& velocitas acquiſita in<emph.end type="italics"></emph.end> E, <lb></lb><emph type="italics"></emph>repræſentatur linea<emph.end type="italics"></emph.end> EQ, <emph type="italics"></emph>& ita <lb></lb>de cæteris. </s> <s id="s.000928">Cur enim celeritatis <lb></lb>augmenta hoc loco triangulis, in ſuperiore autem figura<emph.end type="italics"></emph.end><pb pagenum="109" xlink:href="028/01/149.jpg"></pb><emph type="italics"></emph>lineis metienda edicis? </s> <s id="s.000929">Constat autem lineas<emph.end type="italics"></emph.end> CL, ND, <lb></lb>EQ, <emph type="italics"></emph>&c. </s> <s id="s.000930">vniformi augmento accreſcere, & eſſe, vt<emph.end type="italics"></emph.end> AC <emph type="italics"></emph>ad<emph.end type="italics"></emph.end><lb></lb>CL, <emph type="italics"></emph>ita<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> DN, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> AE <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> EQ, <emph type="italics"></emph>&c. </s> <s id="s.000931">Non <lb></lb>rectè igitur cenſes augmentum velocitatis vniforme eſſe non <lb></lb>poſſe, ſi spatijs æqualibus creſcat æqualiter, & tota illa noui <lb></lb>istius trianguli difformis ſtructura sponte corruit.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000932">Heic idem dicendum, quod & paulò antè, quate<lb></lb>nus parteis lineæ AB contendis habendas pro parti<lb></lb>bus ſpatij, quæ comparentur cum parallelis habitis <lb></lb>pro gradibus velocitatis, nulla habita temporis ratio<lb></lb>ne. </s> <s id="s.000933">Quod autem quæris, <emph type="italics"></emph>Cur hoc loco celeritatis aug<lb></lb>menta triangulis in ſuperiore autem figura lineis metienda <lb></lb>edixerim?<emph.end type="italics"></emph.end> Cauſſam ex eo potes intelligere, quòd cùm <lb></lb>tu duos gradus NM, & MD, v. c. æqualeis facias, <lb></lb>quaſi acquiſitos ex L, & C, ſecundum duos triangulos <lb></lb>LNM, & CMD (tametſi inæquales ſint, & MD ex <lb></lb>LC manente factus, duobus æquiualeat) ideò quem <lb></lb>defectum exprimere non licuit lineâ ND, exprimere <lb></lb>placuerit trapezio LD. Nimirùm, cùm velocitas <lb></lb>ND creetur partim ex LC, promota in MD ſecun<lb></lb>dum quadrangulum, partim ex additamentis ipſi fa<lb></lb>ctis ſecundum triangulum LNM; tu ex velocitate hac <lb></lb>detrahis integrum triangulum LMC: ſicque ex tri<lb></lb>bus ſuperſunt tantum partes velocitatis duæ, quas vt <lb></lb>ſimul iunct is repræſentarem, triangulum à te factum <lb></lb><expan abbr="vacuũ">vacuum</expan> ſupplcui, tranſlato LNM in MCL: cópoſitoque <lb></lb>inde quadrangulo, locum ipſum trianguli tranſlati re<lb></lb>liqui inanem. </s> <s id="s.000934">Fandem autem ob cauſſam relicti ſunt <lb></lb>duo trianguli manes ad ordinem tertium tres ad quar<lb></lb>tum, &c. </s> <s id="s.000935">Exindeque eſt, cur <emph type="italics"></emph>difformis<emph.end type="italics"></emph.end> quidem, ſed <pb pagenum="110" xlink:href="028/01/150.jpg"></pb>iuxta te tamen conſtitutus triangulus ſit; neque pro<lb></lb>pterea cius ſtructura, quatenus eſt tuis decretis confor<lb></lb>mis, ſponte corruat. </s> <s id="s.000936">Addam-ne, cùm lineâ AC <lb></lb>biſecta in S, ductáque lineâ SL contendas ipſe ex <lb></lb>deductis articulo XXXV, & ſequentibus progreſſionem <lb></lb>tuam illam duplum incipere ab S, & mobile tam citò <lb></lb>peruenire ex C in D, quàm ex S in C, ſicque ob <lb></lb>duplum ſpatium velocitatem acquiſitam in D eſſe du<lb></lb>plam velocitatis acquiſitæ in C, atque adeò eſſe ad il<lb></lb>lam vt lineam DN ad lineam CL: addam-ne in<lb></lb>quam, & triangulum fieri exinde adhuc deformius, <lb></lb>& comparationem hanc tuam peruerti, cùm adeò <lb></lb>falſum ſit dicere, vt SC, ad CL, ita SD ad DN? </s> <s id="s.000937">An<lb></lb>non vel ex hoc capite agnoſcere potes, aſſumptis li<lb></lb>neis CL, DN, & parallelis cæteris pro incrementis <lb></lb>velocitatis, non licere vniformitatem, æquabilitatem<lb></lb>ve accelerationis tueri? </s> </p> <p type="main"> <s id="s.000938"><emph type="center"></emph>IN ARTICVLOS IX. X. XI. XII. </s> <s id="s.000939">De Paralogiſmo, qui <lb></lb>Galileo Definitionem ſpuriam impugnanti <lb></lb>obiicitur.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000940"><emph type="italics"></emph>Poſtquàm autem<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei definitionem confirmare, & <lb></lb>communem aliorum deſtruere conatus es, aggrederis numero <lb></lb>x. </s> <s id="s.000941">eam rationem, qua idem Galileus communiorem motus <lb></lb>vniformiter accelerati definitionem abſurditatis arguit, à <lb></lb>paralogiſmo excuſare: ſed fruſtra huius cauſſæ pairocinium <lb></lb>ſuſcipis, cùm nec eam obtinere, nec ſatis plauſibiliter eam de<lb></lb>fendere poßis. </s> <s id="s.000942">Hæc porrò eſt<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei ratio.<emph.end type="italics"></emph.end></s> <s id="s.000943"> Si accelera<lb></lb>tio motus in deſcenſu grauium æqualibus ſpatiis, <lb></lb>æqualia ſumeret velocitatis incrementa, eſſent velo-<pb pagenum="111" xlink:href="028/01/151.jpg"></pb>citates inter ſe, vt emenſa ſpatia: at quoties velocitates <lb></lb>inter ſe ſunt, vt emenſa ſpatia, debent neceſſariò ea <lb></lb>ſpatia aut eodem, aut æquali tempore percurri. </s> <s id="s.000944">Si igi<lb></lb>tur velocitas acquiſita per totam AC, eam rationem <lb></lb>habeat ad velocitatem acquiſitam per AB, <lb></lb><figure id="id.028.01.151.1.jpg" xlink:href="028/01/151/1.jpg"></figure><lb></lb>quam ſpatium AC, ad ſpatium AB, neceſſe eſt, <lb></lb>vt totum ſpatium AC eodem, aut æquali tem<lb></lb>pore decurratur, quo ſpatium AB abſoluitur. <lb></lb></s> <s id="s.000945">Impoſſibile eſt autem, vt corpus deſcendens per <lb></lb>AC, eodem, aut æquali tempore percurrat to<lb></lb>tam AC, quo percurrit partem eius AB, niſi mo<lb></lb>tus fiat in inſtanti. </s> <s id="s.000946">Tam impoſſibile eſt igitur, <lb></lb>vt velocitates in deſcenſu grauium inter ſe ſint, vt <lb></lb>emenſa ſpatia, quàm impoſſibile eſt motum illum fie<lb></lb>ri in inſtanti. <emph type="italics"></emph>Hanc ego rationem Paralogiſmum dico, tu <lb></lb>contendis eſſe veram Demonſtrationem. </s> <s id="s.000947">Vitium ego tan<lb></lb>quam intelligenti breuiùs fortè indicaui: at præoccupato cer<lb></lb>tè aliunde animo, non ſufficienter illud detexi. </s> <s id="s.000948">Exactiùs igi<lb></lb>tur (vt poſtulas) ſingulas huius Ratiocinationis propoſitiones <lb></lb>hoc loco perpendemus. </s> <s id="s.000949">Prima hęc eſt,<emph.end type="italics"></emph.end> Si acceleratio motus <lb></lb>in deſcenſu grauium æqualibus ſpatiis æqualia ſumeret <lb></lb>velocitatis incrementa, eſſent velocitates inter ſe, vt <lb></lb>emenſa ſpatia. <emph type="italics"></emph>Nunc age, quis huius propoſitionis ſenſus <lb></lb>eſſe videtur? </s> <s id="s.000950">Duplicem enim patitur, & quidem valdè di<lb></lb>uerſum, quorum alter verus, alter falſus ſit; & niſi poſteriore <lb></lb>hoc ſenſu illam poſt<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileum vſurpes, concludis omninò ni<lb></lb>hil. </s> <s id="s.000951">Prior ſenſus iſte eſt, Si acceleratio motus in deſcenſu <lb></lb>grauium æqualibus spatiis æqualia ſumat velocitatis augmen<lb></lb>ta; neceſſe eſt, vt hæc eadem augmenta quibuſlibet spatij <lb></lb>partibus acquiſita eandem inter ſerationem obſeruent, quàm<emph.end type="italics"></emph.end><pb pagenum="112" xlink:href="028/01/152.jpg"></pb><emph type="italics"></emph>emenſa ſpatia, & hic ſenſus verus ac neceſſarius eſt. </s> <s id="s.000952">Si <lb></lb>enim intriangulo æqualia spatia deſignentur<emph.end type="italics"></emph.end> AD, DE, EF, <lb></lb><emph type="italics"></emph>&c. </s> <s id="s.000953">& in<emph.end type="italics"></emph.end> D <emph type="italics"></emph>acquiſitus ſupponatur vnus<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.152.1.jpg" xlink:href="028/01/152/1.jpg"></figure><lb></lb><emph type="italics"></emph>gradus, & in<emph.end type="italics"></emph.end> E <emph type="italics"></emph>duo, & tres in<emph.end type="italics"></emph.end> F, <emph type="italics"></emph>manifeſtum <lb></lb>eſt duos gradus, ad quos acceleratio perueniſſe <lb></lb>ponitur in<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>eſſe ad vnum gradum acquiſi<lb></lb>tum in<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>vt ſpatium<emph.end type="italics"></emph.end> AE <emph type="italics"></emph>ad spatium<emph.end type="italics"></emph.end> AD; <lb></lb><emph type="italics"></emph>& ſimiliter gradus treis, qui in<emph.end type="italics"></emph.end> F <emph type="italics"></emph>ſupponun<lb></lb>tur terminare celeritatis augmentum, eſſe ad <lb></lb>gradum vnum ipſius<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>vel ad duos ipſius<emph.end type="italics"></emph.end> E, <lb></lb><emph type="italics"></emph>vt<emph.end type="italics"></emph.end> AF, <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> AD, <emph type="italics"></emph>vel<emph.end type="italics"></emph.end> AE. <emph type="italics"></emph>Et hoc quidem <lb></lb>ſenſu, ſi primam illam<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei vſurpares, vera omninò eſſet, <lb></lb>ac neceſſaria, ſed Aſſumptio, quæ ſubſumitur, falſa eſſet at<lb></lb>que impoßibilis; nempe hæc.<emph.end type="italics"></emph.end></s> <s id="s.000954"> At quoties velocitates inter <lb></lb>ſe ſunt vt emenſa ſpatia (<emph type="italics"></emph>in ſenſu proximè aßignato<emph.end type="italics"></emph.end>) de<lb></lb>bent neceſſariò ea ſpatia aut eodem, aut æquali tem<lb></lb>pore percurri: <emph type="italics"></emph>Sicque iam hac ex parte<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei licet ratio<lb></lb>cinatio corruit. </s> <s id="s.000955">Sed alius item eſſe poteſt primæ illius Propo<lb></lb>ſitionis ſenſus, vt ſeilicet quoties acceleratio velocitatis in deſ<lb></lb>cenſu grauium æqualibus ſpatiis æqualia incrementa acquirit, <lb></lb>integræ velocitates ſecundum ſe totas, & quaſlibet ſui parteis <lb></lb>analogas aeceptæ, & conſiderata, & non tantum acquiſitæ <lb></lb>partibus ſpatii æqualibus incrementa, eam ab initio ad finem <lb></lb>inter ſe rationem obſeruent, quam emenſa ſpatia. </s> <s id="s.000956">Qui ſen<lb></lb>ſus à priore longè diuerſus est, & à te non intenditur modò; <lb></lb>ſed diſtinctè quoque eodem numero x. </s> <s id="s.000957">exprimitur. </s> <s id="s.000958">Ais enim.<emph.end type="italics"></emph.end><lb></lb>Rem certè in hunc modum concipio. </s> <s id="s.000959">Intelligatur <lb></lb>AC, diuiſa in duodecim parteis æqualeis, ac proinde <lb></lb>eius dimidium AB, ſeu ipſi æqualeis DE in ſex; ſint<lb></lb>que primùm duo mobilia, quorum vnum deſcendat <pb pagenum="113" xlink:href="028/01/153.jpg"></pb>ex A, verſus C, eodem momento, quo aliud ex D, <lb></lb>verſus E; notum eſt, ſi vtrumque quidem fer<lb></lb><figure id="id.028.01.153.1.jpg" xlink:href="028/01/153/1.jpg"></figure><lb></lb>retur non accelerato, ſed æquabili motu, <lb></lb>euenturum eſſe, vt velocitate illius exſiſtente <lb></lb>dupla ad velocitatem iſtius, illud perueniret <lb></lb>in C, eodem momento, quo iſtud in E; <lb></lb>quoniam ſpatium ab illo ſuperatum foret <lb></lb>vbique ad ſpatium ab iſto ſuperatum, du<lb></lb>plum; hoc eſt, forent ab illo ſuperatæ duæ <lb></lb>partes, cùm ab iſto vna: ab illo quatuor, cùm ab hoc <lb></lb>duæ, &c. </s> <s id="s.000960">quatenus ſpatia ſe haberent vbique, vt velo<lb></lb>citates; hoc eſt, velocitas per totam AC, eſſet vbique <lb></lb>dupla velocitatis per totam DE. </s> <s id="s.000961">At verò, quoniam <lb></lb>heic agitur de motu non æquabili, ſed continenter <lb></lb>accelerato; ita diſcedant rursùs mobilia eodem tem<lb></lb>pore, vnum ab A, aliud à D, vt ſuccreſcentibus conti<lb></lb>nuò velocitatis gradibus, illud perueniendo in C, ac<lb></lb>quiſierit duodecim, hoc perueniendo in E, ſex: <emph type="italics"></emph>Tum <lb></lb>interrogas,<emph.end type="italics"></emph.end> Quid impediat, quò minùs illud perueniat <lb></lb>in C, eodem tempore, quo iſtud in E? <emph type="italics"></emph>Ego verò reſ<lb></lb>pondeo, nihil certè impedire, ſi tales eſſent, quales deſcribis <lb></lb>velocitate: taleis autem ſine dubio deſcribis, qualeis in prima <lb></lb>illa<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei propoſitione ſignificari putas. </s> <s id="s.000962">At hoc ſenſu hypo<lb></lb>thetica illa Galilei propoſitio falſa eſt, euidenterque impoßi<lb></lb>bilis: cùm nulla prorsùs ratione conſequens inferi poßit ex <lb></lb>antecedente. </s> <s id="s.000963">Hoc enim eſt Antecedens,<emph.end type="italics"></emph.end> Acceleratio ve<lb></lb>locitatis in deſcenſu grauium per totam AC, ita con<lb></lb>tinua ſucceſſione creſcit, vt primùm in B acquiſitus <lb></lb>ſupponatur vnus aliquis velocitatis gradus; & vlteriùs <lb></lb>procedente motu, & continuò increſcente celeritate, <pb pagenum="114" xlink:href="028/01/154.jpg"></pb>duo iam in C velocitatis gradus habeantur. <emph type="italics"></emph>Istad <lb></lb>certè eſt antecedens, & nihil aliud aiunt ij, qui à<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileo ab<lb></lb>ſurditatis arguuntur. </s> <s id="s.000964">Iam ergo vide, vtrum ex hoc antece<lb></lb>dente, rectè tuum illud, & Galilei Conſequens inferatur:<emph.end type="italics"></emph.end> Ergo <lb></lb>velocitas deſcenſus per totam AC ab initio ad finem, <lb></lb>& ſecundum quaſlibet eius parteis conſiderata, perpe<lb></lb>tuò dupla eſt eius velocitatis, qua idem graue per AB <lb></lb>deſcendit. <emph type="italics"></emph>Siue enim<emph.end type="italics"></emph.end> AB <emph type="italics"></emph>coniunctam toti<emph.end type="italics"></emph.end> AC, <emph type="italics"></emph>conſide<lb></lb>res, ſiue vt ſeparatam, qualis eſt<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>ſemper velocitas deſ<lb></lb>cenſus per<emph.end type="italics"></emph.end> AC, <emph type="italics"></emph>quandiù percurritur prior eius pars<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>nec <lb></lb>ſui-ipſius, nec velocitatis per<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>dupla eſt, vt falsò aſſumis, <lb></lb>ſed planè eadem, aut æqualis omninò est. </s> <s id="s.000965">Nempe volumus, <lb></lb>& neceſſariò exigimus (quod ipſa quoque rei natura poſtu<lb></lb>lat) vt motus, qui per totam<emph.end type="italics"></emph.end> AC, <emph type="italics"></emph>& per partem<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>ſiue <lb></lb>per æqualem<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>eadem planè velocitate incipiat, & eadem <lb></lb>velocitate progrediatur per totam<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>& per ipſam<emph.end type="italics"></emph.end> DE: <lb></lb><emph type="italics"></emph>ex<emph.end type="italics"></emph.end> B <emph type="italics"></emph>verò ita velocitas augeatur, vt tandem in<emph.end type="italics"></emph.end> C <emph type="italics"></emph>dupla in<lb></lb>ueniatur eius, qua fuit in<emph.end type="italics"></emph.end> B, <emph type="italics"></emph>vel in<emph.end type="italics"></emph.end> E. H<emph type="italics"></emph>æc enim nostra, <lb></lb>& communis aliorum ſuppoſitio eſt, & primæ propoſitionis à<emph.end type="italics"></emph.end><lb></lb>G<emph type="italics"></emph>alileo aſſumptæ antecedens; ſi tamen aduerſum nos, & non <lb></lb>potiùs aduerſus Chimeras, & Tragalaphos depugnet. </s> <s id="s.000966">At <lb></lb>ex eo antecedente tuumillud, &<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei conſequens neceſſa<lb></lb>ria illatione non priùs inferetur, quàm aliud quodlibet ex <lb></lb>vero falſum eruatur. </s> <s id="s.000967">Prima igitur<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei Propoſitio, eo <lb></lb>ſenſu, quo ab ipſo vſurpatur, & à te intelligitur, falſa eſt, <lb></lb>atque impoßibilis; ideóque tota eius ratiocinatio, non demon<lb></lb>ſtratio, ſed merus Paralogiſmus eſt.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000968">An videri potes operosè quidem, ſed nequicquam <lb></lb>tamen explicare conatum, vt Paralogiſmum oſtendas, <lb></lb>quem quanta moderatione potueram non fuiſſe à te <pb pagenum="115" xlink:href="028/01/155.jpg"></pb>oſtenſum innueram; bonitatem tuam implorando, ſi <lb></lb>fortè liceret mihi dicere, videri poſſe cuipiam, te eum <lb></lb>potiùs eſſe, qui incideres in Paralogiſmum? </s> <s id="s.000969">Quippe <lb></lb>huiuſmodi de re ſola hæc verba habueras, quæ non <lb></lb>pigebit repetere, <emph type="italics"></emph>Vt ſi graue deſcendens per AB, tem<lb></lb>pus quodcumque inſumat, puta quadrantem: ac deinde BC <lb></lb>ipſi AB æquale, dimidio quadrante percurrat: quis neget in<emph.end type="italics"></emph.end><lb></lb>C <emph type="italics"></emph>duplam haberi velocitatem eius, quæ fuit in B? Et-tamen <lb></lb>idem graue totam AC, & dimidium eius AB eodem tem<lb></lb>pore non percurreret.<emph.end type="italics"></emph.end></s> <s id="s.000970"> Scilicet iſthæc ipſa ſunt, ob quæ <expan abbr="cũ">cum</expan> <lb></lb>ego dixerim, videri te <emph type="italics"></emph>Rem controuerſam pro principio <lb></lb>aſſumere:<emph.end type="italics"></emph.end> ais iam te fuiſſe breuiter loquutum, quod pu<lb></lb>târis me <emph type="italics"></emph>intelligentem<emph.end type="italics"></emph.end> ſatis, vt paucis multa caperem: <lb></lb>nunc autem, quia contigit ſecus, & ſaltem virum <emph type="italics"></emph>animo <lb></lb>præoccupatum<emph.end type="italics"></emph.end> es alloquutus, eſſe rem exactiùs, fuſiuſ<lb></lb>que dicendam. </s> <s id="s.000971">Age itaque tu adeò humanus, vt te hu<lb></lb>ius meæ hebetudinis, præoccupationiſque miſe<lb></lb>reat, patere ſaltem lentè incedam, viamque pertentem; <lb></lb>ſi quà poſſim te conſequi. </s> <s id="s.000972">Cùm tu quæ pauca Gali<lb></lb>leus hac de re habet, reduxeris ad ſyllogiſticam quan<lb></lb>dam formam; videtur mihi poſſe non incommodè, vt <lb></lb>res diſtinctiùs percipiatur, ea fieri Aſſumptio, quæ tibi <lb></lb>Propoſitio eſt, ea Propoſitio, quæ Aſſumptio, & Syllo<lb></lb>giſmus proinde ſic inſtitui. </s> </p> <p type="main"> <s id="s.000973"><emph type="italics"></emph>Quoties velocitates ſuntinter ſe, vt emenſa spatia, de<lb></lb>bent neceſſariò ea spatia aut eodem, aut æquali tempore per<lb></lb>curri.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000974"><emph type="italics"></emph>At, ſi acceleratio motus in deſcenſu grauium æqualibus <lb></lb>ſpatiis æqualia ſumeret velocitatis incrementa, eſſent velocita<lb></lb>tes inter ſe, vtemenſa spatia.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="116" xlink:href="028/01/156.jpg"></pb> <p type="main"> <s id="s.000975"><emph type="italics"></emph>Igitur, ſi acceleratio motus in deſcenſu grauium æquali<lb></lb>bus spatiis æqualia ſumeret velocitatis incrementa, deberent <lb></lb>neceſſariò ea ſpatia aut eodem, aut æquali tempore percurri.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000976">Tu Propoſitionem (nomine Aſſumptionis) <emph type="italics"></emph>falſam <lb></lb>ac impoßibilem<emph.end type="italics"></emph.end> dicis: ſed tuo nimirum illo ſenſu;) de <lb></lb>quo dicendum conſequenter) nam alio quidem, quem <lb></lb>diuerſum ais, & Galileo, mihique tribuis, admittere <lb></lb>verum, neceſſariumque cogeris, ob meum illud ratio<lb></lb>cinium, cuius aliquam recitaſti partem. </s> <s id="s.000977">Nihil verò <lb></lb>ex eo repeto; cùm nemo non ſtatim peruideat poſſe <lb></lb>Propoſitionem accipi in duplici caſu, Vno, ſi motus <lb></lb>non acceleratus, ſed æquabilis ſit; Altero, ſi acceleratus, <lb></lb>ſed æquabili tamen progreſſione. </s> <s id="s.000978">Si primo enim, <lb></lb>ſint duo mobilia, quorum alterum ſit velocius, & per<lb></lb>currere debeat ſpatium duplò longius, quod ſit, verbi <lb></lb>cauſsâ, duo ſtadia; manifeſtum eſt duo ab illo ſtadia, <lb></lb>& vnum ab alio, eodem, aut æquali tempore percurri. <lb></lb></s> <s id="s.000979">Sin verò ſecundo, duo mobilia ſint, quorum motus <lb></lb>continenter ſic acceleretur, vt celeritas vnius ſit conti<lb></lb>nenter, ſeu tempore toto, aut eiſdem ſaltem partibus <lb></lb>celeritatis alterius dupla, & ſpatium percurrendum ſit <lb></lb>ſimiliter duplum, veluti rursùs duo ſtadia: manifeſtum <lb></lb>iterum eſt, duo ab illo ſtadia, & vnum ab alio, eodem, <lb></lb>aut æquali tempore percurri. </s> <s id="s.000980">Ac Propoſitionem qui<lb></lb>dem ego ſicſtabilio. </s> <s id="s.000981">Reſtat, vt tu proponas caſum, <lb></lb>qui exceptionem faciat, ac non eſſe veram vniuersè <lb></lb>demonſtres. </s> <s id="s.000982">Porrò nullum habes, præter tuum ſen<lb></lb>ſum, ſeu ipſam quæſtionem, atque concluſionem, de <lb></lb>qua controuerſiam Galileo facis; neque vllum tibi ad <lb></lb>eum conuincendum argumentum ſuppetit, quàm ipſa <pb pagenum="117" xlink:href="028/01/157.jpg"></pb>adhûc controuerſia: Id enim manifeſtum fit, tum ex <lb></lb>verbis illis, quæ paulò antè recitaui, tum ex illis, quæ <lb></lb>habes iam, fuſioribus quidem, ſed eiſdem tamen. </s> <s id="s.000983">Quia <lb></lb>verò tu ad Aſſumptionem (Propoſitionis nomine) hæc <lb></lb>refers; age quid id ſit peruideamus. </s> </p> <p type="main"> <s id="s.000984">Aſſumptio eſt, <emph type="italics"></emph>Si acceleratio motus in deſcenſu gra<lb></lb>uium æqualibus ſpatiis æqualia ſumeret velocitatis incremen<lb></lb>ta, eſſent velocitates inter ſe, vt emenſa spatia.<emph.end type="italics"></emph.end></s> <s id="s.000985"> Tu illam <lb></lb>explanaturus duplicem ipſi ſenſum attribuis. <emph type="italics"></emph>Et prior <lb></lb>quidem iſte est,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>ſi acceleratio motus in deſcenſu gra<lb></lb>uium æqualibus ſpatijs æqualia ſumat velocitatis augmenta, <lb></lb>neceſſe est, vt hæc eadem augmenta quibuſlibet spatij parti<lb></lb>bus acquiſita, eandem inter ſe rationem obſeruent, quàm <lb></lb>emenſa ſpatia.<emph.end type="italics"></emph.end></s> <s id="s.000986"> At ego non ſum Oedipus, poteſque ipſe <lb></lb>cauſſari te non affari intelligentem: ſiquidem non ita <lb></lb>ſum ſolers, vt perſpicere valeam, quid diuerſitatis, aut <lb></lb>explanationis, ſenſus hic, quem facis ſpecialem, <lb></lb>contineat. </s> <s id="s.000987">Poſterior, <emph type="italics"></emph>vt ſcilicet,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>quoties accelera<lb></lb>tio velocitatis in deſcenſu grauium æqualibus spatiis æqualia <lb></lb>incrementa acquirit, integræ velocitates ſecundum ſe totas, & <lb></lb>quaſlibet ſui parteis analogas acceptæ, & conſideratæ, & non <lb></lb>tantum acquiſita partibus ſpatii æqualibus incrementa, ea <lb></lb>ab initio ad finem inter ſe rationem obſeruent, quam emenſa <lb></lb>ſpatia.<emph.end type="italics"></emph.end> Hæc paulò obſcuriùs, fortè propter illud, <emph type="italics"></emph>& <lb></lb>non tantum acquiſita partibus spatii æqualibus incrementa,<emph.end type="italics"></emph.end><lb></lb>quod ad priorem ſenſum attinens, cenſuiſti huic <expan abbr="inter-ſerendũ">inter<lb></lb>ſerendum</expan>. </s> <s id="s.000988">Sed vtcumque ſit; cùm tu ſenſum hunc eun<lb></lb>dem cum eo facias, quem ais à me exprimi diſtinctè; ea <lb></lb>de cauſſa ipſum in confeſſo habeo. </s> <s id="s.000989">Iam cùm ſit Aſ<lb></lb>ſumptio hypothetica, & duas proinde parteis <expan abbr="cõtineat">contineat</expan>. <pb pagenum="118" xlink:href="028/01/158.jpg"></pb><expan abbr="quarũ">quarum</expan> altera Antecedens, altera Conſequens dicatur, <lb></lb>tu ſic vtramque à conditione (vt Dialectici loquuntur) <lb></lb>abſoluis, vt priorem ſenſum antecedenti tribuas, & <lb></lb>poſter orem conſequenti; ac poſtquàm antecedens ex<lb></lb>preſſiſti in linea (expreſſum priùs in triangulo, dum ex<lb></lb>plicares priorem ſenſum) arguas non inferri ex eo legi<lb></lb>timè conſequens, expreſſum iuxta poſteriorem. </s> <s id="s.000990">Tu <lb></lb>igitur tale facis Antecedens. </s> </p> <p type="main"> <s id="s.000991"><emph type="italics"></emph>Acceleratio velocitatis in deſcenſu grauium per<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.158.1.jpg" xlink:href="028/01/158/1.jpg"></figure><lb></lb><emph type="italics"></emph>totam AC, ita continua ſucceßione creſcit, vt pri<lb></lb>mùm in B acquiſitus ſupponatur vnus aliquis ve<lb></lb>locitatis gradus, & vlteriùs procedente motu, & <lb></lb>continuò increſcente celeritate duo iam in C velo<lb></lb>citatis gradus habeantur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000992">Ac tum, poſtquàm dixiſti illos, quià Ga<lb></lb>lile o arguuntur, nihil aliud dicere, videre <lb></lb>me iubes, vtrum ex tali Antecedente, rectè inferatur <lb></lb>tale Conſequens. </s> </p> <p type="main"> <s id="s.000993"><emph type="italics"></emph>Ergo velocitas deſcenſus per totam AC ab initio ad fi<lb></lb>nem, & ſecundum quaſlibet eius parteis conſiderata perpetuò <lb></lb>dupla eſt eius velocitatis, qua idem graue per AB deſcen<lb></lb>dit.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000994">Itaque, cùm neges ſequelam, vt aiunt, hypotheticæ <lb></lb>Aſſumptionis, & in illa cardo negotij verſetur, Ad<lb></lb>moneo dumtaxat circa Antecedens videri loco <emph type="italics"></emph>Veloci<lb></lb>tatis,<emph.end type="italics"></emph.end> reponendam voculam <emph type="italics"></emph>Motus,<emph.end type="italics"></emph.end> & te aut debuiſſe <lb></lb>inſerere, aut ſaltem debere iam ſupponere aduerbium <lb></lb><emph type="italics"></emph>æquabiliter,<emph.end type="italics"></emph.end> aut <emph type="italics"></emph>vniformiter,<emph.end type="italics"></emph.end> proximè ipſum verbum <lb></lb><emph type="italics"></emph>creſcit,<emph.end type="italics"></emph.end> ſiue potius <emph type="italics"></emph>fit<emph.end type="italics"></emph.end> (niſi non <emph type="italics"></emph>velocitatis acceleratio,<emph.end type="italics"></emph.end> ſed <lb></lb><emph type="italics"></emph>velocitas<emph.end type="italics"></emph.end> ſimpliciter ſcribatur) itemque proxime vocem <pb pagenum="119" xlink:href="028/01/159.jpg"></pb><emph type="italics"></emph>celeritate:<emph.end type="italics"></emph.end> adeo proinde, vt Antecedens aut ſit, aut intel<lb></lb>ligatur huiuſmodi. </s> </p> <p type="main"> <s id="s.000995"><emph type="italics"></emph>Acceleratio motus in deſcenſu grauium per totam A<emph.end type="italics"></emph.end>C <lb></lb><emph type="italics"></emph>ita continua ſucceßione æquabiliter fit, vt primùm in B <lb></lb>acquiſitus ſupponatur vnus aliquis velocitatis gradus, & vl<lb></lb>terius procedente motu, & continuò increſcente æquabiliter <lb></lb>celeritate, duo iam in C velocitatis gradus habeantur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000996">Quippe heic agitur de Motu, cuius acceleratio fiat, <lb></lb>ſeu celeritas, velocitas-ve increſcat ſucceſſione conti<lb></lb>nua, non quacumque, ſed æquabili. </s> <s id="s.000997">Nam illa qui<lb></lb>dem acceleratio, quam antè obiiciebam poſſe accipi, <lb></lb>primò ſecundum parteis minuti, deinde ſecundum <lb></lb>parteis horæ, tum ſecundum parteis ſecundi, tandem <lb></lb><expan abbr="ſecundũ">ſecundum</expan> parteis diei, aut quæuis alia huiuſmodi; talis, <lb></lb>inquam, acceleratio continua ſucceſſione fieret, atta<lb></lb>men difformi, inæquabili, qualemque ipſe non es ad<lb></lb>miſſurus, cùm ab initio vſque controuerſiæ ſtatueris <lb></lb>definiti <emph type="italics"></emph>motum æquabiliter acceleratum eum, qui æqualibus <lb></lb>spatijs æqualia celeritatis augmenta acquirat.<emph.end type="italics"></emph.end></s> <s id="s.000998"> Circa Conſe<lb></lb>quens, moneo ſolùm te aut debuiſſe inſerere, aut iam <lb></lb>debere ſupponere mentionem partium <emph type="italics"></emph>analogarum;<emph.end type="italics"></emph.end><lb></lb>quaſi nimirùm eſſe debeat, aut ſaltem intelligi huiuſ<lb></lb>modi Conſequens. </s> </p> <p type="main"> <s id="s.000999"><emph type="italics"></emph>Ergo velocitas deſcenſus per totam A<emph.end type="italics"></emph.end>C <emph type="italics"></emph>ab initio ad fi<lb></lb>nem, & ſecundum quaſlibet eius parteis conſiderata perpetuò <lb></lb>dupla eſt velocitatis deſcenſus eiuſdem mobilis per totam AB <lb></lb>ab initio ad finem, & ſecundum quaſlibet eius parteis, parti<lb></lb>bus ipſius AC analogas, conſideratæ.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001000">Id ſcilicet ipſe iam edixeras poſteriorem exprimens <lb></lb>ſenſum; & perſpicuum eſt inæqualeis lineas, quæ ac-<pb pagenum="120" xlink:href="028/01/160.jpg"></pb>ceptæ fuerint ſecundum ſe totas in ratione aliqua, poſ<lb></lb>ſe deinceps illegitimè comparari ſecundum parteis, <lb></lb>ſi facto æquali partium numero non prima vnius ad <lb></lb>primam alterius, ſed ad decimam referatur, & vniuersè <lb></lb>quælibet ad quamlibet ordinis non ſui. </s> </p> <p type="main"> <s id="s.001001">Hiſce præmiſſis, videndum eſt, quo iure tuſeque<lb></lb>lam neges, & monſtres conſequens non rectè, ac para<lb></lb>logiſticè inferri ex antecedente. </s> <s id="s.001002">Nam neceſſitas qui<lb></lb>dem inferendi ex eo manifeſta eſt, quod Acceleratio <lb></lb>fieri, aut velocitas creſcere non poſſit æquabiliter per <lb></lb>totam AC, neque ſimiliter per totam AB, quin ſi ve<lb></lb>locitas in C dupla ſit velocitatis in B, quælibet partes <lb></lb>analogæ acceptæ per totam AC, duplæ ſint ad analo<lb></lb>gas per totam AB: atque ita, quin velocitas mobilis <lb></lb>deſcendentis per AC ſit perpetuò dupla velocitatis <lb></lb>eiuſdem mobilis deſcendentis per AB. </s> <s id="s.001003">Quod ſanè <lb></lb>adeò eſt manifeſtum, vt neipſe quidem negare id po<lb></lb>tueris, poſtquàm obſeruaſti comparatam primùm à <lb></lb>me lineam AC diuiſam in duodecim parteis cum <lb></lb>linea AC diuiſa in ſex, tanquam cum ſeparata, exiſten<lb></lb>teque, intelligentiæ cauſsâ DE, ac ſubinde intellexi<lb></lb>ſti eſſe omninò neceſſarium, vt idem mobile, ſi velo<lb></lb>eitatem in B, ſimplam, in C verò duplam acquirat, <lb></lb>reperiatur ſimul in fine primæ, & in fine ſecundæ <lb></lb>duodenarum partium; in fine tertiæ, & in fine ſextæ; <lb></lb>in fine ſextæ, & in fine duodecimæ; propter analogiam <lb></lb>ſimplicium partium lineæ AB, & duplicium lineæ AC. <lb></lb>Ecquid-nam ergo iuris iam habes, vt perneges conſe<lb></lb>quutionem? </s> <s id="s.001004">Scilicet his verbis illud explicas, <emph type="italics"></emph>ſiue <lb></lb>enim AB vt coniunctam toti AC conſideres, ſiue vt<emph.end type="italics"></emph.end><pb pagenum="121" xlink:href="028/01/161.jpg"></pb><emph type="italics"></emph>ſeparatam, qualis eſt<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>ſemper velocitas deſcenſus per<emph.end type="italics"></emph.end><lb></lb>AC, <emph type="italics"></emph>quandiù percurritur prior eius pars<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>nec ſui-ipſius, <lb></lb>nec velocitatis per<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>dupla eſt, vt falsò aſſumis, ſed planè <lb></lb>eadem aut æqualis omninò eſt.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001005">Hui tamen! ſiccine exactius, magiſque <lb></lb><figure id="id.028.01.161.1.jpg" xlink:href="028/01/161/1.jpg"></figure><lb></lb>ſufficienter mihi Paralogiſmum iam de<lb></lb>tegis, & proptereáne ægrè fers te mihi <lb></lb>(<expan abbr="|cũ">|cum</expan> intelligentem putares) indicaſſe bre<lb></lb>uiùs ratiocinationis Galileanæ vitium? <lb></lb><emph type="italics"></emph>Semper,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>velocitas deſcenſus per<emph.end type="italics"></emph.end> AC, <lb></lb><emph type="italics"></emph>quandò percurritur prima eius pars<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>nec <lb></lb>ſui ipſius, nec velocitatis per<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>dupla eſt.<emph.end type="italics"></emph.end><lb></lb>Enimverò, non quæritur, vtrum reipsâ dupla ſit, ſed <lb></lb>an duplam eſſe tuo ex principio conſequatur. </s> <s id="s.001006">Nam <lb></lb>noui quidem ego falſum eſſe Conſequens; ſed verè ta<lb></lb>men conſequi ex Antecedente, admiſſo oſtendo. </s> <s id="s.001007">Dicis <lb></lb><emph type="italics"></emph>me id falsò aſſumere;<emph.end type="italics"></emph.end> ego verò non falsò aſſumo, qui <lb></lb>ne aſſumo quidem, ſed ſolum conſequi demonſtro, vt<lb></lb>cumque poſtquàm id demonſtraui, ſubſumere deinde <lb></lb>poſſim, vt oſtendam te tibi repugnare, quòd <expan abbr="cũ">cum</expan> fatea<lb></lb>ris AC, & AB inæqualibus percurri temporibus, prin<lb></lb>cipium tamen id defendas, ex quo fateri ſimul cogaris <lb></lb>eodem, aut æquali tempore percurri. </s> <s id="s.001008">Itaque cùm <lb></lb>heic non agatur de veritate Conſequentis, ſed de ne<lb></lb>ceſſitate, qua conſequitur, ac tu deberes oſtendere <lb></lb>neceſſariò non conſequi, & declarare in quo peceá<lb></lb>rim, inferendo fore velocitatem per totam AC du<lb></lb>plam velocitatis per totam AB, nihil aliud habes, <lb></lb><expan abbr="quã">quam</expan>, <emph type="italics"></emph>non eſſe duplam.<emph.end type="italics"></emph.end></s> <s id="s.001009"> Quod perinde eſt, ac ſi te ponen<lb></lb>te illud Antecedens, <emph type="italics"></emph>Plato eſt lapis,<emph.end type="italics"></emph.end> ego inferam iſtud <pb pagenum="122" xlink:href="028/01/162.jpg"></pb>Conſequens, igitur <emph type="italics"></emph>Plato ſenſu caret:<emph.end type="italics"></emph.end> & te negante <lb></lb>conſequutionem, illam ex eo probem, <emph type="italics"></emph>quòd lapis ſenſu <lb></lb>careat:<emph.end type="italics"></emph.end> ac tum dicas Conſequens <emph type="italics"></emph>non rectè inferri;<emph.end type="italics"></emph.end> & <lb></lb>compulſus ad id probandum, nihil tamen aliud <lb></lb>quàm hoc dicas, <emph type="italics"></emph>Plato enim ſenſu non caret, vt falsò, <lb></lb>aſſumis, ſed planè ſenſu præditus eſt.<emph.end type="italics"></emph.end></s> <s id="s.001010"> Videlicet quæſtio <lb></lb>non erit de veritate Conſequentis, nam ego quoque <lb></lb>Platonem ſenſu carere falſum reputabo: ſed de neceſ<lb></lb>ſitate conſequutionis, quam tu infirmare deberes, ne <lb></lb>euerteret tuum Antecedens; neque ego falsò aſſu<lb></lb>mam, carere Platonem ſenſu, qui ne aſſumam quidem: <lb></lb>ſed neceſſariò ſolummodò, & vt concluſionem dedu<lb></lb>cam; tametſi <expan abbr="deductũ">deductum</expan> aſſumere poſſim, vt oſtendam te <lb></lb>contradicere tibi ipſi, tanquam coactum aſſerere Pla<lb></lb>tonem ſenſu deſtitui, quem aſſeras præditum ſenſu. </s> </p> <p type="main"> <s id="s.001011">Pergis porrò, <emph type="italics"></emph><expan abbr="Nẽpe">Nempe</expan> volumus, & neceſſariò exigimus (quod <lb></lb>ipſa quoque rei natura poſtulat) vt motus, qui per totam<emph.end type="italics"></emph.end><lb></lb>AC, <emph type="italics"></emph>& per partem<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>ſiue per æqualem<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>eadem <lb></lb>planè velocitate incipiat, & eadem velocitate progrediatur, <lb></lb>per totam<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>& per ipſam<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>ex<emph.end type="italics"></emph.end> B <emph type="italics"></emph>verò ita velocitas <lb></lb>augeatur, vt tandem in<emph.end type="italics"></emph.end> C <emph type="italics"></emph>dupla inueniatur eius, quæ fuit in<emph.end type="italics"></emph.end><lb></lb>B, <emph type="italics"></emph>vel in<emph.end type="italics"></emph.end> E. At, optime Vir, quod vis quidem, & <lb></lb>exigis, vt <emph type="italics"></emph>cœptus ex A motus,<emph.end type="italics"></emph.end> ſiue progreſſurus ſit vſque <lb></lb>ad C, ſiue deſiturus in B, <emph type="italics"></emph>eadem planè velocitate incipiat, <lb></lb>& progrediatur vſque ad B,<emph.end type="italics"></emph.end> idipſum eſt, quod poſtulat <lb></lb>ipſa quoque rei natura (vtcumque poſteà cauſſeris me <lb></lb>non inſpexiſſe illam penitiùs.) Quod autem vis, & <lb></lb>exigis, vt velocitas ex B ita augeatur, vt tandem in <lb></lb>C dupla inueniatur eius, quæ fuit in B, idipſum iam <lb></lb>eſt, quod oſtenſum eſt tantùm auerſari Naturam, <pb pagenum="123" xlink:href="028/01/163.jpg"></pb>quantùm auerſatur motum inſtantancum. </s> <s id="s.001012">Quam<lb></lb>obrem, non ſufficit tibi, vt velis, atque exigas velo<lb></lb>citat<gap></gap>m in C duplam eſſe velocitatis in B, ſed reſtat, <lb></lb>vt illud, ſi poſlit, oſtendas. </s> <s id="s.001013">Quomodo verò id vnquam <lb></lb>poſſis, niſi volendo, & exigendo, vt quod quæritur, <lb></lb>tibi concedatur, atque adeò petendo, vt loquuntur, <lb></lb>principium? </s> <s id="s.001014">Idipſum eſt, quod te feciſſe, circa relata <lb></lb>verba, obieci articulo XI. & quod tamen iam repetis <lb></lb>conſtanter. </s> <s id="s.001015">Quippe eò quoque te iam adegit, quem <lb></lb>exiſtimaſti te poſſe diſtinguere priorem ſenſum, à <lb></lb>poſteriore valde diuerſum. </s> <s id="s.001016">Nam poſtquàm dixiſti <lb></lb><expan abbr="eũ">eum</expan> ſenſum <emph type="italics"></emph>verum eſſe, ac neceſſarium,<emph.end type="italics"></emph.end> iſthæc <lb></lb><figure id="id.028.01.163.1.jpg" xlink:href="028/01/163/1.jpg"></figure><lb></lb>verba tua ſequuntur, <emph type="italics"></emph>Si enim in triangulo <lb></lb>æqualia spatia deſignentur<emph.end type="italics"></emph.end> AD, DE, EF, <lb></lb><emph type="italics"></emph>&c. </s> <s id="s.001017">& in<emph.end type="italics"></emph.end> D <emph type="italics"></emph>acquiſitus ſupponatur vnus <lb></lb>gradus, & in<emph.end type="italics"></emph.end> E <emph type="italics"></emph>duo, & tres in<emph.end type="italics"></emph.end> F; <emph type="italics"></emph>manife<lb></lb>ſtum eſt duos gradus, ad quos acceleratio per<lb></lb>ueniſſe ponitur in<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>eſſe ad vnum gradum <lb></lb>acquiſitum in<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>vt spatium<emph.end type="italics"></emph.end> AE, <emph type="italics"></emph>ad spa<lb></lb>tium. </s> <s id="s.001018">AD.<emph.end type="italics"></emph.end></s> <s id="s.001019"> Deprehendere enim ſtatim <lb></lb>licet, quemadmodum idipſum ſupponas, quod pror<lb></lb>sùs controuertitur: nempe in E eſſe duos gradus, vbi <lb></lb>vnus fuerit in D. </s> <s id="s.001020">Niſi verò hoc eſt; quid nam tandem <lb></lb>eſt, quod dicunt petere principium? </s> <s id="s.001021">Subinnueram <lb></lb>ego articulo eodem id mouere te, quòd velocitas ac<lb></lb>quiſita in C (reſumendo nempelineam ABC) ſit re<lb></lb>uerâ maior, quàm acquiſita in B; ſed tu attendere <lb></lb>noluiſti ex eo, quòd ſit maior, non ſequi tamen eſſe <lb></lb>duplam; ratus ſcilicet te penitiùs inſpexiſſe rei natu<lb></lb>ram, ac eo principio ſemper abductus, de quo tota eſt <pb pagenum="124" xlink:href="028/01/164.jpg"></pb>controuerſia; itemque opinione illa, quod in trian<lb></lb>gulo, lineæ baſi parallelæ repræſentare gradus veloci<lb></lb>tates valeant, ſi partes cruris alterutrius ipſis reſpon<lb></lb>dentes repræſentent ſpatia; non aduertendo, quî iſti <lb></lb>gradus inæquales ſint, & à ſeipſis differant, dum <lb></lb>acquiruntur, & dum manent; & quid incommodi ex <lb></lb>hac repræſentatione trahatur. </s> <s id="s.001022">Videtur ſaltem occaſio <lb></lb>dubitandi fieri debuiſſe, poſtquàm admonitus à me, <lb></lb>falſum deprehendiſti id Experimentum, cui ſoli in<lb></lb>nixus, prounciâras velocitatem duplam eſſe ex du<lb></lb>pla altitudine; ac ſaltem obſeruaſti globum cadentem <lb></lb>ex A in C, hoc eſt ex altitudine duarum <lb></lb><figure id="id.028.01.164.1.jpg" xlink:href="028/01/164/1.jpg"></figure><lb></lb>ſui diametrorum, non eleuare cum oppoſita <lb></lb>lance duplum eius ponderis, quod eleuat ex <lb></lb>A in B, hoc eſt ex altitudine vnius: ſed res eſt <lb></lb>poſteà fuſiùs dicenda. </s> <s id="s.001023">Heic ſolùm moneo, <lb></lb>quod ſubdis <emph type="italics"></emph>tuam, & communem aliorum ſuppoſi<lb></lb>tionem eſſe primæ Propoſitionis<emph.end type="italics"></emph.end> (ſeu ſuperioris Aſ<lb></lb>ſumptionis) G<emph type="italics"></emph>alilei Antecedens,<emph.end type="italics"></emph.end> eſſe <expan abbr="illã">illam</expan> quidem <lb></lb>tuam, aliorumque ſuppoſitionem, ipſamque falſam, <lb></lb>ac impoſſibilem; ſed à Galileo tamen hypotheticè ſo<lb></lb>lùm vſurpari, & Antecedens fieri, vt quid ex ea incom<lb></lb>modi neceſſariò ſequatur, demonſtret. </s> <s id="s.001024">Vnde & <lb></lb>quod ais, <emph type="italics"></emph>niſi aduerſus<emph.end type="italics"></emph.end> C<emph type="italics"></emph>himæras, & Tragelaphos depugnet,<emph.end type="italics"></emph.end><lb></lb>vides quonam ſenſu accipiendum ſit; & quod ſupereſt, <lb></lb>ipſe iam agnoſcis, an eius rationem <emph type="italics"></emph>merum eſſe Paralo<lb></lb>giſmum<emph.end type="italics"></emph.end> probâris vllo argumento. </s> </p> <p type="main"> <s id="s.001025"><emph type="italics"></emph>Quòd ſi tamen præoccupatus contrariis decretis animus <lb></lb>tuus, <expan abbr="nondũ">nondum</expan> clarißimam veritatis huius lucem plenè perſpicit, <lb></lb>ac penitùs agnoſcit,<emph.end type="italics"></emph.end> C<emph type="italics"></emph>oncipe in triangulo ABC partes lineæ<emph.end type="italics"></emph.end><pb pagenum="125" xlink:href="028/01/165.jpg"></pb><emph type="italics"></emph>AC non iam spatij parteis æqualeis deſignare, ſed temporis. <lb></lb></s> <s id="s.001026">Tunc ex tuis, & Galilei principijs facilè agnoſces velocita<lb></lb>tem in E, hoc eſt in fine ſecundi temporis acquiſitam, veloci<lb></lb>tatis in D acquiſitæ duplam eſſe, perpetuóque<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.165.1.jpg" xlink:href="028/01/165/1.jpg"></figure><lb></lb><emph type="italics"></emph>velocitates, & tempora in eadem eſſe ratione. <lb></lb></s> <s id="s.001027">Hoc autem conſtituto, tuis ego, &<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei <lb></lb>armis ita aduerſum te inſurgo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001028">Et verò opperior. </s> </p> <p type="main"> <s id="s.001029"><emph type="italics"></emph>Si velocitatis incrementa tempori bus æqua<lb></lb>libus acquiſita eam inter ſe rationem obſerua<lb></lb>rent, quam tempora, neceſſariò ipſæ quoque <lb></lb>velocitates perpetuò eſſent inter ſe, vt tempora, <lb></lb>eſſetque, exempli gratiâ, velocitas duobus temporibus æquali<lb></lb>bus acquiſita velocitatis primo tempore acquiſitæ dupla.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001030">Scilicet iſta tibi eſt hypothetica Propoſitio. </s> <s id="s.001031">Aſſum<lb></lb>tio ſequitur. </s> </p> <p type="main"> <s id="s.001032"><emph type="italics"></emph>At quoties velocitas quælibet alterius eſt dupla, neceſſe eſt, <lb></lb>vt eodem, aut æquali tempore à velocitate dupla ſpatium <lb></lb>decurratur duplum eius, quod percurritur à velocitate ſubdu<lb></lb>pla.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001033">Concluſionem ſubtices; nam quod ſequitur eſt <lb></lb>quaſi Subſumptum. </s> <s id="s.001034">Quæſo te verò, ecquam nam <lb></lb>poſſes exinde deducere, conſtante Syllogiſmo ex ter<lb></lb>minis quatuor; neque tertio termino, vt decuit in hy<lb></lb>potheſi, vnà cum Propoſitionis aut antecedente, aut <lb></lb>conſequente aſſumpto. </s> <s id="s.001035">Huiuſmodi enim videtur <lb></lb>fuiſſe debere Aſſumptio. </s> </p> <p type="main"> <s id="s.001036"><emph type="italics"></emph>At quoties velocitas quælibet est alterius dupla, velocita<lb></lb>tis incrementa temporibus æqualibus acquiſita eam inter ſe <lb></lb>rationem obſeruant, quam tempora.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="126" xlink:href="028/01/166.jpg"></pb> <p type="main"> <s id="s.001037">Ac tum Concluſio fuiſſet. </s> </p> <p type="main"> <s id="s.001038"><emph type="italics"></emph>Igitur ſi velocitas quælibet eſſet alterius dupla, neceſſariò <lb></lb>ipſæ quóque velocitates perpetuò eſſent inter ſe, vt tempora, <lb></lb>eſſetque, exempli gratiâ, velocitas duobus temporibus acquiſi<lb></lb>ta velocitatis primo tempore acquiſitæ dupla.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001039">Agnoſcis autem ecquid nam aduerſum me heinc <lb></lb>concludatur. </s> <s id="s.001040">Sed de Aſſumptione tamen tua, <expan abbr="tanquã">tanquam</expan> <lb></lb>habenda eſſet legitima, vt dicam, ea, vt poſſit quadam<lb></lb>tenus cum propoſitione cohærere, neceſſe eſt ita ſup<lb></lb>pleatur. </s> </p> <p type="main"> <s id="s.001041"><emph type="italics"></emph>Quoties velocitas quælibet<emph.end type="italics"></emph.end> duobus temporibus acqui<lb></lb>ſita <emph type="italics"></emph>alterius<emph.end type="italics"></emph.end> primo tempore acquiſitæ <emph type="italics"></emph>est dupla; neceſſe <lb></lb>eſt, vt eodem, aut æquali tempore<emph.end type="italics"></emph.end> (hoc eſt aggregato duo<lb></lb>rum temporum) <emph type="italics"></emph>à velocitate dupla ſpatium decurratur du<lb></lb>plum eius, quod percurritur<emph.end type="italics"></emph.end> (tempore nempe vno, ſeu pri<lb></lb>mo) <emph type="italics"></emph>à velocitate ſubdupla.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001042">Tunc autem addo eſſe neceſſe, vt percurratur ſpa<lb></lb>tium non modo duplum, ſed & quadruplum primi: ſi <lb></lb>velocitas quidem acquiſita æquabiliter fuerit (qualis <lb></lb>illa eſt, qua de agimus) quatenus dum ſecundus veloci<lb></lb>tatis gradus tempore ſecundo acquiritur, & per ipſum <lb></lb>par ſpatium illi, quod decurſum fuit tempore primo, <lb></lb>percurritur, percurruntur ſimùl duo alia per gradum <lb></lb>velocitatis primo tempore acquiſitum, ac in vigore <lb></lb>perſeuerantem, veluti iam antè declaratum eſt. </s> <s id="s.001043">Sed <lb></lb>ecce Subſumis. </s> </p> <p type="main"> <s id="s.001044"><emph type="italics"></emph>Si igitur primo tempore AD, spatium PM percurra<lb></lb>tur à velocitate ſubdupla primo illo toto tempore acquiſita, <lb></lb>eodem tempore ſimul percurretur ſpatium PN ſpatii PM <lb></lb>duplum à velocitate dupla toto tempore AE acquiſita.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="127" xlink:href="028/01/167.jpg"></pb> <p type="main"> <s id="s.001045">Cùm <emph type="italics"></emph>dicis eodem tempore,<emph.end type="italics"></emph.end> hoc eſt <emph type="italics"></emph>primo,<emph.end type="italics"></emph.end> vnde quæſo <lb></lb>aſſumis? </s> <s id="s.001046">Nam in Aſſumptione quidem non <lb></lb><figure id="id.028.01.167.1.jpg" xlink:href="028/01/167/1.jpg"></figure><lb></lb>diſtinxeras vtrius velocitatis reſpectu idem, <lb></lb>aut æquale acciperes, & procliue fuit, vt <lb></lb>acciperes reſpectu duplæ, cui reſponderent <lb></lb>duo tempora, ſiue, vt expreſſi, aggregatum <lb></lb>temporum duorum, vnde & ſubſumendum <lb></lb>fuit. </s> </p> <p type="main"> <s id="s.001047"><emph type="italics"></emph>Si primo tempore AD, ſpatium PM per<lb></lb>curratur à velocitate ſubdupla, futurum vt toto <lb></lb>tempore AE<emph.end type="italics"></emph.end> (ſiue duobus temporibus, aut aggregato <lb></lb>duorum) <emph type="italics"></emph>percurratur spatium PN ſpatij PM duplum.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001048">Quo caſu rursùs addo futurum, vt non modò du<lb></lb>plum, ſed etiam quadruplum percurratur. </s> </p> <p type="main"> <s id="s.001049"><emph type="italics"></emph>Sicque eodem tempore ab eodem mobili percurretur totum <lb></lb>spatium PN, & eius dimidium PM, quod eſt impoßibile, <lb></lb>niſi motus fieret in inſtanti.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001050"><emph type="italics"></emph>Eodem,<emph.end type="italics"></emph.end> hoc eſt, <emph type="italics"></emph>primo,<emph.end type="italics"></emph.end> nullatenus ſequitur; <emph type="italics"></emph>eodem,<emph.end type="italics"></emph.end> id <lb></lb>eſt, <emph type="italics"></emph>aggregato<emph.end type="italics"></emph.end> duorum, ita vt totum ſpatium PN per<lb></lb>curratur duobus, & dimidium PM illorum primo, ſe<lb></lb>quitur quidem, ſed addendum, percurri inſuper alia <lb></lb>duo ſpatia: quæ duo aliis iuncta, motu, qui fiat ſuc<lb></lb>ceſſiue, non in <expan abbr="inſtãti">inſtanti</expan>, percurrantur. </s> <s id="s.001051">Enimverò, vt Sub<lb></lb>ſumptum tuo ſenſu probes, & te perinde, atque me, <lb></lb>mutatis ſo ùm terminis, ratiocinari planum facias, hiſ<lb></lb>ce verbis proſequeris. </s> </p> <p type="main"> <s id="s.001052"><emph type="italics"></emph>Nam, vt modo ratiocinandi tuo etiam vtar, ſumpto quo<lb></lb>piam alio ſpatio<emph.end type="italics"></emph.end> RO, <emph type="italics"></emph>spatio<emph.end type="italics"></emph.end> PM <emph type="italics"></emph>æquali; concipiantur duo <lb></lb>mobilia, quorum vnum per<emph.end type="italics"></emph.end> PN <emph type="italics"></emph>eodem momento moueri in<lb></lb>cipiat velocitate dupla, quo alterum per<emph.end type="italics"></emph.end> RO <emph type="italics"></emph>deſcendit velo-<emph.end type="italics"></emph.end><pb pagenum="128" xlink:href="028/01/168.jpg"></pb><emph type="italics"></emph>citate ſubdupla: tum neceſſe fuerit, vt quibuſlibet temporis <lb></lb>momentis continuò partes spatii<emph.end type="italics"></emph.end> PM <emph type="italics"></emph>duplo maiores percur<lb></lb>rantur, quàm ſint partes ſpatii<emph.end type="italics"></emph.end> RO, <emph type="italics"></emph>quæ ab alio mobili iiſ<lb></lb>dem momentis ſubdupla velocitate decurruntur. </s> <s id="s.001053">Quo igi<lb></lb>tur tempore mobile lentius ſpatium<emph.end type="italics"></emph.end> RO <emph type="italics"></emph>totum percurrerit, <lb></lb>eodem alterum mobile duplò velocius ſpatium<emph.end type="italics"></emph.end> PN <emph type="italics"></emph>etiam <lb></lb>abſoluerit. </s> <s id="s.001054">Et quoniam, te iudice, alia ratio non eſt, ſiue spa<lb></lb>tium<emph.end type="italics"></emph.end> RO, <emph type="italics"></emph>aut<emph.end type="italics"></emph.end> PM, <emph type="italics"></emph>à toto ſpatio<emph.end type="italics"></emph.end> PN <emph type="italics"></emph>ſeiunctum, ſiue ei<lb></lb>dem coniunctum ſupponatur, neceſſarium planè fuerit, vt <lb></lb>etiam ab vno, eodemque mobili, vno, eodemque tempore to<lb></lb>tum spatium<emph.end type="italics"></emph.end> PN, <emph type="italics"></emph>& eius dimidium<emph.end type="italics"></emph.end> PM <emph type="italics"></emph>percurratur; <lb></lb>quod certum est eſſe impoßibile, niſi motus fieret in inſtanti. <lb></lb></s> <s id="s.001055">Hæc ratiocinatio, variatis tantum terminis, de quibus contro<lb></lb>uerſia eſt, tota (vt vides) tua est.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001056">Imò, non tantum meam agnoſco, ſed inuariatis <lb></lb>etiam terminis, & qualem omninò aduerſum te dedu<lb></lb>xi, agnoſco; adeò vt mirer ipſum te, illam aduerſum <lb></lb>te comparatam, non variatis terminis retorquere in <lb></lb>me, ſed mutato nomine, vſurpare aduerſus teipſum. <lb></lb></s> <s id="s.001057">Nam, vt mutares terminos, de quibus, vt ais, contro. <lb></lb></s> <s id="s.001058">uerſia eſt, debueras idipſum, quod ego ratiocinando <lb></lb>habui pro <emph type="italics"></emph>Spatio,<emph.end type="italics"></emph.end> habere pro <emph type="italics"></emph>Tempore,<emph.end type="italics"></emph.end> quod pro <emph type="italics"></emph>Tempo<lb></lb>re,<emph.end type="italics"></emph.end> habere pro <emph type="italics"></emph>Spatio,<emph.end type="italics"></emph.end> cùm alterum alter arguamus, <lb></lb>quòd velocitas exæquetur à me quidem <emph type="italics"></emph>Tempori,<emph.end type="italics"></emph.end> à te <lb></lb>verò <emph type="italics"></emph>Spatio.<emph.end type="italics"></emph.end></s> <s id="s.001059"> Sic autem accepta linea PM pro tempo<lb></lb>re AD, & PN pro tempore AB, proſequi potuiſſes <lb></lb>hoc modo. </s> </p> <p type="main"> <s id="s.001060"><emph type="italics"></emph>Nam vt modo ratiocinandi tuo etiam vtar, ſumpto quo<lb></lb>piam alio tempore<emph.end type="italics"></emph.end> RO, <emph type="italics"></emph>tempori<emph.end type="italics"></emph.end> PM <emph type="italics"></emph>æquali, concipiamus <lb></lb>duo mobilia, quorum vnum per<emph.end type="italics"></emph.end> PN <emph type="italics"></emph>eodem ſpatio moueri<emph.end type="italics"></emph.end><pb pagenum="129" xlink:href="028/01/169.jpg"></pb><emph type="italics"></emph>incipiat velocitate dupla, quo alterum per<emph.end type="italics"></emph.end> RO <emph type="italics"></emph>deſcendit <lb></lb>velocitate ſubdupla; tum neceſſe fuerit, vt quibuſlibet ſpa<lb></lb>tij partibus continuò momenta temporis<emph.end type="italics"></emph.end> PM <emph type="italics"></emph>duplò matora <lb></lb>percurrantur, quam ſint momenta temporis<emph.end type="italics"></emph.end> RO, <emph type="italics"></emph>quæ ab <lb></lb>aliò mobili iiſdem partibus ſubdupla velocitate decurruntur. <lb></lb></s> <s id="s.001061">Quo igitur spatio mobile lentius tempus<emph.end type="italics"></emph.end> RO <lb></lb><figure id="id.028.01.169.1.jpg" xlink:href="028/01/169/1.jpg"></figure><lb></lb><emph type="italics"></emph>totum percurrerit, eodem alterum mobile duplò <lb></lb>velocius tempus<emph.end type="italics"></emph.end> PN <emph type="italics"></emph>etiam abſoluerit. </s> <s id="s.001062">Et quo<lb></lb>niam te iudice alia ratio non est, ſiue tempus<emph.end type="italics"></emph.end><lb></lb>RO, <emph type="italics"></emph>aut<emph.end type="italics"></emph.end> PM <emph type="italics"></emph>à toto tempore<emph.end type="italics"></emph.end> PN <emph type="italics"></emph>ſeiunctum, <lb></lb>ſiue eidem coniunctum ſupponatur: neceſſarium <lb></lb>planè fuerit, vt etiam ab vno, eodemque mobili, <lb></lb>vno eodemque ſpatio totum tempus<emph.end type="italics"></emph.end> PN, <emph type="italics"></emph>& <lb></lb>eius dimidium<emph.end type="italics"></emph.end> PM <emph type="italics"></emph>percurratur, quod certum <lb></lb>eſt eſſe impoßibile, niſi motus fieret in puncto.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001063">Hoc ſanè modo fuiſſes ratiocinatus <emph type="italics"></emph>variatis tan<lb></lb>tum terminis,<emph.end type="italics"></emph.end> ac facere mihi quandam reſpondendi ne<lb></lb>ceſſitatem viſus fuiſſes. </s> <s id="s.001064">Nunc autem, cùm terminos <lb></lb>controuerſos non varies, ac nihil concludas aduerſum <lb></lb>me, ſed illud omninò, atque eodem modo, quod eſt <lb></lb>aduerſus te concluſum: eſt planè cur mirer ſic captare <lb></lb>te ex teipſo triumphum. </s> <s id="s.001065">Nam & cum alioquin ita <lb></lb>habes. </s> </p> <p type="main"> <s id="s.001066"><emph type="italics"></emph>Hæc ratiocinatio, variatis tantum terminis de quibus <lb></lb>controuerſia eſt, tota, vt vides, tua eſt; quam ſi vt legitimam <lb></lb>admittis, tuis ipſe plagis concluſus es: ſin autem reiicis, & ab<lb></lb>ſurdamagnoſcis, non rectè facis, dum nullo modo dißimilem, <lb></lb>tanquam demonſtrationem defendis, & hanc eius loco tibi <lb></lb>repoſitam Paralogiſmum iam eſſe, & non niſi eadem diſtin<lb></lb>ctione diſſoluendum fateri teneris.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="130" xlink:href="028/01/170.jpg"></pb> <p type="main"> <s id="s.001067">Cùm, inquam, ſic habes, perſpicis omninò, quo <lb></lb>iure me dicas iis plagis concluſum, quibus tu potiùs à <lb></lb>me irretitus teipſum implicueris magis: aut-quàm <lb></lb>meritò Paralogiſmum cenſeas, quod ratiocinium priùs <lb></lb>probâris, & nunc tanti putaueris, vt tuum inde ratio<lb></lb>cinum duxeris eſſe confirmandum. </s> <s id="s.001068">Et pergis qui<lb></lb>dem, </s> </p> <p type="main"> <s id="s.001069"><emph type="italics"></emph>Nempe aliud eſt æqualibus ſiue spatiis, ſiue temporibus <lb></lb>æqualia velocitatis augmenta acquiri, eaque eandem inter ſe <lb></lb>rationem ſeruare, quam æqualiaſiue spatia, ſiue tempora ob<lb></lb>ſeruant; & aliud velocitates ipſas integras ſecundum ſe totas, <lb></lb>& ſingulas earum parteis analogas ab initio ad finem totius <lb></lb>motus inter ſe comparatas, in eadem eſſe ratione, quæ inter <lb></lb>æqualia ſiue tempora, ſiue spatia emenſa reperiatur. </s> <s id="s.001070">Pri<lb></lb>mum illud verum eſſe nihil repugnat, at ſecundum istud fal<lb></lb>ſum, & impoßibile est; quod ſi rectè<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus aduertiſſet, <lb></lb>Paralogiſmum nobis pro demonſtratione non obtruſiſſet.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001071">Verumtamen, ne confunde quæſo tempora cum <lb></lb>ſpatiis; cum ais aliud eſſe <emph type="italics"></emph>æqualibus ſiue ſpatiis, ſiue tem<lb></lb>poribus, &c.<emph.end type="italics"></emph.end></s> <s id="s.001072"> Siquidem & facta ratiocinatione nihil <lb></lb>concluſiſti contra tempora, vt te putaſti concludere; <lb></lb>ſed ſolùm contra ſpatia, quatenus à me fuerant impe<lb></lb>tita: & tempora aliunde cum velocitatibus comparata <lb></lb>nullam agnoſcunt diſtinctionem, qualem te putas in<lb></lb>uehere: cùm & totæ velocitates, & ipſarum partes, ſeu <lb></lb>augmenta eandem ſemper proportionem cum tempo<lb></lb>ribus, partibuſque corum analogis ſeruent. </s> <s id="s.001073">Quin<lb></lb>etiam, quod ſpectat ad ſpatia, declaratum iam eſt, <lb></lb>quàm irrito conamine ſic diſtinguas, quatenus de mo<lb></lb>tu non quomodocumque, ſed æquabiliter accelerato <pb pagenum="131" xlink:href="028/01/171.jpg"></pb>agitur; ſtupendumque eſt, te in eo hærere, quòd Gali<lb></lb>leus non aduerterit falſum, ac impoſſibile eſſe, quod <lb></lb>ſecundum ais, hoc eſt, <emph type="italics"></emph>velocitates ipſas integras, &c.<emph.end type="italics"></emph.end> ſi<lb></lb>quidem iſtud eſſe falſum, impoſſibileque non modò <lb></lb>aduertit, ſed etiam oſtendit, quod tu recuſas aduertere, <lb></lb>conſequi ex ea, quam tu ſequeris, opinione. </s> <s id="s.001074">Recuſas, <lb></lb>inquam, & ita habes, quaſi idipſum pro principio vero, <lb></lb>atque neceſſario à ſe credito vſurpauerit; ac interim <lb></lb>fuiſſe ab eo Paralogiſmum obtruſum ais, quem nuilla<lb></lb>tenus oſtendiſti, & profeſſus oſtendere, incidiſti ipſe in <lb></lb>Paralogiſmum. </s> </p> <p type="main"> <s id="s.001075"><emph type="italics"></emph>Sed aliam quoque Propoſitionem, optime<emph.end type="italics"></emph.end> G<emph type="italics"></emph>aſſende, non <lb></lb>minùs falſam, atque impoßibilem numero xi. </s> <s id="s.001076">in fine mihi af<lb></lb>fingis; dum ais me ad vulgatam motus accelerati definitionem <lb></lb>conſequenter loquentem, velle in deſcenſu per totum spatium <lb></lb>AC bifariam diuiſum in B, partem BC tranſcurri<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.171.1.jpg" xlink:href="028/01/171/1.jpg"></figure><lb></lb><emph type="italics"></emph>in dimidio eius temporis, quo percurritur AB; ex <lb></lb>qua falſa ſuppoſitione, ſequenti numero vnum In<lb></lb>commodum, & ad finem Responſionis tuæ alia plura <lb></lb>longè abſurdißima deducis, quæ tanquam conſectaria <lb></lb>ex meis principiis, ac decretis neceſſariò illata mihi <lb></lb>obiectas.<emph.end type="italics"></emph.end> V<emph type="italics"></emph>team igitur Propoſitionem ſemel tracte<lb></lb>mus, eius examen in commodiorem locum reſerua<lb></lb>bimus.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001077">Cùm tu Caput magni momenti perſtringas adeò <lb></lb>obiter; non poſſum ego non ſaltem duo, aut tria quæ<lb></lb>dam adnotare. </s> <s id="s.001078">Quî enim Imprimis intactum præ<lb></lb>teream, quod <emph type="italics"></emph>me affingere tibi<emph.end type="italics"></emph.end> ais <emph type="italics"></emph>Propoſitionem falſam; <lb></lb>ac impoſßibilem, dum aio te ad vulgatam motus definitionem <lb></lb>conſequenter loquentem, velle in deſcenſu per totum ſpatium<emph.end type="italics"></emph.end><pb pagenum="132" xlink:href="028/01/172.jpg"></pb><emph type="italics"></emph>A<emph.end type="italics"></emph.end>C, <emph type="italics"></emph>bifariam diuiſum in B, partem BC tranſcurri in <lb></lb>dimidio eius temporis, quo percurritur AB?<emph.end type="italics"></emph.end> Etenim, quæ<lb></lb>ſo tuam fidem, an tua, an alterius fuerint, quæ ſunt iam <lb></lb>ſuperiùs verba recitata? </s> <s id="s.001079">Suſceperas ipſe oſtendendum <lb></lb>in illa Galilei Aſſumptione Paralogiſmum, & præmi<lb></lb>ſeras, <emph type="italics"></emph>non vno modo tantum, ſed pluribus intelligi poſſe, <lb></lb>quomodo velocitates ſint inter ſe, vt emenſa spatia; licet <lb></lb>eadem spatia, neque eodem, neque æquali tempore percur<lb></lb>rantur:<emph.end type="italics"></emph.end> ac tum deligens modum vnum, qui præ cæte<lb></lb>ris id præſtaret, atque idcircò Aſſumptionem Paralo<lb></lb>giſmi conuinceret, iſthæc met ſubieciſti verba, <emph type="italics"></emph>Vt ſi <lb></lb>graue deſcendens per AB, tempus quodcumque inſumat, putà <lb></lb>quadrantem; ac deinde BC ipſi AB æquale dimidio qua<lb></lb>drante percurrat; quis neget in<emph.end type="italics"></emph.end> C <emph type="italics"></emph>duplam haberi velocita<lb></lb>tem eius, quæ fuit in B? </s> <s id="s.001080">Et tamen idem graue totam AC, <lb></lb>& dimidium eius AB eodem tempore non percurreret.<emph.end type="italics"></emph.end><lb></lb>Subinde autem quaſi re abſolutè cófecta proſequutus <lb></lb>es, <emph type="italics"></emph>Aſſumptio igitur Galilei falſa eſt, & totæ eius ratiocinatio <lb></lb>merus Paralogiſmus.<emph.end type="italics"></emph.end></s> <s id="s.001081"> Quæſo ergo te, quid tibi affinxi? <lb></lb></s> <s id="s.001082">Agnoſcis tua verba, an non? <emph type="italics"></emph>Propoſitionem,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>fal<lb></lb>ſam, ac impoßibilem?<emph.end type="italics"></emph.end> Eſto verò, illam iam falſam, ac <lb></lb>impoſſibilem agnoſeas; at tunc ſaltem veram, atque <lb></lb>neceſſariam habuiſti, cùm illa ſola vſus fueris ad oſten<lb></lb>dendum Paralogiſmum. </s> <s id="s.001083">Nam ſi falſam quidem tunc <lb></lb>quoque, ac impoſſibilem habuiſti, quomodo probaſti <lb></lb>id, quod intendiſti? </s> <s id="s.001084">Et, ſi ſenſiſti poſſe eam tibi, tan<lb></lb>quam falſam, ac impoſſibilem negari, quanam proui<lb></lb>dentia ipſam communiiſti? </s> <s id="s.001085">An oſtenſurus Paralogiſ<lb></lb>mum, voluiſti ſponte te exhibere paralogiſtam ridi<lb></lb>culum, vt puta non alio principio, quam falſo, atque <pb pagenum="133" xlink:href="028/01/173.jpg"></pb>impoſſibili vtens, & quo pernegato, nudus, ac iner<lb></lb>mis, cùm te tamen tantopere oſtentaſſes, reperireris? <lb></lb>Sed qualemcumque habueris: ſaltem ego ſum bona fi<lb></lb>de vſus, neque affinxi quicquam tibi; cùm non aliam <lb></lb>tibi Propoſitionem tribuerim, niſi, quam tu ipſe pro <lb></lb>principio ad conuincendum Galileum vſurpaueris, <lb></lb>quamque iam etiam falſam, impoſſibilemque dicere <lb></lb>non poſſis, quin arguas te nihil confeciſſe, ſed ope<lb></lb>ram planè luſiſſe, in Galileum cùm inſultaſti: ac per<lb></lb>peram fuiſſe gloriatum its verbis, <emph type="italics"></emph>Aſſumptio igitur Ga<lb></lb>lilei falſa eſt, & tota eius ratiocinatio merus Paralogiſmus.<emph.end type="italics"></emph.end><lb></lb> An dices Propoſitionem fuiſſe conditionalem? </s> <s id="s.001086">Si di<lb></lb>cas, eadem eſt ruina. </s> <s id="s.001087">Siquidem facta conditionis ap<lb></lb>poſitione, ſuppoſitio aut vera tibi, ac neceſſaria, aut <lb></lb>falſa, ac impoſſibilis fuit. </s> <s id="s.001088">Si prius, vides contradictio<lb></lb>nem, qua falſam iam, ac impoſſibilem agnoſcis; ſi po<lb></lb>ſteriùs, vides ludibrium, cui te fuiſti expoſiturus. </s> <s id="s.001089">An <lb></lb>dices te poſteà cenſuiſſe difficile determinatu eſſe, <lb></lb>quod tempus per primam, quod per ſecundam deſ<lb></lb>cenſus partem inſumatur; ac ideò cœniſſe compara<lb></lb>tionem non ab vſque initio, ſed ab ipſo ſolùm me<lb></lb>dio primæ partis? </s> <s id="s.001090">Si dicas, declaras te quidem ſubdu<lb></lb>bitaſſe poſtmodùm, an hoc fortè principium non eſſet <lb></lb>verum, neceſſariumque: ſed concedendum eſt inte<lb></lb>rim, te, cùm ipſum heic vſurpaſti, aut non habuiſſe ip<lb></lb>ſum falſum, ac impoſſibile; aut vltrò voluiffe exhibere <lb></lb>te Sophiſten planè exſibilandum: quod abſit tamen vt <lb></lb>cenſeam. </s> <s id="s.001091">Vtcumque ſit, ſaltem ego nihil affinxi. </s> <s id="s.001092">De<lb></lb>inde, quod dixerim <emph type="italics"></emph>te fuiſſe conſequenter ad definitionem <lb></lb>vulgarem loquutum,<emph.end type="italics"></emph.end> nihil ſanè; affinxi; cùm neceſſe <pb pagenum="134" xlink:href="028/01/174.jpg"></pb>omninò ſit, v<gap></gap> velocitatibus, ac ſpati<gap></gap>s eadem ſe ratio<lb></lb>ne habentibus, vbicumque aſſumpto æquali ſpatio <lb></lb>v<gap></gap>itas <gap></gap>ſt dupla, ibi ſit præc sè temporis dimidium; <lb></lb>& plan<gap></gap> proinde ſequatur, vt aſſumpta linea BC æqua<lb></lb><gap></gap>pſi A<gap></gap> cum velocitate decurſus dupla, ſi AB qui<lb></lb>dem depu<gap></gap> certo tempore, vt quadrante horæ, ipſa <lb></lb>BC percurratur octante, ſeu dimidio quadrantis. </s> <s id="s.001093">Po<lb></lb>ſtremò, quod conqueteris <emph type="italics"></emph>me ex hac falſa ſuppoſitione <lb></lb>deducere numero ſequente vnum Incommodum<emph.end type="italics"></emph.end> (vt putà da<lb></lb>to tempore, quo decurſa ſemel fuerit pars AB, tempus <lb></lb>aliud ipſi æquale attingi nulla ratione poſſe, niſi ſu<lb></lb>perato ſpatio infinito) <emph type="italics"></emph>ac deinde ad finem Responſionis alia <lb></lb>plura longè abſurdißima, quæ tanquam conſectaria ex tuis <lb></lb>principiis, ac decretis neceſſariò illata tibi obiectem:<emph.end type="italics"></emph.end> verum <lb></lb>quidem eſt; ſed neſcio quamobrem tanti momenti <lb></lb>Incommodum cenſueris ita præteruolandum, præter<lb></lb>labendo ſcilicet, prætextu retractandi ipſum, ſeu attin<lb></lb>gendi vel deuiter, ob examen propoſitionis reſerua<lb></lb>tum in commodiorem locum. </s> <s id="s.001094">Sed vtcumque ſit, re<lb></lb>putare: non potes, abunde eſſe, quòd propoſitionem, <lb></lb>ex qua illud deducitur, falſam iam, ac impoſſibilem <lb></lb>habeas; cùm & obſtent quæ mox obieci de impugna<lb></lb>to Paralogiſmo, & comperiaris non ſatisfeciſſe, cùm <lb></lb>idem Incommodum iteratò obieci articulo xlij. </s> <s id="s.001095"></s> <s id="s.001096">tan<lb></lb>quam conſequens ex tuo decreto cum hac propoſi<lb></lb>tione congruo, de ſpatiis emenſis, temporibus æqua<lb></lb>libus, in ratione continuò dupla. </s> </p> <p type="main"> <s id="s.001097">Priuſquam hæc de Paralogiſmo, quem Galileo ob<lb></lb>ieciſti, dimittam, meminiſſe iuuat obieciſſe me tibi arti<lb></lb>culis XXXVI, & XXXVIII. fuiſſe te non ſecus ratiocina-<pb pagenum="135" xlink:href="028/01/175.jpg"></pb>tum, quàm Galileum: atque idcircò ſi ille quidem Pa<lb></lb>ralogiſmum admiſerit, incidiſſe te, recidiſſeque <lb></lb><figure id="id.028.01.175.1.jpg" xlink:href="028/01/175/1.jpg"></figure><lb></lb>in cundem: ac oſtendere vel ex ea ſola ratiocina<lb></lb>tione tua, quæ relata eſt articulo XXXIII. quemad<lb></lb>modum ex tuis principiis demonſtrare liceat, <emph type="italics"></emph>ſi <lb></lb>velocitates ſicut ſpatia ſint,<emph.end type="italics"></emph.end> fore <emph type="italics"></emph>vt totum, & pars <lb></lb>eodem, aut æquali tempore percurrantur.<emph.end type="italics"></emph.end> Aſſumptâ <lb></lb>ergo, quæ illeic, lineâ, ideò probas <emph type="italics"></emph>ſpatium<emph.end type="italics"></emph.end> DE, <lb></lb><emph type="italics"></emph>eodem tempore tranſcurri, quo<emph.end type="italics"></emph.end> SD; quia <emph type="italics"></emph>cùm<emph.end type="italics"></emph.end> AD <lb></lb><emph type="italics"></emph>dupla ſit ipſius<emph.end type="italics"></emph.end> AS, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> AE <emph type="italics"></emph>ipſius<emph.end type="italics"></emph.end> AD, <emph type="italics"></emph>neceſſe ſit ve<lb></lb>locitatem in<emph.end type="italics"></emph.end> D <emph type="italics"></emph>duplam eſſe velocitatis in<emph.end type="italics"></emph.end> S, <emph type="italics"></emph>& veloci<lb></lb>tatem in<emph.end type="italics"></emph.end> E <emph type="italics"></emph>velocitatis in<emph.end type="italics"></emph.end> D. </s> <s id="s.001098">Cùm & aliunde, <emph type="italics"></emph>velo<lb></lb>citas per totam<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>dupla ſit velocitatis per totam<emph.end type="italics"></emph.end><lb></lb>SD; quatenus <emph type="italics"></emph>quodlibet ſpatium incœptum ab<emph.end type="italics"></emph.end> A, <lb></lb><emph type="italics"></emph>& terminatum inter<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>duplum eſt alterius <lb></lb>ſpatii, quod ſit item incœptum ab<emph.end type="italics"></emph.end> A, <emph type="italics"></emph>& terminatum <lb></lb>inter<emph.end type="italics"></emph.end> S, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> D; Dico aut te inde nihil conclude<lb></lb>re, aut ſic licere argumentari. </s> </p> <p type="main"> <s id="s.001099"><emph type="italics"></emph>Si<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> SD, <emph type="italics"></emph>eodem tempore percurruntur, quia veloci<lb></lb>tas à<emph.end type="italics"></emph.end> D <emph type="italics"></emph>in<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>dupla eſt velocitatis ab<emph.end type="italics"></emph.end> S <emph type="italics"></emph>in<emph.end type="italics"></emph.end> D. </s> </p> <p type="main"> <s id="s.001100">Igitur, <emph type="italics"></emph>AD, & A<emph.end type="italics"></emph.end>S, <emph type="italics"></emph>eodem tempore percurrentur, quia <lb></lb>velocitas, ab A in D dupla eſt velocitatis ab A in<emph.end type="italics"></emph.end> S. </s> </p> <p type="main"> <s id="s.001101">Et ſimiliter, <emph type="italics"></emph>AE, & AD eodem tempore percurrentur; <lb></lb>quia velocitas ab<emph.end type="italics"></emph.end> A <emph type="italics"></emph>in<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>dupla eſt velocitatis ab<emph.end type="italics"></emph.end> A <emph type="italics"></emph>in<emph.end type="italics"></emph.end> D. </s> </p> <p type="main"> <s id="s.001102">Ac rurſus, quia vt velocitas per totam DE dupla <lb></lb>eſt velocitatis per totam SD, ita velocitas per totam <lb></lb>SD debet eſſe dupla velocitatis per totam PS, & ve<lb></lb>locitas per totam PS, velocitatis per aliud vlterius di<lb></lb>midium, acita porrò, quantum licebit ſubdiuidere ad <lb></lb>vſque punctum A, ſicque demum velocitas per totam <pb pagenum="136" xlink:href="028/01/176.jpg"></pb>AE repenetur dupla velocitatis per totam AD, & ve<lb></lb>locitas per totam AD velocitatis per totam AS; Dico <lb></lb>aut te nihil concludere, aut ſic licere ratiocinari. </s> </p> <p type="main"> <s id="s.001103">Si <emph type="italics"></emph>DE, &<emph.end type="italics"></emph.end> SD <emph type="italics"></emph>eodem tempore percurruntur, quia velo<lb></lb>citas per totam<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>dupla eſt velocitatis per totam<emph.end type="italics"></emph.end> SD. </s> </p> <p type="main"> <s id="s.001104">Igitur, <emph type="italics"></emph>AD, &<emph.end type="italics"></emph.end> AS <emph type="italics"></emph>eodem tempore percurrentur, quia <lb></lb>velocitas per totam<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>dupla eſt velocitatis per totam<emph.end type="italics"></emph.end> AS. </s> </p> <p type="main"> <s id="s.001105">Et ſimiliter, AE <emph type="italics"></emph>&<emph.end type="italics"></emph.end> DA <emph type="italics"></emph>eodem tempore percurrentur, <lb></lb>qui velocitas per totam<emph.end type="italics"></emph.end> AE, <emph type="italics"></emph>dupla eſt veloci tatis per to<lb></lb>tam<emph.end type="italics"></emph.end> AD. </s> </p> <p type="main"> <s id="s.001106">Quo, & non aliomodo Galileus, & ego ratiocina<lb></lb>ti ſumus. </s> <s id="s.001107">Adderem concludi eodem planè modo, per<lb></lb>curri AF triplum, AG quadruplum, &c. </s> <s id="s.001108">tempore eo<lb></lb>dem, quo eandem AD; verùm res deductu perfacilis <lb></lb>eſt, iuxta ea quæ pari ratione deducis ſequentibus <lb></lb>articulis; & eſt iam aliunde tempori parcendum. </s> </p> <p type="main"> <s id="s.001109"><emph type="center"></emph>IN ARTICVLOS XIII. XIV. XV. XVI. XVII. XVIII. </s> <s id="s.001110">De <lb></lb>Poſtulato Galilei, Circa motum ſuper æque altis, <lb></lb>non æquè inclinatis planis.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001111"><emph type="italics"></emph>Tranſeo igitur ad numerum xiv. </s> <s id="s.001112">in quo cùm initio, at<lb></lb>que in fine<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei Poſtulatum veriſimile potiùs, quàm aut per <lb></lb>ſe euidens, aut ex euidentibus demonſtratum, cum eodem<emph.end type="italics"></emph.end> G<emph type="italics"></emph>a<lb></lb>lileo agnoſcis, candide omninò facis: ſed id planè ſufficit, vt <lb></lb>cætera quoque, quæ ab eodem Galileo ex illo Poſtulato inferun<lb></lb>tur, veriſimilia tantum, & minimè demonſtrata cenſeantur: <lb></lb>eumque proinde nobis de motu accelerato, non ſcientiam (vt <lb></lb>eam vocat) ſed opinionem tantum tradidiſſe, quod ſolùm con<lb></lb>cludo.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="137" xlink:href="028/01/177.jpg"></pb> <p type="main"> <s id="s.001113">At concludere ſimùl debes, aut in ipſa Scientiæ <lb></lb>voce <expan abbr="hæreſcendũ">hæreſcendum</expan>; aut ſi ipſi non licuit vocem vſurpare, <lb></lb>cùm ſe nouam ſcientiam inuchere profeſſus eſt; licere <lb></lb>adhûc minùs tibi, qui illam Pſeudo-ſcientiam vocans, <lb></lb>profiteris te veram, ac certam in eius locum ſubſti<lb></lb>tuere; quatenus tradita ab illo experimentis innititur, <lb></lb>quæ nullius hactenus falſitatis conuicta ſint; tua iis <lb></lb>ſuffulcitur, quæ conuicta ſint nullius eſſe veritatis. </s> </p> <p type="main"> <s id="s.001114"><emph type="italics"></emph>Quæ verò de Libro Torricellij posteà adiungis (etſi ea non <lb></lb>viderim) partim vera, partim falſa, aut ſaltem incerta eſſe <lb></lb>non dubito. </s> <s id="s.001115">Duas certè eius Propoſitiones primas ego quo<lb></lb>que de globis euidenter demonstro; at quomodo ex prioribus <lb></lb>illis duabus Propoſitionibus poſteriores inferantur, ſatis non <lb></lb>video, niſi<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei principia ſupponantur. </s> <s id="s.001116">Cùm enim globi <lb></lb>pondere æquales<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>&<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.177.1.jpg" xlink:href="028/01/177/1.jpg"></figure><lb></lb>F <emph type="italics"></emph>planis<emph.end type="italics"></emph.end> AC, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> CD <lb></lb>(<emph type="italics"></emph>vel<emph.end type="italics"></emph.end> CB) <emph type="italics"></emph>inſiſtentes, <lb></lb>momenta ad deſcenſum <lb></lb>retineant in reciproca, <lb></lb>& permutata ratione planorum, ob eamque cauſſam momen<lb></lb>ta ipſius<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>ſint ad momenta ipſius<emph.end type="italics"></emph.end> F, <emph type="italics"></emph>vt<emph.end type="italics"></emph.end> CB (<emph type="italics"></emph>ſiue<emph.end type="italics"></emph.end> CD) <emph type="italics"></emph>ad<emph.end type="italics"></emph.end><lb></lb>CA; <emph type="italics"></emph>non apparet vnde euidenter concludi poßit<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>qui pau<lb></lb>cioribus momentis deorſum voluitur, & magis à motu perpen<lb></lb>diculari diſtrahitur, eundem nihilominus gradum velocitatis <lb></lb>acquirere in<emph.end type="italics"></emph.end> A, <emph type="italics"></emph>quem globus<emph.end type="italics"></emph.end> F <emph type="italics"></emph>in<emph.end type="italics"></emph.end> B <emph type="italics"></emph>acquiſierit. </s> <s id="s.001117">Nam quod <lb></lb>ais tarditatem motus spatij longitudine compenſari, conie<lb></lb>ctando quidem aſſeris; at (quod ad Poſtulati per ſe, & ex <lb></lb>terminis minimè euidentis neceſſarium eſſet) nulla id ratione <lb></lb>demonstras.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001118">Quod de Propoſitionibus Torricellij ais, cognoſces <pb pagenum="138" xlink:href="028/01/178.jpg"></pb>id pleniùs, de quo dubitas, vbi legeris earum proba<lb></lb>tiones. </s> <s id="s.001119">Quod autem ais <emph type="italics"></emph>me coniectando, non vlla ratione <lb></lb>demonſtrando tarditatem motus ſpatij longitudine compenſari <lb></lb>dixiſſe:<emph.end type="italics"></emph.end> adiicere debes, nihil fuiſſe neceſſe præter ipſam, <lb></lb>non coniect <expan abbr="irã">iram</expan>, ſed <expan abbr="euidentiã">euidentiam</expan> proponere: cùm te con<lb></lb>tendente <emph type="italics"></emph>globum per plana æque-alta, ſed inæqualiter in<lb></lb>clinata pareis velocitatis gradus in fine decenſus non acquirere;<emph.end type="italics"></emph.end><lb></lb>ac non demonſtrante, ſed dumtaxat notum dicente, <lb></lb><emph type="italics"></emph>tantò minoribus momentis deſcendere globum per planum, <lb></lb>quantò minus accliue fuerit:<emph.end type="italics"></emph.end> excepi, <emph type="italics"></emph>non videre me, quomodo <lb></lb>id concluderes, quatenùs non aſſumeres planum, quantò mi<lb></lb>nùs accliue eſt, tantò eſſe quoque prolixius. </s> <s id="s.001120">Etenim notum <lb></lb>quidem eſſe acquiri minores velocitatis gradus in minùs de<lb></lb>cliui, quod ſit decliutori æquale: at ſi, vt minus decliue, ita <lb></lb>etiam prolixius ſit, notum quoque eſſe velocitatem in fine illius <lb></lb>quæſitam eſſe poſſe æqualem velocitati in fine decliuioris ac<lb></lb>quiſitæ, prolixitate nempe deſcenſus paruitatem incremento<lb></lb>rum velocitatis compenſante Proſequeris.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001121"><emph type="italics"></emph>Multa etiam totis numeris xv. </s> <s id="s.001122">xvi & xvii. </s> <s id="s.001123">adducis, ve <lb></lb>experimentum<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei de<emph.end type="italics"></emph.end> P<emph type="italics"></emph>endulorum vibratione, & ad <lb></lb>æqualem altitudinem aſcenſu defenda<gap></gap>, ſed fateris tamen, quod <lb></lb>contendo, pendula eiuſmodi neque ad eandem, vnde ipſa demiſ<lb></lb>ſa ſunt, altitudinem aſcendere, neque ad æqualem ſemper, ſi <lb></lb>ex punctis ad lineam horizontalem diuerſimodè comparatis, <lb></lb>ſuspendantur; huiuſque etiam rei, ac diuerſitatis cauſſas, at<lb></lb>que impedimenta inquiris, quæ ſi abeſſent, tum eadem pendu<lb></lb>la ad æqualem perpetuò altitudinem præcisè conſcenſura <lb></lb>diuinas, non autem demonſtras.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001124">At beatus ſum ſaltem, ſi non abſque aliqua, & cui <lb></lb>nih lrefragetur, veriſimili ratione, diuinem. </s> </p> <pb pagenum="139" xlink:href="028/01/179.jpg"></pb> <p type="main"> <s id="s.001125"><emph type="italics"></emph>Sed, vt tu ipſe agnoſcis, demonſtrationes quæro, non veriſi<lb></lb>militudines, aut ſuſpiciones.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001126">Tu verò & optimè facis, & beatior me longè es, ſi <lb></lb>demonſtrationes adinuenias, nec ea amplexeris, quæ <lb></lb>apertè falſa cùm ſint, ne veriſimilitudinis quidem, aut <lb></lb>ſuſpicionis nomen mereantur. </s> </p> <p type="main"> <s id="s.001127"><emph type="italics"></emph>Quòd autem in Confirmationem adducis quatuor globos <lb></lb>quatuor distinctis filis ſic appenſos, vt primi longitudo ſit <lb></lb>vnius pedis, ſecundi quatuor, tertij nouem, quarti ſexdecim: <lb></lb>aiſque eos, ſi ex quapiam altitudine ſimul dimittantur, ſuas <lb></lb>inter ſe vibrationes ita componere, vt dum quartus globus <lb></lb>vnam perficiet, tertius duas, ſecundus treis, & primus quatuor <lb></lb>abſoluat. </s> <s id="s.001128">Hæc, inquam, & quæ inde colligis, nec certiora <lb></lb>ſunt, nec exactiùs cum experientia congruunt, quàm ea, qui<lb></lb>bus confirmandis aſſumpta ſunt. </s> <s id="s.001129">Etſi enim in paucis ali<lb></lb>quibus vibrationibus ea ratio vtcúmque obſeruari videatur; <lb></lb>breut tamen interrumpitur, vt ſæpius à me experientia <lb></lb>combrobatum est; cuius etiam rationem indicat, qui noua<emph.end type="italics"></emph.end><lb></lb>G<emph type="italics"></emph>alilei placita Gallicè reddidit lib.<emph.end type="italics"></emph.end> 1. <emph type="italics"></emph>artic.<emph.end type="italics"></emph.end> 17. <emph type="italics"></emph>vbi ipſe quo<lb></lb>que ſe expertum eſſe aſſerit, vibrationes omneis eiuſdem pen<lb></lb>duli æquali tempore perpetuò non abſolui: quod tamen neceſ<lb></lb>ſarium eſſet, vt conſenſus ille vibrationum diutiùs perma<lb></lb>neret.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001130">Illud de Pendulis experimentum ita certum eſt, vt <lb></lb>falſum nunquam deprehenderim, quoties aſſumun<lb></lb>tur, & quandiù manent longitudinum exquiſitè ea<lb></lb>rumdem. </s> <s id="s.001131">Nam quia non ponderis, ſed longitudinis <lb></lb>variatio vibrationum celeritatem, aut tarditatem va<lb></lb>riat, ideò niſi quatuor illa pendula aſſumantur exqui<lb></lb>ſitè longitudinum præſcriptarum, fiet ſenſim, vt quod <pb pagenum="140" xlink:href="028/01/180.jpg"></pb>pendulum ſatis exquiſitè conſonare videbatur cum <lb></lb>cæteris, vibrationum euariet, aut accelerando, ſi vel <lb></lb>tantillum breuius æquo fuerit, aut retardando, ſi tan<lb></lb>tillum prolixius. </s> <s id="s.001132">Et aliunde quia filum, niſi metalli<lb></lb>cum ſit, diducitur ſenſim, prolixiuſque euadit, dum <lb></lb>partim tortum detorquetur, partim pondere pertra<lb></lb>ctum tenuatur; idcircò inde quoque fit, vt niſi cauea<lb></lb>tur, ne fiat variatio, longitudinis, vibrationes, quæ per <lb></lb>initia conſonanter inter ſe fiebant, decreſcant ſenſim, <lb></lb>ac denique diſcrepare deprehendantur. </s> <s id="s.001133">Heinc ſemper <lb></lb>mihi conſtitit, quod pendulum primò diſcrepare acce<lb></lb>lerando animaduerti, fuiſſe aliquantulum æquo bre<lb></lb>uius; quod remorando, aliquantò prolixius: vt pro<lb></lb>inde non mirer & tibi; & authori, <expan abbr="quẽ">quem</expan> citas, deprehen<lb></lb>ſam fuiſſe aliquam vibrationum inconſtantiam, & in<lb></lb>æqualitatem. </s> <s id="s.001134">Cæterùm res ipſa in ſe eſt omninò cer<lb></lb>ta: & vel ex eo, quod deprehendiſti vibrationes ſal<lb></lb>tem peraliquod tempus ita conſonare, vt pendulum <lb></lb>ſexdecim pedum vibrationem ſemel dumtaxat perage<lb></lb>ret, dum pendulum nouem, perageret bis, pendulum <lb></lb>quatuor, ter: pendulum vnius, quater; potuiſti intelli<lb></lb>gere, quàm hæc egregiè congruant cum iis, quibus <lb></lb>confirmandis fuere vſurpata; cum tu interim tale nihil <lb></lb>in tuæ ſententiæ confirmationem profere poſſis. </s> </p> <p type="main"> <s id="s.001135"><emph type="italics"></emph>Opponis numero xviij. </s> <s id="s.001136">non ſatis àme refelli, aut erroris <lb></lb>argui ea experimenta, quibus<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus accelerationem motus <lb></lb>in deſcenſu grauium tam per aërem, quàm per plana quælibet <lb></lb>inclinata confirmat: nihil <gap></gap>ue à me ad luci expostulas, præter <lb></lb>experiundi modum diſſici<gap></gap>em variiſque erroribus o<gap></gap> noxium. <lb></lb></s> <s id="s.001137">Nimirum eo loco id ſolùm efficere volui, vt quilibet intellige-<emph.end type="italics"></emph.end><pb pagenum="141" xlink:href="028/01/181.jpg"></pb><emph type="italics"></emph>ret, minùs mirum videri, ſi Galileus errauerit: cùm non niſi <lb></lb>experimento its erroribus obnoxio vſus fuerit, qui nullâ dili<lb></lb>gentiâ vitaripoſſe videantur. </s> <s id="s.001138">Satis autem eadem illa expe<lb></lb>rimenta erroris poſtmodùm reuincenda videbantur, ſi longé <lb></lb>aliam accelerationis rationem in deſcenſu grauium interuenire <lb></lb>demonſtrarem.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001139">Non repugnaſſem, ſi demonſtraſſes; at demonſtraſ<lb></lb>ſe non conſtitit. </s> </p> <p type="main"> <s id="s.001140"><emph type="center"></emph>IN ARTICVLOS XIX. XX. XXI. XXII. </s> <s id="s.001141">De <lb></lb>Experimentis circaictum; impetum-ve grauium <lb></lb>cadentium; ad explorandum impetuſ-ne, vt <lb></lb>ſpatium increſcat.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001142"><emph type="italics"></emph>Reprehendis item numero xix, quod nulla ſpeciali Expe<lb></lb>rientia confirmem, quod experientià conſtare affirmo, nempe<emph.end type="italics"></emph.end><lb></lb>Corpus graue quodcumque ex qualibet altitudine per <lb></lb>aërem cadens, & percutiens vt libet, perpetuò ex alti<lb></lb>tudine dupla duplò ampliùs, & ex tripla, quadruplave <lb></lb>diſtantia, triplò, quadruploque fortiùs percutere. <lb></lb><emph type="italics"></emph>Nempe vide bam ſatis manifestum eſſe id eodem Experimento <lb></lb>comprobari poſſe, quo idipſum poſtmodum oſtenſurus eram in <lb></lb>globo. </s> <s id="s.001143">Non fuit igitur cum operæ, ac temporis iactura du<lb></lb>plex ingerenda Experientia, vbi pluſquam abundè ſufficere <lb></lb>potuit vnica.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001144">Hactenus de Confirmatione tuæ illius Aſſumptio<lb></lb>nis, quam ſuperiùs retulimus, vbi de Controuerſiæ <lb></lb>Statu. </s> <s id="s.001145">Sequitur videamus quid habeas de impugna<lb></lb>ta Probatione, ad quam ſpectabat Primum membrum <lb></lb>Poſterioris partis Operis totius. </s> <s id="s.001146">Quippe ratus te euer<lb></lb>tiſſe funditus Galilei ſcientiam, ac profeſſus te illi <pb pagenum="142" xlink:href="028/01/182.jpg"></pb>veram, certamque ſubſtituere, ducendum cenſueras <lb></lb>initium ab ipſa Experientia, tanquam à germano eius <lb></lb>fundamento. </s> <s id="s.001147">Quandoquidem porrò his me affatus <lb></lb>verbis fueras, <emph type="italics"></emph>Primùm ego te, optime<emph.end type="italics"></emph.end> G<emph type="italics"></emph>aſſende, ad claras, <lb></lb>facileis, atque indubitatas Experientias prouoco, & in ijs ar<lb></lb>bitrum te, ac iudicem habere vehementer gaudeo. </s> <s id="s.001148">Prima peti<lb></lb>tur ex impetu, quo globus, aut graue aliud corpus quodcumque <lb></lb>per <expan abbr="aẽrem">aerrem</expan> sponte naturæ deorsùm cadit, ac percutit, &c.<emph.end type="italics"></emph.end><lb></lb>Quis heic loci non exſpectaſſet pluſquàm vnicam <expan abbr="Ex-perientiã">Ex<lb></lb>perientiam</expan>? </s> <s id="s.001149">Quis exiſtimaſſet te ex vnica facere primam, <lb></lb>& ſecundam? </s> <s id="s.001150">Quis non credidiſſet à te, niſi omneis, niſi <lb></lb>plurimas, ſaltem plureis vnâ peractas, ob illud, <emph type="italics"></emph>corpus <lb></lb>graue quodcumque?<emph.end type="italics"></emph.end> Certè, cùm ſtatim repetens, <emph type="italics"></emph>conſtare <lb></lb>facilè experientiâ<emph.end type="italics"></emph.end> dixiſſes <emph type="italics"></emph>corpus graue quodcumque ex <lb></lb>qualibet altitudine per <expan abbr="aẽrem">aerrem</expan> cadens, & percutiens, vt libet, <lb></lb>&c.<emph.end type="italics"></emph.end> non ſperare non potui aliquam aliam Experien<lb></lb>tiam, præter vnicam in Bilance factam, in quam glo<lb></lb>bus cadens, & percutiens, neque eſt corpus graue <lb></lb>quodcumque, neque vt-libet cadit, percutitque. </s> <s id="s.001151">Sed<lb></lb>nimirùm tu talem Fxperientiam, tametſi foret vnica, <lb></lb>tanti faciendam eſſe cenſuiſti, vt eſſet inſtar omnium, <lb></lb>ac veritatem ſic demonſtraret, vt facit ver non vna <lb></lb>hirundo. </s> <s id="s.001152">Et, ſi talem quidem ipſam inueniſſem, qua<lb></lb>lem ſperandam feceras, <emph type="italics"></emph>facilem, claram, indubitatam,<emph.end type="italics"></emph.end> ac, <lb></lb>verbo vno vt dicam, <emph type="italics"></emph>veram:<emph.end type="italics"></emph.end> abfuiſſem profectò, vt <lb></lb>aliam te importunè rogitarem; fuiſſet illa enim abun<lb></lb>dè, & ſatis. </s> <s id="s.001153">Nunc autem, cùm eam longè ſecus ſe ha<lb></lb>bere compererim, & tu ipſe non auſis ampliùs, qua<lb></lb>lem priùs diuendere, ſicuti mox videndum eſt; quis <lb></lb>non aliam mecum abs te expetiiſſet? </s> </p> <pb pagenum="143" xlink:href="028/01/183.jpg"></pb> <p type="main"> <s id="s.001154"><emph type="italics"></emph>Quare quæ deinceps numeris xx. </s> <s id="s.001155">xxi. </s> <s id="s.001156">& xxii. </s> <s id="s.001157">adiicis, <lb></lb>fruſtrà ſunt: cùm ex iis etiam vltrò datis, nihil aduerſus inſi<lb></lb>nuatam à nobis Experientiam, aut omninò contra nos (ob <lb></lb>Exemplorum, quibus vteris, dißimilitudinem) concludas.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001158"><emph type="italics"></emph>Fruſtrà ſunt,<emph.end type="italics"></emph.end> in quis; ſed nimirùm, quia quod repo<lb></lb>neres, non fuit, & prætextu Exemplorum, quæ articulis <lb></lb>XXI, & XXII. habentur, diſſimulare viſum eſt, quæ op<lb></lb>poſui XX. circa varia Experimenta. </s> <s id="s.001159">Siquidem illa in eo <lb></lb>recenſui, quæ tu videbaris potuiſſe præſertim intelli<lb></lb>gere, cùm diceres <emph type="italics"></emph>rem Experientiâ facilè conſtare in graui <lb></lb>quocumque;<emph.end type="italics"></emph.end> ac oſtendi ipſa non eſſe, qualia tu dicebas, <lb></lb><emph type="italics"></emph>facilia, clara, indubitata;<emph.end type="italics"></emph.end> teque ideò ſollicitaui, vt decla<lb></lb>rares quemadmodum conſtaret tibi grauia ex altitu<lb></lb>dine dupla decidentia impetus eſſe duplò maioris, tri<lb></lb>plò ex tripla, &c. </s> <s id="s.001160">Tu verò, cùm quid reſponderes (aut <lb></lb>dic ſaltem, quomodo poſſim id interpretari) non ſup<lb></lb>peteret, factum ſatis eſſe putaſti, ſi ea diceres <emph type="italics"></emph>eſſe fruſtrà.<emph.end type="italics"></emph.end><lb></lb>Sed fruſtrà fuerint, quatenus ex te fruſtrà requiſiui quæ <lb></lb>laterent te; at non fuere fruſtrà, vt oſtenderem, te non <lb></lb>debuiſſe id, quod in te minimè eſſet, oſtentare. </s> <s id="s.001161">Certè <lb></lb>enim iam non potuiſti illud, quod mox, prætexere, <lb></lb><emph type="italics"></emph>non eſſe tibi operæ, temporiſque faciendam iacturam;<emph.end type="italics"></emph.end> cùm <lb></lb>excitatæ difficultates <expan abbr="manifeſtũ">manifeſtum</expan> fecerint, quàm vtiliter <lb></lb>operam, tempuſque in iis impendiſſes. </s> <s id="s.001162">Quanquam & <lb></lb>nulla vnquam poteſtin rebus huiuſcemodi diligentia <lb></lb>eſſe ſuperflua; ipſeque teſtor fuiſſe te, quod ſpectat ad <lb></lb>me, ampliùs præſtiturum paucis quibuſdam verſibus <lb></lb>explicantibus vnicum, de quo conſtaret, Experimen<lb></lb>tum; quàm opere toto, totiſque ratiociniis; ac in eo <lb></lb>ſum ſemper, vt ſi vel deinceps proferre poſſis vnicum, <pb pagenum="144" xlink:href="028/01/184.jpg"></pb>manus vltrò dem, & totum quicquid conſcripſero, <lb></lb>deuoueam, flammiſque addicam. </s> <s id="s.001163">Quippe fiuſtrà ſint <lb></lb>mille ratiocinia, ſi vel vnicum refragetur Experimen<lb></lb>tum; vt fruſtra ſomniemus monteis aureos, qui abeant <lb></lb>ſtatim vel minima expergefactione in fumum. </s> <s id="s.001164">Quod <lb></lb>ad ea ſpectat, quæ habeo ſequentibus articulis, tu <lb></lb>Exempla dicis, vt poſſis diſſimilitudinem cauſſari; cùm <lb></lb>Experimenta ſint, quæ ad rem attineant, ac ſupparia <lb></lb>ſaltem ſint iis, quibus controuerſia dirimenda videa<lb></lb>tur. </s> </p> <p type="main"> <s id="s.001165">Nam, ne <expan abbr="hæreã">hæream</expan> in ſingulis, & <expan abbr="dicã">dicam</expan> ſaltem quidpiam <lb></lb>de Primo; <expan abbr="Notũ">Notum</expan> eſt, ſi vaſe cylindrico oppleto, integra <lb></lb>momento ſubducatur baſis, totum aquæ contentæ cy<lb></lb>lindrum ſtatim effluxurum, eo modo, quo ſtatim elabe<lb></lb>retur cylindrus marmoreus, aut quiuis alius ſolidus, ſi <lb></lb>eodem vaſe contineretur. </s> <s id="s.001166">Vt autem in cylindro mar<lb></lb>moreo cadente non velociùs deſcendit pars ſuprema, <lb></lb>quàm infima, aut intermedia quælibet, quòd omnes <lb></lb>ex æquo ferantur deorſum, & par conficiant ſpatium, <lb></lb>pariterque accelerentur; ita concipimus in aqueo non <lb></lb>velociùs deſcendere partem ſupremam, quàm infi<lb></lb>mam, aut quamlibet mediam, ſed parem eſſe omnium <lb></lb>deſcenſum, omniumque accelerationem; atque id<lb></lb>circò perinde eſſe ſupremæ parti aquæ, ſiue aqua ſub<lb></lb>ſit, ſiue nulla ſit: quatenus quæ ſubeſt, tantum præce<lb></lb>dendo aufugit, quantum ipſa poteſt conſequendo in<lb></lb>ſtare: ac fieri proinde, vt ſuprema aqua ad baſin dela<lb></lb>bens, tanto deſcendat tempore, quanto ſi ex eadem <lb></lb>altitudine per aërem delaberetur. </s> <s id="s.001167">Iam, cùm exiguum <lb></lb>folùm foramen ad ipſam baſin aperitur, idem propor-<pb pagenum="145" xlink:href="028/01/185.jpg"></pb>tione contingit. </s> <s id="s.001168">Nam ſiſolus quidem eſſet cylindiulus <lb></lb>aquæ reſpondens ipſi foramini, manifeſtum eſt ipſum <lb></lb>perinde effluxurum, ac totum cylindrum baſi tota <lb></lb>aperta. </s> <s id="s.001169">Quoniam verò talis cylindrulus copioſiore <lb></lb>aqua ambitur, non ideò quidem minùs effluit, ſed <lb></lb>efficitur, vt dum pars ſuprema antecedenteis conſequi<lb></lb>tur, circumſtantes aquæ ſupremæ partes in ipſius lo<lb></lb>cum propter fluxilitatem ſubeant, ac pari modo, con<lb></lb>tinente<gap></gap>que ſequantur, deſcendant, ac effluant; aliis <lb></lb>nimirum, aliiſque indeſinenter ſubſtitutis, ab ipſa vſque <lb></lb>ſuperficie, quæ idcircò ſemper complanata appareat, <lb></lb>quovſque ſub effluxus finem excauetur, dum quæ ſu<lb></lb>pereſt aqua parcior eſt, quàm vt perinde facilè, abun<lb></lb>deque confluere poſſit. </s> <s id="s.001170">Itáque etiam foramine aper<lb></lb>to, aqua ſumma in locum baſeos, ipſumve foramen <lb></lb>tanta velocitate cadit, quanta per aërem caderet; ac <lb></lb>licet proinde de eiusimpetu ex effluxu non ſecus iudi<lb></lb>care, quàm ex ipſo caſu; vt pote cùm effluendo cadat, <lb></lb>& cadendo effluat; ac pari ſemper tempore ex ſummo <lb></lb>ad imum perueniat. </s> <s id="s.001171">Vide igitur an Exemplum diſſi<lb></lb>mile ſit, & non potiùs Experimentum (ſuppar mini<lb></lb>mùm) illiuſmet rei, de qua agitur: & quia quæritur, an <lb></lb>impetus exprimatur duplex ex altitudine dupla, an ex <lb></lb>quadrupla, iſtud verò experimentum (ſeu exemplum <lb></lb>mavis) duplum probat ex altitudine quadrupla, non <lb></lb>dupla; agnoſce quo iure dicas quæ habentur memo<lb></lb>ratis articulis <emph type="italics"></emph>fruſtra eſſe, ac iis etiam vltrò datis, nihil me <lb></lb>aduerſus inſinuatam à te experientiam, aut omninò contra <lb></lb>te, ob exemplorum, quibus vtor, dißimilitudinem concludere.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="146" xlink:href="028/01/186.jpg"></pb> <p type="main"> <s id="s.001172"><emph type="center"></emph>IN ARTICVLOS XXIII. XXIV. XXV. XXVI. XXVII. <lb></lb>XXVIII. </s> <s id="s.001173">De Experimento in Bilance facto, ac <lb></lb>aliud reuerâ probante, quàm velocitates <lb></lb>eſſe ſicut ſpatia.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001174"><emph type="italics"></emph>At numero xxiii, & quatuor ſequentibus Controuerſiæ <lb></lb>caput attingis, cùm Experientiam de globo per aërem deciden<lb></lb>te examinas. </s> <s id="s.001175">Jngenuè enim fatendum eſt, in mentem mibi <lb></lb>nunquam incidiſſe, vt inquirerem, an globus ex vnius dia<lb></lb>metri altitudine decidens, poſſet vltra æquilibrium, & pondus <lb></lb>ſibi æquale ampliùs aliquid attollere.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001176">Commendanda ſanè ingenua confeſſio (quan<lb></lb>quam addendum fuiſſe videtur, <emph type="italics"></emph>non incidiſſe tibi in <lb></lb>mentem, vt inquireres,<emph.end type="italics"></emph.end> non modò, <emph type="italics"></emph>an globus ex vnius dia<lb></lb>metri altitudine decidens, poſſet vltra æquilibrium, & pondus <lb></lb>ſibi æquale, ampliùs aliquid attollere:<emph.end type="italics"></emph.end> ſed etiam, <emph type="italics"></emph>an globus <lb></lb>idem æquilibrium, & pondus ſibi æquale ex dimidio, quadran<lb></lb>te, octante, & penè dicam ex vncia altitudinis ſuæ diametr<gap></gap><lb></lb>attolleret;<emph.end type="italics"></emph.end> cùm præciſio ſit inter plus, & minus, & ipſe <lb></lb>in vtramque partem aberrâris tantopere) Commen<lb></lb>dandumid, inquam; ſed cùm iſtud ſit, vt præclarè ais, <lb></lb><emph type="italics"></emph>Controuerſiæ caput,<emph.end type="italics"></emph.end> quatenus hoc vnum Experimentum <lb></lb>fuit, quo res controuerſa determinaretur, <expan abbr="cõprobare-turque">comprobare<lb></lb>turque</expan> à te: patere me duo quædam ſubmirari. </s> <s id="s.001177">Vnum, <lb></lb>cur adeò ſolemniter prouocaſſes me <emph type="italics"></emph>ad facileis, claras, <lb></lb>indubitatas Experientias,<emph.end type="italics"></emph.end> quæ controuerſiæ caput face<lb></lb>rent, ac Demonſtrationem tuam, ſcientiamque totam <lb></lb>conſtabilirent: cùm ecce habens vnicam, videri iis <lb></lb>poſſes, qui rerum amantes verbis non capiuntur, ita <lb></lb>oſcitanter illam peregiſſe, vt nihil eſſet minùs, quàm <pb pagenum="147" xlink:href="028/01/187.jpg"></pb>quod diceretur. </s> <s id="s.001178">Profectò niſi vſus fuiſſes voce <emph type="italics"></emph>Præ<lb></lb>ciſionis,<emph.end type="italics"></emph.end> aliiſque conſimilibus, videri dumtaxat potuiſ<lb></lb>ſes opinione præoccupatus, ac præ illius a more, voluiſ<lb></lb>ſe non opinionem experientiæ, ſed experientiam <lb></lb>opinioni accom modare: Nunc autem non video, cur <lb></lb>tot paginis, tantoque apparatu inſtiteris (etiam tot <lb></lb>cautiones adhibendas iis, qui rem experiri ſcrupulo<lb></lb>ſiùs vellent, præſcribens) vt te expertum crederemus, <lb></lb><emph type="italics"></emph>naturam illud in globo peculiare ac proprium eſſe voluiſſe, <lb></lb>vt eius diameter præciſa eſſet menſura illius altitudinis, ex <lb></lb>qua, &c.<emph.end type="italics"></emph.end> ac iterùm, <emph type="italics"></emph>hanc eſſe inter globos, & alias figu<lb></lb>ras differentiam, quòd in globis diameter altitudines præcis è <lb></lb>definiat, vnde pondus, &c.<emph.end type="italics"></emph.end></s> <s id="s.001179"> Alterum, cur huiuſimodi Ex<lb></lb>perimento deprehenſo falſo; hoc eſt, cùm verùm iam <lb></lb>non ſit, vt contenderas, <emph type="italics"></emph>conſtare Experientiâ corpus graue <lb></lb>quodcumque ex qualibet altitudine per aërem cadens, & <lb></lb>percutiens vt libet, perpetuò ex altitudine dupla dupla præcisè <lb></lb>ampliùs, & ex tripla, quadruplave diſtantia, triplò, qua<lb></lb>druplove fortiùs percutere;<emph.end type="italics"></emph.end> cur, inquam, pergas etiam<lb></lb>num eam Ratiocinationem habere, imò & acriter <lb></lb>tueri pro Phyſica Demonſtratione, quam non alij <lb></lb>fundamento, quàm huic vnico Experimento ſuper<lb></lb>exſtruxeris? </s> <s id="s.001180">Hoc ſanè eſt, quod mihi videtur faten<lb></lb>dum ſimùl ingenuè fuiſſe, ac parcendum ſimùl labo<lb></lb>ri, quo æque te exerceres, ac me, quemque declinare <lb></lb>potucras, ſi neque meam Reſponſionem, neque tuas <lb></lb>Vindicias eſſe cuulgandas cenſuiſſes; cùm alioquin <lb></lb>iam deſtitutus omni argumento, quo Demonſtra<lb></lb>tionem ſuffulcias, ludere videaris omnem operam, dum <lb></lb>operosè adeò in ea propugnanda deſudas. </s> </p> <pb pagenum="148" xlink:href="028/01/188.jpg"></pb> <p type="main"> <s id="s.001181"><emph type="italics"></emph>In quo tu quidem fœlicior fuiſti; ſed vereor non pa<lb></lb>rùm, ne accuratior illa tua experientia neutiquam tuæ parti <lb></lb>ſuffragetur; quamuis dicas com nodè ad<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei mentem <lb></lb>accidiſſe, vt globus non-niſi ex quatuor diametrorum altitu<lb></lb>dine decidens attollere potuerit duplum eius ponderis, quod ex <lb></lb>vnius diametri eleuatione ſummum extulerat; ſicut nec tri<lb></lb>plum, niſi ex altitudine diametrorum nouem, &c. </s> <s id="s.001182">Ego enim <lb></lb>tuo exemplo inductus, cùm idem tentare item voluerim; ne<lb></lb>que globum ex vnius diametri altitudine, ſuum pondus toties <lb></lb>multiplicatum attollere comperi; neque ad duplicatum, tri<lb></lb>plicatumque pondus eleuandum, ad tantam altitudinem attolli <lb></lb>debuiſſe. </s> <s id="s.001183">Vſus ſum quidem bilance obuia, & fortaßis non ita <lb></lb>exacta, & globo Porphyretico vnciæ<emph.end type="italics"></emph.end> 1, <emph type="italics"></emph>drachm<emph.end type="italics"></emph.end> 2 <emph type="italics"></emph>ſatis exactè. <lb></lb></s> <s id="s.001184">Reperi autem hunc globum repetita aliquoties operatione ex <lb></lb>vnius diametri altitudine eleuare ſolùm vncias<emph.end type="italics"></emph.end> 5, <emph type="italics"></emph>dr.<emph.end type="italics"></emph.end> 2 <emph type="italics"></emph>(neſcio <lb></lb>an vitio bilancis acciderit, vt maius pondus non extulerit) at <lb></lb>idem globus duplum illius ponderis, ex diametris tribus, tri<lb></lb>plum ex quinque, quadruplum ex ſeptem, quintuplum ex <lb></lb>nouem ſustulit; interruptus autem nihil vlteriùs tentare po<lb></lb>tui. </s> <s id="s.001185">Ex his autem adhûc vides (quod totius controuerſiæ ca<lb></lb>put eſt) æqualibus spatiis æqualia acquiri velocitatis aug<lb></lb>menta. </s> <s id="s.001186">Hanc ego tamen operationem tibi tanquam exactam <lb></lb>non propono, quia necdum mihi per otium licuit eam adhi<lb></lb>bere diligentiam, quamres huius momenti pro ſuo merito po<lb></lb>ſtulat: ſed vt te quoque ad exactam illius rei experientiam <lb></lb>inuitem; ex qua tota de motu accelerato controuerſia diri<lb></lb>menda videatur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001187">Poſtrema hæc verba, quàm eſſent te digna; niſi <lb></lb>aliunde Demonſtrationem, quod mox obiiciebam, ita <lb></lb>propugnares, acſi foret iam controuerſia à te dirempta<gap></gap><pb pagenum="149" xlink:href="028/01/189.jpg"></pb>Et quod inuitas quidem me ad experiundum iterùm; <lb></lb>ſcito me iterum expertum, ac adhibitos mihi fuiſſe ad<lb></lb>iutores inſigni peritia, & in experiundo ſedulitate, ac <lb></lb>diligentia claros Petrum Petitum, & Danielem <lb></lb>Auberium Maurerium; ac nihil tamen vnquam mihi, <lb></lb>quale tu narras, contigiſſe. </s> <s id="s.001188">Nam vſurpatis globis <lb></lb>duobus altero plumbeo vnius vnciæ, altero ligneo <lb></lb>drachmæ vnius cum triente, fuit ſemper eadem proxi<lb></lb>mè ratio, quam in Reſponſione iam deſcripſi, exhibita; <lb></lb>& cùm aberratum ab ea ſenſibiliùs eſt, ecce quid <expan abbr="adhũc">adhunc</expan> <lb></lb><expan abbr="præſtitũ">præſtitum</expan> fuerit iis numeris, quos ipſe habes. </s> <s id="s.001189">Plumbeus, <lb></lb>cùm ex diametro vna extuliſſet vncias 7, dr. </s> <s id="s.001190">1: extu<lb></lb>lit deinceps ex tribus 11, 3: ex quinque 14, 2: ex ſeptem <lb></lb>16, 3: ex nouem 17, 6: cùm iuxta tuam obſeruationem <lb></lb>efferre debuiſſet ex tribus 14, 2: ex quinque 21, 3: ex <lb></lb>ſeptem 28, 4: ex nouem 35. 5. Ligneus, <expan abbr="cũ">cum</expan> ex diametro <lb></lb>vna extuliſſet drachmas quindecim, extulit deinceps <lb></lb>ex tribus 24, ex quinque 30, ex ſeptem 36, ex <lb></lb>nouem 41: Cùm debuiſſet per te efferre ex tribus 30, <lb></lb>ex quinque 45, ex ſeptem 60: ex nouem 75. Immane <lb></lb>quanto diſcrimine! Et non cauſſor quidem proptereà <lb></lb>cuam fidem; ſed eſt cur demirer profitentem te <emph type="italics"></emph>veram, <lb></lb>ac certam ſcientiam<emph.end type="italics"></emph.end> in hac Experientia, vt <emph type="italics"></emph>clara, facili, <lb></lb>indubia<emph.end type="italics"></emph.end> fundatam, ſic iam hærere, quaſi priùs expertus <lb></lb>nihil fueris; ac non auſis hanc operationem, tanquam <lb></lb>certam proponere, partim Bilancis incuſans vitium, <lb></lb>quæ exacta fortè non fuerit, partim quampiam occu<lb></lb>pationem, quæ te obſeruantem interruperit. </s> <s id="s.001191">Profe<lb></lb>ctò enim Tu, ſi quis alius, certus eſſe huius rei debuiſti; <lb></lb>vt qui non modò fueris profeſſus te certam de ipſa <pb pagenum="150" xlink:href="028/01/190.jpg"></pb>ſcientiam tradere; ſed etiam iam ſcientiæ, ſeu Demon<lb></lb>ſtrationis, qua feceris certam, Vindicias conſcribas. <lb></lb></s> <s id="s.001192">Non moror item, quòd poſtquàm mihi fœlicitati cui<lb></lb>piam vertiſti, <emph type="italics"></emph>incidiſſe mihi in mentem vt quidpiam, quod <lb></lb>tu non inq<gap></gap>iſi ſſes, inquirerem<emph.end type="italics"></emph.end> (vtcumque ea videri poſſit <lb></lb>non tam fuiſſe fœlicitas, quàm non-nihil maior circa <lb></lb>rem non raram, neque inexſpectatam atter<gap></gap>tio) non <lb></lb>moror, inquam, quòd temperâris aduerſatiuâ, <emph type="italics"></emph>ſed ve<lb></lb>reor:<emph.end type="italics"></emph.end> quippe cùm fauente mihi Experientia ſponſorem <lb></lb>me dem, non eſſe quamobrem de me, deque Galileo <lb></lb>verearis, quatenus dixi <emph type="italics"></emph>pondus duplum non eleuari ante <lb></lb>caſum ex altitudine quadrupla, neque triplum ante caſum ex <lb></lb>nonupla, &c.<emph.end type="italics"></emph.end> ſed eſſe quamobrem verearis de te, qui <lb></lb>præſtare perinde te, refragante Experientiâ, ſponſorem <lb></lb>non poſſis. </s> </p> <p type="main"> <s id="s.001193">Non inſto demùm quanto oporteat te tuæ ſon<lb></lb>tentiæ amore teneri, qui etiam quæſieris ex qualicum<lb></lb>que illo progreſſu remedium, quò iubere poſſes <lb></lb>viderem, <emph type="italics"></emph>ex his adhûc (quod totius controuerſiæ caput <lb></lb>foret) æqualibus spatiis æqualia acquiri velocitatis augmen<lb></lb>ta:<emph.end type="italics"></emph.end> cùm, vt præteream me longè ſecus inter experiun<lb></lb>dum vidiſſe, vti ex facta gemina comparatione clarum <lb></lb>eſt; tu, mendoſo etiam progreſſu, tanquam vero ſup<lb></lb>poſito, id videre me iubeas, quod ne ipſe quidem aut <lb></lb>videas, aut videre poſſis. </s> <s id="s.001194">Siquidem, vt videres, opor<lb></lb>teret quemadmodum velocitas acquiſita ex ſpatio, al<lb></lb>titudineve diametri vnius, exprimitur eleuatione pon<lb></lb>deris vnciarum 5, dr. </s> <s id="s.001195">2: ita acquiſitam ex ſpatio duplo, <lb></lb>ſiue ex altitudine diametrorum duntaxat duarum, <lb></lb>exprimi eleuatione dupli ponderis, vnciarum videlicet <pb pagenum="151" xlink:href="028/01/191.jpg"></pb>10, dr. </s> <s id="s.001196">4; & ex triplo, ſiue ex altitudine diam etrorum <lb></lb>trium, eleuatione tripli, ſeu <expan abbr="vnciatũ">vnciatum</expan> 15, dr. </s> <s id="s.001197">6, cùm tu ta<lb></lb>men videas eleuari duplum, ſiue vncias 10, dr. </s> <s id="s.001198">4, non <lb></lb>ex ſpatio duplo, ſed ex triplo, ex quo eleuari oporteret <lb></lb>non duplum, ſed triplum, ſeuvncias 15, dr. </s> <s id="s.001199">6. Idipſum <lb></lb>dico de cæteris ad vſque altitudinem diam etrorum <lb></lb>nouem, ex qua attolli oporteret ponderis nonuplum, <lb></lb>ſeu vncias 47, dr. </s> <s id="s.001200">2, non, vt ais, quintuplum ſolùm, ſeu <lb></lb>vncias 26, dr. </s> <s id="s.001201">2. An placuit tibi progreſſus ille per nume<lb></lb>ros impareis, vnum, tria, quinque, ſeptem, nouem, quo<lb></lb>rum ſuntinter ſe interualla æqualia? </s> <s id="s.001202">Atqui oporteret <lb></lb>hoc caſu ex diametro vna nihil attolli ponderis, ac ſu<lb></lb>peratis deinde duabus diametris, attolli pondus ſim<lb></lb>plum, ſiue vncias 5, dr. </s> <s id="s.001203">2, & ſuperatis adhûc duabus du<lb></lb>plum, & adhûc duabus triplum, &c: cùm tu velis ta<lb></lb>men ex altitudine nulla, quaſi cyphra, ad altitudinem <lb></lb>vſque integræ diametri, quaſi vnius, attolli pondus ſim<lb></lb>plum, ſeu vncias 5, dr. </s> <s id="s.001204">2, adeò proinde, vt ſi per ſpatia <lb></lb>æqualia <expan abbr="mẽſurata">menſurata</expan> diametris procedere velis, neceſſe ſit, <lb></lb>vt poſt primam diametrum, cui velocitatem attollen<lb></lb>tem ſimplum attribuis, accipias ſecundam, cui attol<lb></lb>lentem duplum attribuas, &c. </s> <s id="s.001205">Dicerem id fortè placuiſſe, <lb></lb>quòd exiſtimâris videri vtcumque congruere cum eo, <lb></lb>quod defendispoſteà, primum primæ partis dimidium, <lb></lb>quaſi pro nihilo haberi, ac numerandum motum dun<lb></lb>taxat ab initio vſque ſecundi dimidii, & pergendum <lb></lb>per <expan abbr="ſecundã">ſecundam</expan>, tertiam, & cæteras parteis, quarum quæli<lb></lb>bet duo dimidia contineat. </s> <s id="s.001206">Verum, vt taceam notum <lb></lb>eſſe, quàm parùm cohærenter id fieret, nihil eſt cur <lb></lb>tempus in coniectando teram, cùm etiam pigeat terere <pb pagenum="152" xlink:href="028/01/192.jpg"></pb>in iis, quæ dicuntur apertè. </s> </p> <p type="main"> <s id="s.001207"><emph type="italics"></emph>Sed memineris totius ſummi ponderis ex vnius diametri <lb></lb>altitudine eleuati, non eſſe in ſequentibus operationibus acci<lb></lb>piendum duplum, triplum, quadruplum, &c. </s> <s id="s.001208">ſed ſolius exceſ<lb></lb>ſus vltra æquilibrium aſſumendum eſſe duplum, triplum, qua<lb></lb>druplum, &c. </s> <s id="s.001209">quærimus enim accelerationis, ac velocitatis <lb></lb>effectum, ad quem non pertinet æquilibrium.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001210">Nequicquam profectò ſollicitus es. </s> <s id="s.001211">Vtcumque enim <lb></lb>exiſtimâris id eſſe <expan abbr="neceſſariũ">neceſſarium</expan>, donec ea tibi inſedit opi<lb></lb>nio, vt ex totidem diametris totidem præcisè eleuaren<lb></lb>tur pondera, præter æquilibrium, globo paria: nunc ta<lb></lb>men, cùm videas nihil eſſe neceſſe adſtringi, neque ad <lb></lb>diametrum, neque ad pondus (imò neque ad figuram <lb></lb>globi, ſi modò corpus eiuſmodi ſit, quod lancem ex <lb></lb>æquo circa medium afficiat) ſed liberum eſſe quamli<lb></lb>bet altitudinem pro prima aſſumere, & quodlibet pon<lb></lb>dus, quod ſummum ex ea attolletur pro pondere pri<lb></lb>mo: conſtat tale pondus, quodcum que illud ſit, & <lb></lb>æquilibrio quidem comprehenſo, germanam eſſe men<lb></lb>ſuram eius impetus, qui exprimitur ex caſu à tali altitu<lb></lb>dine; cùm ſi aliquid addatur tali ponderi, impetus ſit <lb></lb>minor, ſi detrahatur aliquid, etiam ex æquilibrio, ſit <lb></lb>maior. </s> <s id="s.001212">Quanquam & ſi perſtes putare detrahendum <lb></lb>eſſe <expan abbr="æquilibriũ">æquilibrium</expan>, nihil erit quamobrem repugnem, aut <lb></lb>quamobrem ipſe proptereà lucratus aliquid videaris, <lb></lb>cùm eo detracto tam ex primo, quàm cæteris ponderi<lb></lb>bus, quæ pondera ſuperfutura, ſunt pari progreſſione <lb></lb>ſint conſequutura. </s> <s id="s.001213">Nam in exemplo quidem tuo, v g. <lb></lb>ſeu numeros 5.2, 10.4, 15.6, 21, 26.2, detracto æqui<lb></lb>librio, ſeu comprehenſo habeas (quod tibi fortaſſis <pb pagenum="153" xlink:href="028/01/193.jpg"></pb>exprimendum fuit) eadem continuò erit progreſſio <lb></lb>quinarii numeri cum quadrante, ſeu dr. </s> <s id="s.001214">2; vt putà, ſeu <lb></lb>dicas 4.2, 9.4, 14.6, 20, 25.2: ſeu 6.2, 11.4, 16.6, 22, 27.2. <lb></lb>Sed res eſt per ſe ſatis manifeſta. </s> </p> <p type="main"> <s id="s.001215"><emph type="italics"></emph>Nunc autem, Vir perſpicacißime, cùm in ea tota re <lb></lb>diligentiam tuam, ac ſolertiam vehementer probem, & exa<lb></lb>ctiorem adhûc à te exſpectem; perinde probare non poſſum <lb></lb>quæ ſequuntur reliqua: & primùm quod ais numero xxviii. <lb></lb></s> <s id="s.001216">fore, vt ſi penes globorum diametros menſurandæ eſſent eo<lb></lb>rum velocitates, demißi ex eadem altitudine globi duo eiuſ<lb></lb>dem materiæ, ſed mole inæquales, pari celeritate non deſcen<lb></lb>derent. </s> <s id="s.001217">Ponis autem exempli gratiâ duos globos, quorum <lb></lb>vnus ſit diametro decies maiore, quàm alter, & minorem <lb></lb>hunc dicis decuplò velociùs altero moueri. </s> <s id="s.001218">Sed ſagacitas tua <lb></lb>hoc loco non aduertit primùm, à maiore globo vnius diametri <lb></lb>deſcenſu tantum velocitatis acquiri, quantum à minore globo <lb></lb>decem diametrorum deſcenſu acquiritur: nihilque omninò re<lb></lb>ferre, ſi è duabus velocitatibus inter ſe æqualibus altera plu<lb></lb>reis in parteis ſubdiuidatur, quæ ſimùl iunctæ alteram exæ<lb></lb>quent; ſicut nec ratio acceleratæ velocitatis per quodlibet <lb></lb>spatium variabitur, ſi partes eiuſdem ſpatij æquales ab vno <lb></lb>minores deſignentur, ab altero maiores. </s> <s id="s.001219">Deinde, illud etiam <lb></lb>non aduertit, vt ſi penes spatii parteis æqualeis in quacumque <lb></lb>ratione acceptas, accelerationis velocitas menſuretur, futurum <lb></lb>omninò ſit, vt perinde eorumdem globorum diametris ea<lb></lb>dem quoque accelerationis velocitas menſuretur; præſertim ſi <lb></lb>diametri (vt in propoſito exemplo) ſupponantur commenſu<lb></lb>rabiles; quod & ex ipſa rei natura, & ex proximè adducto <lb></lb>eius exemplo, qui ſpatium quodlibet, per quod fieret deſcenſus, <lb></lb>nunc maiores in parteis diuideret, nunc in minores, euidenter<emph.end type="italics"></emph.end><pb pagenum="154" xlink:href="028/01/194.jpg"></pb><emph type="italics"></emph>manifeſtum eſt. </s> <s id="s.001220">Non rectè igitur concludis globos eiuſdem <lb></lb>naturæ, ſed mole inæqualeis, inæquali velocitate deſcenſuros, <lb></lb>ſi penes eorum diametros expenderentur eorum velocitates.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001221">Quoniam igitur me tam parùm eſſe perſpicacem, <lb></lb>ſagacemque, arguis, vt quod dixi de duobus globis <lb></lb>non aduerterim; age diſquiramus, tua-ne perſpicacia, <lb></lb>& ſagacitas aduerterit ſatis eam, quam inſtituiſti ani<lb></lb>maduerſionem. </s> <s id="s.001222">Ego quidem ſoleo in rebus, quæ di<lb></lb>cuntur graues, grauitatem duplicem (duplexve pon<lb></lb>dus) diſtinguere. </s> <s id="s.001223">Vnam appello Simplicem, eam nem<lb></lb>pe, quæ conuenit rei etiam quieſcenti: vt putà qualem <lb></lb>habet lapis, dum immotus terram ſuppoſitam pre<lb></lb>mit, aut claua immota ſuppoſitum cuneum. </s> <s id="s.001224">Alteram <lb></lb>Adiectitiam voco, eam putâ, quæ rei ex motu accele<lb></lb>rato aduenit, & deſinente motu euaneſcit; qualem ſci<lb></lb>licet habet lapis, prout ex alto decidit, aut claua, prout <lb></lb>tum decidit, tum robuſta quoque impingitur manu. <lb></lb></s> <s id="s.001225">Cùm verò ſimplex grauitas menſura adiectitiæ ſit, qua<lb></lb>tenus pro exceſſu grauitatis ſimplicis, quo vnum cor<lb></lb>pus ſuperat aliud, exceſſus quoque eſt adiectitiæ, ſi <lb></lb>vtrumque quidem ex eadem decidat altitudine: ideò <lb></lb>ſimplici grauitate duorum corporum pondere inæqua<lb></lb>lium data, habeo adiectitiam vtriuſque ex pari caſu <lb></lb>acquiſitam, in eadem ratione, proportioneve, qua ſim<lb></lb>plicem: Adeò vt, ſi ſimplex vnius ſit librarum decem, <lb></lb>& alterius centum; vbi adiectitia prioris fuerit centum, <lb></lb>poſterioris futura ſit mille. </s> <s id="s.001226">Et quia grauitas vtriuſque <lb></lb>adiectitia ex effectu, ſeu percuſſione in rem ſubiectam <lb></lb>facta cognoſcitur: ideò rem attendo penes percuſſio<lb></lb>nem, quatenus ipſa notior eſt, faciléque intelligitur, <pb pagenum="155" xlink:href="028/01/195.jpg"></pb>vbi percuſſio facta per vnum corporum illorum nota <lb></lb>fuerit, notam quoque eam fore, quæ fict per alterum: <lb></lb>adeò vt ſi, exempli gratiâ, prius corpus in vnam bi<lb></lb>lancis lancem decidens eam percuſſionem faciat, qua <lb></lb>altera cum pondere centum librarum attollatur, deci<lb></lb>dens poſterius eam facturum ſit, qua attollatur cum <lb></lb>pondere librarum mille. </s> <s id="s.001227">Iam, cùm tua verba fuerint, <lb></lb><emph type="italics"></emph>Tantam præcisè corporis eſſe velocitatem, quantus impetus, <lb></lb>quantàque ipſa percußio fuerit: impetum enim omnem, & <lb></lb>percußionem ex velocitate eſſe, imò impetum ipſum velocita<lb></lb>tem eſſe nullóque hæc ab inuicem diſcrimine dirimi: vt me<lb></lb>ritò proinde quaratione accreſcit velocitas, eadem impetus, & <lb></lb>percußio augeantur:<emph.end type="italics"></emph.end> eapropter licet dicere velocitates <lb></lb>corporum illorum in fine motus ita ſe habere, vt ſi à <lb></lb>priore acquiſiti ſint decem gradus velocitatis, quibus <lb></lb>pondus decem librarum adauctum ſit vſque ad cen<lb></lb>tum, acquiſiti etiam fuerint decem gradus à poſteriore, <lb></lb>quibus pondus centum librarum adauctum fuerit vſ<lb></lb>que ad mille. </s> <s id="s.001228">Et certè iſta graduum velocitatis æquali<lb></lb>tas in proportione partium grauitatis adie ctitiæ funda<lb></lb>ta, dici poteſt cauſſa cur duo corpora pondere, ſiue <lb></lb>grauitate ſimplici ſummè inæqualia (vt ſi alterum pen<lb></lb>dat libras mille, alterum non ampliùs, quàm vnciam) <lb></lb>æquali cadant tempore; vnde & viciſſim arguantur <lb></lb>eſſe æqui-velocia. </s> </p> <p type="main"> <s id="s.001229">Accedamus propiùs ad hypotheſin. </s> <s id="s.001230">Oſtendere <lb></lb>volui velocitatis gradus menſurandos non eſſe, vt tu <lb></lb>aſſerebas, penes globorum diametros, quæ menſura<lb></lb>rent ſingulos caſus. <emph type="italics"></emph>Sunto enim,<emph.end type="italics"></emph.end> inquam, <emph type="italics"></emph>globi, verbi <lb></lb>caußâ, duo ex eadem materia, quorum vnus ſit diametro<emph.end type="italics"></emph.end><pb pagenum="156" xlink:href="028/01/196.jpg"></pb><emph type="italics"></emph>decies maiore, quàm alius, & dimittatur vterque ex eadem<gap></gap><lb></lb>altitudine: tunc, quia minor decidet per diametros decuplò <lb></lb>plureis, quàm mator, fiet, vt attollat pondera ſibi æqualia <lb></lb>decuplò multipliciora, quàm attollat maior ex ſibi æqualibus: <lb></lb>Quare & ſequitur, vtper idem ſpatium feratur decuplò ve<lb></lb>lociùs, ac decuplò citiùs, temporeve decies breuiore perue<lb></lb>niat ad lancem, quàm maior: hoc autem conſtat quàm falſum <lb></lb>ſit; cùm, &c.<emph.end type="italics"></emph.end></s> <s id="s.001231"> Conſidera iam, an quid dicerem, non ad<lb></lb>uerterim. </s> <s id="s.001232">Eſto pondus maioris globi mille vnciarum, <lb></lb>& clatus globus vna ſui diametro ſupra lancem, in eam <lb></lb>dimittatur; tum gradum velocitatis iuxta te acquiſie<lb></lb>rit, quo lancem percutiens alteram attollat cum pon<lb></lb>dere vnciarum mille, præter æquilibrium. </s> <s id="s.001233">Eſto pon<lb></lb>dus minoris, vnius, & dimittatur ſimiliter globus ex <lb></lb>vna ſui diametro, tum etiam gradum velocitatis vnum <lb></lb>iuxta te acquiſierit, quo lancem vnam percutiens alte<lb></lb>ram attollet cum pondere vnius vnciæ vltra æquili<lb></lb>brium. </s> <s id="s.001234">Attollatur poſteà, & dimittatur minor globus <lb></lb>ex ſecunda ſui diametro, tum velocitatis gradus acqui<lb></lb>ſierit duos, quibus attollantur duæ vnciæ, ac pari modo <lb></lb>ex tertia diametro attollentur tres, ex quarta quatuor, <lb></lb>& ſic deinceps, quovſque ex decima, hoc eſt ex altitu<lb></lb>dine, è qua dimiſſus fuerit maior globus, attollantur <lb></lb>decem. </s> <s id="s.001235">Itaque ex duobus illis globis ex eadem altitu<lb></lb>dine dimiſſis, percutiet minor lancem impetu decuplò <lb></lb>maiore, proportione ſui ponderis, quàm maior ſui reſ<lb></lb>pectu percutiat (cùm ille ſcilicet attollat decuplum ſui <lb></lb>ponderis, iſte attollat ſolùm tantumdem). Igitur &, <lb></lb>cùm impetus, ac velocitas idem ſint, erit velocitas mi<lb></lb>noris maior decuplò per illud ſpatium, quàm maioris, <pb pagenum="157" xlink:href="028/01/197.jpg"></pb>ſicque globus minor illud tempore decies breuiore, <lb></lb>quàm maior percurret. </s> <s id="s.001236">Atque ego quidem ſic ad rem <lb></lb>aduerti. </s> <s id="s.001237">Ais iam tu, <emph type="italics"></emph>meam ſagacitatem non aduertiſſe, à <lb></lb>maiore globo vnius diametri deſcenſu tantum velocitatis ac<lb></lb>quiri, quantum à minore globo decem diametrorum deſcenſu <lb></lb>acquiritur.<emph.end type="italics"></emph.end></s> <s id="s.001238"> Verùm cùm ego aduerterim rem ſe reipſa <lb></lb>ita habere: aduerti tamen ſimùl id aduerſari tuis de<lb></lb>cretis, vnde & tua ſagacitas aduertiſſe duntaxat vide<lb></lb>tur quid fieret, non verò quid ex propriis aſſertionibus <lb></lb>ſequeretur. </s> <s id="s.001239">Pergis <emph type="italics"></emph>nihil omninò referre, ſi ex duabus ve<lb></lb>locitatibus inter ſe æqualibus altera plureis in parteis ſub<lb></lb>diuidatur. </s> <s id="s.001240">quæ ſimùl iunctæ alteri exæquentur, ſicut nec ratio <lb></lb>acceleratæ velocitates per quodlibet ſpatium variabitur, ſipar<lb></lb>tes eiuſdem spatii æquales ab vno minores deſignentur, ab <lb></lb>alio maiores:<emph.end type="italics"></emph.end> at nihil refert quidem, ſi velocitates æqua<lb></lb>les ſint, vt illæ reuerâ per illud ſpatium ſunt: ſed pluri<lb></lb>mùm refert, ſi inæquales ſint, vt tuis ex decretis eſſe de<lb></lb>ducuntur, Quod deinde ſubdis, diuerſum non eſt. </s> </p> <p type="main"> <s id="s.001241"><emph type="center"></emph>IN ARTICVLOS XXIX. XXX. XXXI. XXXII. XXXIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001242"><emph type="center"></emph>De Tempore, quo R. P. colligit parteis ſpatij <lb></lb>ſingulas decurſum non iri.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001243"><emph type="italics"></emph>Nihilo rectiùs numero xxx: etiam reprehendis, quòd <lb></lb>ſine respectu ad tempus definitionem accelerati motus aut <lb></lb>inquiſierim, aut etiam conſtituerim. </s> <s id="s.001244">Etſi enim priùs accele<lb></lb>rationem motus cum partibus spatij, quàm cum partibus <lb></lb>temporis æqualibus contulerim, cùm tamen vtrumque abun<lb></lb>dè, ac diligenter eadem Epiſtola factum à me cerneres; ſatis <lb></lb>iuſtam huius reprebenſionis anſam accipere inde non potuiſti.<emph.end type="italics"></emph.end><pb pagenum="158" xlink:href="028/01/198.jpg"></pb><emph type="italics"></emph>Voluiſſes fortaßis (quod ſine dubio facere potui) vt motum <lb></lb>vniformiter acceleratum potius definirem eſſe eum,<emph.end type="italics"></emph.end> qui tem<lb></lb>poribus æqualibus velocitatis augmenta in continua <lb></lb>ratione dupla reciperet: <emph type="italics"></emph>ſed cùm Galileus æqualia cele<lb></lb>ritatis incrementa partibus temporis æqnalibus tribueret, <lb></lb>procliue fuit, vt æqualia illa velocitatis augmenta statim ſpa<lb></lb>tij potiùs, quàm temporis partibus æqualibus attribuerentur. <lb></lb></s> <s id="s.001245">Sed hæc leuiora ſunt.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001246">Dictum hucvſque eſt de tuæ Demonſtrationis Aſ<lb></lb>ſumptione. </s> <s id="s.001247">Probare deinceps voluiſti conſequutionem <lb></lb>Propoſitionis; veruntamen duo quaſi membra huiuſce <lb></lb>Probationis fuerunt. </s> <s id="s.001248">Nam poſtquàm ex tuo ſupe<lb></lb>riore Experimento collegiſti <emph type="italics"></emph>ex dupla diſtantia celerita<lb></lb>tem acquiri duplam, ex tripla triplam, &c.<emph.end type="italics"></emph.end> agendum eſſe <lb></lb>deinceps cenſuiſti de Tempore, quòd <emph type="italics"></emph>ad ipſum quoque <lb></lb>celeritas motus respectum includat:<emph.end type="italics"></emph.end> ac ſubinde adnixus es <lb></lb>declarare <emph type="italics"></emph>Primùm,<emph.end type="italics"></emph.end> non ſic decurri parteis ſpatij, vt ſe<lb></lb>cunda percurratur dimidio temporis, quo prima, tertia <lb></lb>triente, quarta quadrante, &c. </s> <s id="s.001249">vtcumque id videatur <lb></lb>ſequi ex ratione illa increſcentis ſpatiorum inſtar ce<lb></lb>leritatis: <emph type="italics"></emph>Secundò<emph.end type="italics"></emph.end> autem ſic potiùs decurri, vt initio <lb></lb>ſumpto ab inferiore primæ partis dimidio, quod cer<lb></lb>to tempore percurratur, ſecunda, quæ eius dimidij ſit <lb></lb>dupla, percurratur pari tempore: tertia verò triente <lb></lb>eiuſdem temporis, tanquam reſpondens infimo eiuſ<lb></lb>dem primæ partis trienti: quarta quadrante, vt reſ<lb></lb>pondens quadranti, atque ita de cæteris; Ex quibus <lb></lb>ſubinde ſequatur, vt quemadmodum pars ſecunda <lb></lb>æquali tempore percurritur, ſic percurrantur duæ ſi<lb></lb>mùl ſequentes; ſic quatuor ſimùl ſuccedentes; ſic <pb pagenum="159" xlink:href="028/01/199.jpg"></pb>aliæ octo, &c. </s> <s id="s.001250">Itaque dicendum eſt prius de priore <lb></lb>capite. </s> <s id="s.001251">Interim <expan abbr="autẽ">autem</expan> (circa id, quod heic obiicis) Recte<lb></lb>ne, ſit, an perperam factum, quod admonuerim <emph type="italics"></emph>non de<lb></lb>buiſſe temporis mentionem in definitione accelerati motus <lb></lb>omitti;<emph.end type="italics"></emph.end> contextus meus, quem retexere nihil eſt opus, <lb></lb>ſatis oſtendit. </s> <s id="s.001252">Quod autem deinceps <emph type="italics"></emph>Epistola eadem <lb></lb>acceleratum motum non minùs diligenter cum tempore, quàm <lb></lb>cum ſpatio contuleris:<emph.end type="italics"></emph.end> idipſum arguit non debuiſſe mi<lb></lb>norem temporis rationem <emph type="italics"></emph>in eo definiendo<emph.end type="italics"></emph.end> haberi, quàm <lb></lb>ſpatii (vt præteream potuiſſe quoque haberi non<lb></lb>nihil maiorem, quatenus à me inſinuatum eſt) ac futu<lb></lb>ram deinceps fuiſſe comparationem tam cum illo, <lb></lb>quàm cum iſto cohærentiorem. </s> <s id="s.001253">Quod ſubiicis <emph type="italics"></emph>me <lb></lb>fortaßis voluiſſe;<emph.end type="italics"></emph.end> idipſum eſt, quod potiùs veritatis amo<lb></lb>re voluiſſem, ſi licuiſſet quidem per te: ſed nihil heic <lb></lb><expan abbr="præuertendũ">præuertendum</expan> eſt: non ſanè, <emph type="italics"></emph>quòd iſta ſunt leuia;<emph.end type="italics"></emph.end> quandò <lb></lb>in iis cardo controuerſiæ vertitur: ſed quòd ſit de ra<lb></lb>tione dupla temporibus æqualibus ſpeciatim dicen<lb></lb>dum inferiùs. </s> </p> <p type="main"> <s id="s.001254"><emph type="italics"></emph>Grauius eſt, optime<emph.end type="italics"></emph.end> G<emph type="italics"></emph>aſſende, quòd numero xxxi. </s> <s id="s.001255">xxxii. <lb></lb></s> <s id="s.001256">xxxiii. </s> <s id="s.001257">non ſolum contra expreſſam Epistolæ meæ ſententiam, <lb></lb>ſed contra euidentem quoque Demonſtrationis lucem velis à me <lb></lb>ea dici, quæ verbis expreßis nego, quæque falſa eſſe non tan<lb></lb>tum pronuncio, ſed clarè etiam, atque euidenter demonſtro: ex <lb></lb>iiſque deinde, tanquam meis, ea mihi abſurda affingas, in <lb></lb>quæ nemo, quantumvis hebes impingat. </s> <s id="s.001258">Demonſtrare certé <lb></lb>debueras ea, quæ à me <expan abbr="tanquã">tanquam</expan> falſa reiecta vide bas, ex consti<lb></lb>tutis à me principiis nihilominus ſequi, antequam eadem, vt <lb></lb>mea decreta impeteres: imò id ſolum faciendum tibi fuerat, <lb></lb>vt me caußæ præuaricatorem euinceres, qui ea ipſa falſa<emph.end type="italics"></emph.end><pb pagenum="160" xlink:href="028/01/200.jpg"></pb><emph type="italics"></emph>demonſtrarem, quæ ex meis nihilominus principiis clara, eui<lb></lb>dentique ratione inferrentur. </s> <s id="s.001259">Quid enim tibi opus fuit mul<lb></lb>tis paginis impugnare ea, quæ iam expugnaſſem: & conquiſi<lb></lb>tis vndique rationibus falſa oſtendere, quæ falſa eſſe prior <lb></lb>agnoſcerem? </s> <s id="s.001260">Et tamen nihil eſt in tota tua Epiſtola aliud, in <lb></lb>quo acrius, animoſiuſque depugnes.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001261">Quomodo quæſo, optimus, & non peſſimus po<lb></lb>tiùs eſſem, ſi is quidem, quem tu me hoc articulo de<lb></lb>pingis, forem? </s> <s id="s.001262">Verùm, quia num tibi quid affinxerim: <lb></lb>num quædam à te reiecta vt falſa, ex tuis principiis ſe<lb></lb>qui non oſtenderim; num poſtquam tu quædam ex<lb></lb>pugnaſti vt falſa, ego non tam illa, quàm ex illis vt <lb></lb>tuis, cætera ſuperfluè impugnauerim; quia, inquam <lb></lb>num iſta ſe verè, falſóve habeant, cognoſcendum eſt <lb></lb>ex ijs, quæ à te ſubiiciuntur; idcircò nihil eſt, <lb></lb><figure id="id.028.01.200.1.jpg" xlink:href="028/01/200/1.jpg"></figure><lb></lb>quod ad iſta regeri generatim debeat. </s> </p> <p type="main"> <s id="s.001263"><emph type="italics"></emph>Atque in primis, eandem iterùm mihi Propoſitio<lb></lb>nem affingis, quam iam ſupra numero<emph.end type="italics"></emph.end> 7. <emph type="italics"></emph>indicaui, <lb></lb>& in hunc locum examinandam reieci. </s> <s id="s.001264">Vis enim, <lb></lb>& ſiue demonſtratione,s&sſine vlla vel probabili ratione <lb></lb>ais, & quaſi pro tuo iure ſupponis,<emph.end type="italics"></emph.end> graue deſcen<lb></lb>dens per ſpatium AB in parteis quotlibet <lb></lb>æqualeis diuiſum, percurrere partem ſecundam <lb></lb>DE, in dimidio eius temporis, quo percurritur <lb></lb>prior pars AD, <emph type="italics"></emph>& quod idem est,<emph.end type="italics"></emph.end> partem DE per<lb></lb>curri velocitate dupla eius velocitatis, qua tranſ<lb></lb>curritur AD. </s> </p> <p type="main"> <s id="s.001265">Quàm falsò repetas hanc Propoſitionem tibi <lb></lb>à me affictam, feci abundè manifeſtum, cùm id <lb></lb>obiter non ſum prætergreſſus, quod tu citato <pb pagenum="161" xlink:href="028/01/201.jpg"></pb>loco, hoc eſt, in articulum xii, attigeras obiter ſolùm. <lb></lb></s> <s id="s.001266">Quippe tuis verbis recitatis, & deducta occaſione, ob <lb></lb>quam illa texueras, demonſtratum eſt tuam fuiſſe, <lb></lb>quam iam inficiaris, expreſſam ſententiam; heincque <lb></lb>adeò probatum manet me non modò probabili, ſed <lb></lb>conuincenti etiam ratione (niſi te velis Paralogiſtam, <lb></lb>quod abſit vt cenſeam, ridiculoſiſſimum haberi) ac <lb></lb>non meo iure, ſed ex tuis verbis hanc ſuppoſitionem, <lb></lb>quaſi tuam ſupponere, G<emph type="italics"></emph>raue deſcendens per spatium <lb></lb>AB in parteis quotlibet æqualeis diuiſum, percurrere partem <lb></lb>ſecundam DE<emph.end type="italics"></emph.end> (quæ illeic fuit BC) <emph type="italics"></emph>in dimidio eius tem<lb></lb>poris, quo percurritur prior pars AD<emph.end type="italics"></emph.end> (quæ illeic AB) & <lb></lb>quod idem eſt, <emph type="italics"></emph>partem DE percurri veiocitate dupla eius, <lb></lb>velocitatis, qua tranſcurritur AD.<emph.end type="italics"></emph.end></s> <s id="s.001267"> Sequitur. </s> </p> <p type="main"> <s id="s.001268"><emph type="italics"></emph>At Primum, quid amabò, caußæ est, cur cùm antè nume<lb></lb>ro tuæ Reſponſionis X. volueris velocitatem per totam AE <lb></lb>duplam eſſe velocitatis per primam partem AD, idque ex <lb></lb>meis quoque principiis neceſſarium eſſe aſſerueris: nunc, mutato <lb></lb>conſilio, velocitatem per ſolam partem DE velocitatis per <lb></lb>partem AD acquiſitæ duplam eſſe contendas: & quidem, vt <lb></lb>ais, ex principiis item meis?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001269">Quid cauſſæ ſit, quæris? </s> <s id="s.001270">Non ſanè mutatio conſilij <lb></lb>in me; ſed quæ falſorum principiorum, incommodo<lb></lb>rumque ex iis deductorum variatio in te obſeruatur. <lb></lb></s> <s id="s.001271">Nam quòd velis quidem velocitatem acquiſitam in E <lb></lb>eſſe duplam velocitatis acquiſitæ in D, vt ſpatium AE, <lb></lb>ſpatij AD duplum eſt: contendo iam velocitatem, qua <lb></lb>percurritur DE, eſſe duplam eius, qua tranſcurritur AD, <lb></lb>ſeu, quæ acquiritur per AD: &, quòd tu contendas ab <lb></lb>A, vſque ad E, augeri æquabiliter, idcircò ſum argu-<pb pagenum="162" xlink:href="028/01/202.jpg"></pb>mentatus articulo illo velocitatem per totam AE, du<lb></lb>plam eſſe velocitatis per totam AD. </s> <s id="s.001272">Cùm hoc autem <lb></lb>ſuo iam loco demonſtratum abundè ſit: ideò illud ſo<lb></lb>lùm, quod tu huius loci facis proprium, eſt attenden<lb></lb>dum. </s> <s id="s.001273">Quæſo itaque; cùm velis in D acqui ſitum eſſe <lb></lb>vnum velocitatis gradum, & duos in E, an velis gradum <lb></lb>acquiſitum in D, manere per ipſam DE, ac eſſe vnum <lb></lb>ex iis duobus, qui acquiſiti reperiuntur in E; an nolis? <lb></lb></s> <s id="s.001274">Si velis; igitur peripſam DE ſunt duo gradus, vnus <lb></lb>nempe manens, & alius, qui interim acquiritur. </s> <s id="s.001275">Si no<lb></lb>lis; igitur oportet duos gradus, qui ſunt in E, acquiſi<lb></lb>tos eſſe per ſolam DE. An-non ergo vtrovis modo <lb></lb>neceſſe eſt velocitatem per ſolam DE, duplam eſſe <lb></lb>eius, quæ acquiritur per AD? </s> <s id="s.001276">Dilemma eſt, neutrum<lb></lb>que eſt membrum, circa quod liceat tergiuerſari. </s> <s id="s.001277">Nam <lb></lb>circa ſecundum quidem, dicere nihil potes: cùm id <lb></lb>ſit tamen reuerâ tuum; quatenus, vt ſuperiùs quoque <lb></lb>adnotatum eſt, vis velocitatem acquiſitam per totam <lb></lb>DE, eſſe duplam acquiſitæ in D, & acquiſitam in D <lb></lb>perire: nam alioquin in E velocitas iam eſſet tripla, ſi<lb></lb>ue in E tres gradus eſſent: cùm eſſe tu velis ſolùm duos, <lb></lb>& acquiſitos quidem per ſolam DE. </s> <s id="s.001278">Circa primum <lb></lb>autem ſi fortaſſis dicas manere quidem primum gra<lb></lb>dum, ſed nihil agere; ſequetur ſolo ſecundo gradu, qui <lb></lb>per DE acquiretur, agente, partem DE tempore ni<lb></lb>hilo breuiore tranſcurri, quàm ipſam AD: cùm etiam <lb></lb>per te percurratur minùs, quam dimidio. </s> <s id="s.001279">Et, ſi dicas <lb></lb>agere: Aut ob ſui conſtantiam duplò aget ampliùs, <lb></lb>quàm per AD, vt ſuperiùs deduximus; & tunc incom<lb></lb>modum ſequetur, quod ſuprà quoque oſtenſum eſt; <pb pagenum="163" xlink:href="028/01/203.jpg"></pb>quatenus DE percurretur præcisè triente primi tem<lb></lb>poris; & ſecundum tempus integrum non effluet, niſi <lb></lb>ſub partem ſpatij octauam, quod tu vis effluere cum <lb></lb>ipſa ſecunda: Aut certè tantumdem; & tunc, quia etiam <lb></lb>tantumdem aget, qui gradus acquiretur per ipſam <lb></lb>DE: recurret idipſum, quod tu refugis; nempe partem <lb></lb>DE percurri velocitate dupla illius, qua decurſa fuerit <lb></lb>AD. </s> </p> <p type="main"> <s id="s.001280"><emph type="italics"></emph>Sed neutram Propoſitionem probas, aut ex ſtatutis à me <lb></lb>principiis vlla ratione deducis: & vt priorem iam ſuprà fal<lb></lb>ſam euici; ita nunc iſtam eſſe impoßibilem, hac ratione cui<lb></lb>denter demonſtro.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001281">Imò de Priore quidem apertè probaui; neque tu <lb></lb>quicquam aliud, quàm, vt aiunt, principium petiiſti: <lb></lb>& cùm te iam dicis euiciſſe eam falſam; notum eſt quæ<lb></lb>ſtionem non eſſe, an falſam euiceris, ſed an euiceris <lb></lb>non-tuam, ſeu ex tuis principiis minimè deductam. </s> <s id="s.001282">De <lb></lb>Poſteriore etiam rem feci apertam; neque cùm ego <lb></lb>inſtiti nullum eſſe in mea argumentatione Paralo<lb></lb>giſmum, tu potuiſti vllum oſtendere: & cum iam ſuſci<lb></lb>pis demonſtrandum eam eſſe impoſſibilem, minimè <lb></lb>attendis quæſtionem non eſſe, an impoſſibilis ſit, ſed <lb></lb>ex tuis ne deducta principiis. </s> </p> <p type="main"> <s id="s.001283"><emph type="italics"></emph>Ex ſtatutis à me principiis, neceſſe eſt, vt graue quodcum<lb></lb>que per spatium quodlibet, putà AB deſcendens, æqualibus <lb></lb>temporibus spatia continuò maiora, ac maiora decurrat in con<lb></lb>tinua ratione dupla.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001284"><emph type="italics"></emph>Ex ſtatutis,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>principiis:<emph.end type="italics"></emph.end> imò hæc tibi con<lb></lb>cluſio eſt; quæ & falſa eſt, & non probabitur deinceps <lb></lb>à te, niſi ex ipſiſinet principiis, quæ vt falſa ſunt, ita <pb pagenum="164" xlink:href="028/01/204.jpg"></pb>nunc per ipſam à te circulo inſigni probantur. </s> <s id="s.001285">Sed <lb></lb>tuum eſto principium; quid inde? </s> </p> <p type="main"> <s id="s.001286"><emph type="italics"></emph>At hoc dato, neceſſarium etiam eſt, vt quanto tempore gra<lb></lb>ue deſcendens percurrit ſecundam partem DE, tantò præcisè <lb></lb>spatium duplò minus antè percurrerit; nempe SD, quod <lb></lb>ſupponitur dimidium ſuperioris spatij AD.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001287">An-non agnoſcis circulum? </s> <s id="s.001288">Neque enim alia ratio<lb></lb>ne probas ſpatia continuò percurri in ratione dupla, <lb></lb>quàm quia ſupponis tanquam principium, partem DE <lb></lb>percurri tanto tempore, quantò dimidium SD. </s> <s id="s.001289">Sed <lb></lb>& hoc eſto. </s> </p> <p type="main"> <s id="s.001290"><emph type="italics"></emph>Neceſſe eſt igitur, vt partes SD, & DE æquali <lb></lb>tempore percurrantur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001291">Imò impoſſibile eſt; tantum abeſt, vt neceſſarium; <lb></lb>neque in te eſt, vt neceſſitatem probes, niſi priùs oſten<lb></lb>deris velocitates eſſe vt ſpatia, quod tantum abeſt, vt <lb></lb>hactenus quidem præſtiteris, quin potiùs præſtare co<lb></lb>natus, tuo in Bilance Experimento, ipſo euentu fueris <lb></lb>deluſus. </s> <s id="s.001292">Quanquam eſto & iſtud quoque. </s> </p> <p type="main"> <s id="s.001293"><emph type="italics"></emph>At Tempus, quo percurritur SD pars inferior ipſius <lb></lb>AD, neceſſariò breuius eſt tempore, quo decurritur pars <lb></lb>ſuperior AS (alioquin motus per AD æquabilis eſſet, non <lb></lb>autem acceleratus, vt per ſe manifeſtum eſt.)<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001294">Admitto id quidem, ſed independenter ex tuis <lb></lb>principiis. </s> </p> <p type="main"> <s id="s.001295"><emph type="italics"></emph>Pars igitur DE non percurritur in dimidio totius tem<lb></lb>poris, quo decurritur AD, ſed in tempore aliquantò breuiore.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001296">Id quoque admitto; ſed omninò ex aliis principiis, <lb></lb>quàm tuis. </s> </p> <p type="main"> <s id="s.001297"><emph type="italics"></emph>Et conſequenter pars DE non tranſcurritur velocitate<emph.end type="italics"></emph.end><pb pagenum="165" xlink:href="028/01/205.jpg"></pb><emph type="italics"></emph>dupla eius velocitatis, qua percurritur AD, ſed velocitate <lb></lb>maiore.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001298">Et hoc admitto denique; verùm aliis prorsùs, quàm <lb></lb>tuis principiis perſuaſus. </s> </p> <p type="main"> <s id="s.001299"><emph type="italics"></emph>Ad hanc Demonſtrationem quid profers?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001300">Hem! quid profero? </s> <s id="s.001301">Videlicet Primò tefalſa vſur<lb></lb>pare principia, neque alia lege concludere ex ipſis ve<lb></lb>rum, quàm ſi quis ex eo, quod aſſumat <emph type="italics"></emph>arbores omneis <lb></lb>eſſe in cælo,<emph.end type="italics"></emph.end> & <emph type="italics"></emph>Lunam eſſe arborem,<emph.end type="italics"></emph.end> concludat <emph type="italics"></emph>Lunam <lb></lb>eſſe in cælo.<emph.end type="italics"></emph.end></s> <s id="s.001302"> Secundò, committere te, vt vulgo aiunt, cir<lb></lb>culum, incidereve in Diallelum; vti obiter inſinuatum <lb></lb>eſt, & tota ex ſerie tui operis conſtat. </s> <s id="s.001303">Tertiò, te noua <lb></lb>contradictione temetipſum inuoluere, dum coactus vi <lb></lb>ſuperioris dilemmatis, dicere teneris velocitatem per <lb></lb>DE duplam eſſe velocitatis per AD, & nunc aſſumis, <lb></lb>aut te probaſſe contendis eandem velocitatem per <lb></lb>DE duplam eſſe velocitatis per SD, quod ſit ſolùm di<lb></lb>midium ipſius DE. </s> <s id="s.001304">Quartò te rursùs eâ implicari, <lb></lb>quòd cùm huc vſque volueris acquiſitos eſſe ab A in <lb></lb>E duos gradus, qui ſimùl iuncti ſint duplum illius, qui <lb></lb>acquiſitus eſt ex A in D; velis iam eoſdem duos gra<lb></lb>dus eſſe duplum illius, qui ſolummodò ſit acquiſitus <lb></lb>ex S in D. </s> <s id="s.001305">Quintò te idcircò omnia perturbare; qua<lb></lb>tenus quicquid hactenus dixiſti de ſpatio in parteis <lb></lb>æqualeis diuiſo, & incipiendo quidem ab A, vt proba<lb></lb>res velocitates acquiſitas eſſe vt ſpatia; de ſpatiis iam, <lb></lb>ac velocitatibus ita loqueris, vt ſi incipiendum ſit ab S, <lb></lb>neglecto prorſus dimidio AS. Sextò, non reſponde<lb></lb>re te quæſtioni; quoniam quæſtio eſt, non an veloci<lb></lb>tas per ſolam DE ſit dupla velocitatis per AD; ſed an <pb pagenum="166" xlink:href="028/01/206.jpg"></pb>eſſe duplam ſequatur ex tuis principiis, veluti præmo<lb></lb>nitum eſt. </s> <s id="s.001306">Poſtremò te vitiosè id oſtendere, quatenus <lb></lb>aſſumis vnum ex tuis principiis, cum quo Propoſitio <lb></lb>huiuſmodi non cohæreſcat: cùm id non ſufficiat, niſi <lb></lb>oſtendas; te aut non habere aliud principium, quàm <lb></lb>aſſumptum hoc: aut habere quidem, ſed ex nullo ta<lb></lb>men ipſorum illam conſequi: aut habere iure eam de te <lb></lb>ſiduciam, vt impoſſibile ſit te tibi contradicere, ac <lb></lb>non clarè perſpicere quid ex principio quolibet vel ſe<lb></lb>quatur, vel non ſequatur. </s> </p> <p type="main"> <s id="s.001307"><emph type="italics"></emph>Eam certe, vt legitimam admittis?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001308">Quin imò quàm varias ob cauſſas cenſeam reiicien<lb></lb>dam, tanquam ſpuriam, habes. </s> </p> <p type="main"> <s id="s.001309"><emph type="italics"></emph>At, quod à te inexspectatum fuit, addis (quod in pari <lb></lb>caſu etiam aliàs facis) inde vel maximè mea decreta reuelli, <lb></lb>quòd ex iis adeò pugnantia concludantur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001310">Quamobrem verò id à me eſſe debuit inexſpecta<lb></lb>tum; tibi præſertim, viro ſapienti, cui nihil continge<lb></lb>re ex inopinato debet? </s> <s id="s.001311">An quia putâras non debere <lb></lb>me tua decreta expendere, ſed in tua verba, quaſi man<lb></lb>cipium domino addictum iurare? </s> <s id="s.001312">An quia volueras, <lb></lb>vt ſi quid falſum, aut repugnans occurreret, id non <lb></lb>tam lenirem, vt conatus ſum facere, quàm omninò diſ<lb></lb>ſimularem? </s> <s id="s.001313">An quia contenderas, vt quicquid id fo<lb></lb>ret, nihil aliud, quam plauderem, & nihil conſcientiam <lb></lb>reueritus, creditæ mihi veritati remitterem nuncium, vt <lb></lb>tibi adularer? </s> <s id="s.001314">Horum nihil credo: ſed tamen non ſa<lb></lb>tis perſpicio, quî id fecerim præter tuam ſpem; niſi <lb></lb>quòd iſtorum tuorum decretorum tanta perſuaſione <lb></lb>certus fueris, vt quemadmodum eatenus incideras in <pb pagenum="167" xlink:href="028/01/207.jpg"></pb>creminem, qui quicquam repugnans in ijs deprehen<lb></lb>diſſet (ſic enim poſteà memoras) ita ego minimus <lb></lb>omnium, in quos poſſes incidere, impar prorſus forem, <lb></lb>à quo quicquam tale deprehenderetur. </s> </p> <p type="main"> <s id="s.001315"><emph type="italics"></emph>Id, mi<emph.end type="italics"></emph.end> G<emph type="italics"></emph>aſſende, ſi adducta demonſtratione diceres, tuo <lb></lb>iure vtique diceres: at ſine demonstratione, ſine vlla veriſimi<lb></lb>litudine id non ſemel tantum dicere, ſed inculcare <gap></gap>, ſed <lb></lb>inſtare etiam acriùs, & tanquam de conſtanti victoria trium<lb></lb>phare, vide an iſtud ſit ingenitæ moderationis tuæ, atque etiam <lb></lb>dignitatis.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001316">Imò, mi Cazræe, Tuipſe, quo iure in me ſic inſultes, <lb></lb>Vide. </s> <s id="s.001317">Iacturam fortè faciam vnius, aut alterius pagi<lb></lb>næ; ſed neceſſitatem profectò imponis retexendi quid<lb></lb>piam ex ijs, ob quæ ita inueheris. </s> <s id="s.001318">Conquereris, quòd, <lb></lb><emph type="italics"></emph>meo iure, & ſine vlla demonſtratione, aut veriſimilitudine di<lb></lb>xerim, atque inculcârim tua decretainde maximè reuelli, quòd <lb></lb>adeò pugnantia exijs concludantur.<emph.end type="italics"></emph.end> (nam quòd alioquin <lb></lb>tanquam de conſtanti victoria triumphârim, hoc eſt, <lb></lb>exſultabundus geſtierim, & quaſi thraſofuerim gloria<lb></lb>tus; id vt à me alienum eſt, ita Deo propitio, nuſquam <lb></lb>deprehendes.) Itaque id-ne abſque iure, & ſine vlla <lb></lb>demonſtratione, aut veriſimilitudine fecerim, perui<lb></lb>deamus. </s> <s id="s.001319">Verba tua fuerant vt retuli, articulo XXXI. <lb></lb><emph type="italics"></emph>Cùm enim ex ſuperioribus iam euidenter co<gap></gap> in naturali <lb></lb>grauium deſcenſu ſemper ex dupla diſtantia celeritatem haberi <lb></lb>duplam, & ex tripla diſtantia triplam, atque ita deinceps ea<lb></lb>dem ratione celeritatem augeri; nihil procliuius eſſe potest, <lb></lb>quàm vt quis existimet accelerationem illam fieri per ſubdi<lb></lb>uiſionem primi cuiuſlibet temporis in parteis ſemper minores, <lb></lb>pro multitudine, & ratione spatiorum æqualium, quæ motu<emph.end type="italics"></emph.end><pb pagenum="168" xlink:href="028/01/208.jpg"></pb><emph type="italics"></emph>decurruntur: ita videlicet, vt pars ſecunda spatii abſoluatur <lb></lb>dimidia parte temporis, quo prima decurſa eſt: & tertia pars <lb></lb>ſpatii tertia parte eiuſdem primi temporis percurratur, & ita <lb></lb>de cæteris.<emph.end type="italics"></emph.end></s> <s id="s.001320"> Excepi ego, <emph type="italics"></emph>heic profectò rurſus mirari tuam <lb></lb>ſagacitatem par eſt, quatenùs eam non fugit error, qui ex poſi<lb></lb>tione à te aſſerta conſequitur, tametſi ipſe non conſequi, ex iis, <lb></lb>quæ ſequuntur, contendas.<emph.end type="italics"></emph.end></s> <s id="s.001321"> Duo heic fuerunt: <emph type="italics"></emph>Vnum,<emph.end type="italics"></emph.end> Er<lb></lb>rorem eſſe, quòd ſecundum ſpatium æquale percurra<lb></lb>tur dimidio illius temporis, quo primum; tertium trien<lb></lb>te, quartum quadrante, atque ita de reliquis: <emph type="italics"></emph>Alterum,<emph.end type="italics"></emph.end><lb></lb>huiuſmodi errorem conſequi ex tua pofitione, quòd <lb></lb>celeritates ſe habeant vt ſpatia, atque adeò, quod ex <lb></lb>duplo diſtantiæ celeritas habeatur dupla, ex triplo tri<lb></lb>pla, &c. </s> <s id="s.001322">Et <emph type="italics"></emph>de Priore<emph.end type="italics"></emph.end> quidem non fuit controuerſia, <lb></lb>cùm tu eſſe errorem & confeſſus fueris, & aliquot <lb></lb>etiam argumentis oſtenderis. <emph type="italics"></emph>De Poſteriore<emph.end type="italics"></emph.end> tota lis <lb></lb>fuit, an nempe huiuſmodi error tuis ex principiis, ſeu <lb></lb>ex poſitione mox memorata ſequeretur, an-non. </s> <s id="s.001323">Et, <lb></lb>ſi ſequeretur, an cùm deinceps & errorem oſtenderes, <lb></lb>& ex eo admiſſo repugnantia deduceres, non reuerâ <lb></lb>oſtenderes, ac deduceres aduerſus teipſum, vt cuius er<lb></lb>ror reuerâ eſſet, tanquam neceſſariò deductus ex tuis <lb></lb>principiis. </s> </p> <p type="main"> <s id="s.001324">Iam verò illum ex tuis principiis, ſeu propoſitione <lb></lb>memorata ſequi, ex eo argumentatus ſum, quòd tem<lb></lb>pora eſſent increſcentium velocitatum ſubmultiplicia: <lb></lb>adeò, vt quod ſpatium æquale ſecundum dupla velo<lb></lb>citate percurritur, dimidio temporis percurratur, quo <lb></lb>primum: & quod tertium tripla, triente; quod quar<lb></lb>tum quadrupla, quadrante, atque ita de cæteris. <pb pagenum="169" xlink:href="028/01/209.jpg"></pb>Subiunxi autem, <emph type="italics"></emph>atque ego quidem huc-vſque nullum video <lb></lb>paralogiſmum:<emph.end type="italics"></emph.end> ac tum ſum conatus ex errore ſuppo<lb></lb>ſito deducere abſurditatem. </s> <s id="s.001325">Quæſo igitur, an meo <lb></lb>iure, & ſine vlla, niſi demonſtratione, ſaltem veriſimili<lb></lb>tudine dixerim hunc errorem ex tuis principiis deduci? <lb></lb></s> <s id="s.001326">Et cùm fuerim conteſtatus in mea ſeu demonſtratio<lb></lb>ne, ſeu veriſimili ratione nullum ſubeſſe paralogiſ<lb></lb>mum; cur tu, ſi quempiam eſſe putaſti, verè ſubeſſe <lb></lb>non oſtendiſti? </s> <s id="s.001327">Nam quòd fueris ratiocinatus ex con<lb></lb>cluſione illa <expan abbr="quã">quam</expan> ſtatutum à te principium dixiſti, ve<lb></lb>locitatem per ſecundam partem non eſſe duplam ve<lb></lb>locitatis per primam, id non arguit illud non ſequi ex <lb></lb>alio tuo principio, ex quo aliunde etiam potuerit per <lb></lb>media quæpiam alia mendoſa illa concluſio trahi: ac <lb></lb>potiſſimùm, cum ſit adeò verum, quod dicitur vulgò, <lb></lb><emph type="italics"></emph>ex poſito vno abſurdo conſequi poſſe innumera.<emph.end type="italics"></emph.end></s> <s id="s.001328"> Quam<lb></lb>obrem neque vllus exinde concludi poteſt paralogiſ<lb></lb>mus; neque non conſtat quàm variè tua ratiocinatio <lb></lb>peccet, quámque mea illa confiimetur ex confecto <lb></lb>dilemmate, quod repetere nihil eſt neceſſe. </s> <s id="s.001329">Quæſo <lb></lb>etiam, potueriſ-ne paulò antè exaggerere <emph type="italics"></emph>debuiſſe me <lb></lb>primùm demonſtrare ea, quæ à te tanquam falſa reiecta vi<lb></lb>de bam, ex conſtitutis à te principiis nihilominus ſequi, ante<lb></lb>quam eadem, vt tua decreta impeterem,<emph.end type="italics"></emph.end> &c. </s> <s id="s.001330">Scilicet res <lb></lb>præſtita fuerat, & ita quidem, vt te inuitaſſem, ad de<lb></lb>tegendum paralogiſmum, ſi quem ſubeſſe exiſtimares. <lb></lb></s> <s id="s.001331">Miſſum autem facio, vt non modo hoc præterm ſeris, <lb></lb>ſed diſſimulâris etiam incommodum ex hac poſitione <lb></lb>deductum de Progreſſione illa ſpatiorum pluſquam <lb></lb>tripla eodem articulo ſupputata; niſi quod ad calcem <pb pagenum="170" xlink:href="028/01/210.jpg"></pb>eius obiter meminiſti, non tanquam incommodi, ſed <lb></lb>tanquam veræ progreſſionis, quam vano labore re<lb></lb>quiſierim. </s> </p> <p type="main"> <s id="s.001332">Ad duosarticulos ſequenteis, nempe XXXII, & XXXIII, <lb></lb>potiſſimùm ſpectat, quod rursùs es ante conqueſtus <lb></lb><emph type="italics"></emph>me non ſolùm contra expreſſam Epiſtolæ tuæ ſententiam, ſed <lb></lb>contra euidentem quoque demonſtrationis lucem velle à te ea <lb></lb>dici, quæ verbis expreßis negas, quæque falſa eſſe non tantum <lb></lb>pronuncias, ſed clare etiam, atque euidenter demonſtras.<emph.end type="italics"></emph.end></s> <s id="s.001333"> At <lb></lb>quomodo quæſo dicere id potes; cùm ex iam dictis <lb></lb>quæſtio ſit duplex; <emph type="italics"></emph>vna,<emph.end type="italics"></emph.end> an ſit error, percurri ſecundum <lb></lb>ſpatium dimidio temporis, quo primum, tertium trien<lb></lb>re, &c. <emph type="italics"></emph>altera,<emph.end type="italics"></emph.end> an is error ſequatur ex tuis principiis. <lb></lb></s> <s id="s.001334">Tu verò ſic me impetas, quaſi litem tibi mouerim de <lb></lb>prima, non autem ſolùm de ſecunda; & cùm deberes <lb></lb>ipſe tueri errorem non ſequi ex tuis principiis, qua ſola <lb></lb>de re agitur; oſtendas ſolùm errorem eſſe; qua de re nuļ <lb></lb>la eſt controuerſia? </s> <s id="s.001335">Heinc mihi initium articuli XXXII. <lb></lb>fuit, <emph type="italics"></emph>Demonſtras ipſe alia ratione (ſed nimirùm aduerſum te) <lb></lb>non fieri accelerationem pro ſubdiuiſione iſta temporis:<emph.end type="italics"></emph.end> ac tum <lb></lb>recitata membratim tua demonſtratione, aſſenſi vbi<lb></lb>que te verè errorem, incommodumque concludere; ac <lb></lb>monui ſolùm conſtanter, te concludere aduerſus te<lb></lb>ipſum, quatenus error, incommodumque ex tuis prin<lb></lb>cipiis conſequeretur. </s> <s id="s.001336">An dicere igitur potes, <emph type="italics"></emph>me con<lb></lb>tra expreſſam ſententiam, & demonſtrationem tuam velle <lb></lb>te ea dicere, quæ verbis expreßis pronuncias, &c.<emph.end type="italics"></emph.end> cùm non <lb></lb>modò noluerim, verùm ne cogitârim quidem. </s> <s id="s.001337">Sic <lb></lb>cùm articulo XXXIII. oſtendiſſes rurſus tuo modo, ex <lb></lb>comparatione ſecundæ partis cum inferiore primæ di-<pb pagenum="171" xlink:href="028/01/211.jpg"></pb>midio conſequi aliud In<lb></lb>commodum: non repugnaui ego ſimiliter, quin tuo modo <lb></lb>oſtendiſſes; imò & expreſsè admiſi incommodum, <lb></lb>quaſi à te oſtenſum; & excepi ſolùm <emph type="italics"></emph>nihil eſſe, quod ma<lb></lb>gis principij falſitatem proderet, quàm tot repugnantium, at<lb></lb>que abſurdorum capitum deductio.<emph.end type="italics"></emph.end></s> <s id="s.001338"> An ergo etiam illeic <lb></lb>negaui te dicere quæ diceres, aut demonſtrare, quæ de<lb></lb>monſtrares: & non potiùs ſemper in eo ſolùm fui, quòd <lb></lb>cognitus error à te in ſeipſo, & in conſequente multi<lb></lb>plici incommodo; non foret tamen perſpectus in <lb></lb>cauſſa, ſeu in principio antecedente: eo modo, quo po<lb></lb>teſt deformitas pueri agnoſci, & probro haberi ab eo, <lb></lb>qui poteſt non agnoſcere eſſe ſe illius <expan abbr="parentẽ">parentem</expan>; & fami<lb></lb>liare illud eſt, <emph type="italics"></emph>mutato nomine, de te fabula narratur?<emph.end type="italics"></emph.end> <expan abbr="Verũ">Verum</expan> <lb></lb>hæc ſatis, vt inde conſter, tua-ne fuerit iuſta quercla. </s> </p> <p type="main"> <s id="s.001339"><emph type="italics"></emph>Vt porrò ex tuis etiam, &<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei principiis rem euincam, <lb></lb>& eapropemodum omnia, quæ tam acriter nobis obiectas, & <lb></lb>tanquam abſurda tantopere inſectaris, tibi nobiſcum eſſe <lb></lb>communia demonſtrem. </s> <s id="s.001340">Concipe in triangulo AB<emph.end type="italics"></emph.end>C, <emph type="italics"></emph>& <lb></lb>in eius latere AC parteis æqualeis non iam<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.211.1.jpg" xlink:href="028/01/211/1.jpg"></figure><lb></lb><emph type="italics"></emph>ſpatij, ſed temporis<emph.end type="italics"></emph.end> AD, DE, EF, <emph type="italics"></emph>&c. <lb></lb></s> <s id="s.001341">& in<emph.end type="italics"></emph.end> D <emph type="italics"></emph>acquiſitum quem volueris gra<lb></lb>dum velocitatis, expreſſum linea<emph.end type="italics"></emph.end> DG; <emph type="italics"></emph>erit <lb></lb>ex tuis, &<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei principiis acquiſitus in<emph.end type="italics"></emph.end><lb></lb>E <emph type="italics"></emph>gradus ſecundus expreſſus linea<emph.end type="italics"></emph.end> EH, <emph type="italics"></emph>ſic<lb></lb>que velocitas in<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>dupla erit velocitatis in <lb></lb>D.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001342">Quamobrem igitur aggreſſus ar<lb></lb>gumentari ad hominem, & demon<lb></lb>ſtrare tanta volens aduerſus Galileum, <lb></lb>ac me, in ipſo limineaberras? </s> <s id="s.001343">Scilicet neque Galilei, <pb pagenum="172" xlink:href="028/01/212.jpg"></pb>neque mea ſententia eſt, <emph type="italics"></emph>acquiſitum in E gradum ſecun<lb></lb>dum exprimi lineâ EH,<emph.end type="italics"></emph.end> ſed huius lineæ dimidio ſo<lb></lb>lum: ſiquidem tota linea EH non ſecundum modò <lb></lb>gradum exprimit, acquiſitum abvſque D, verùm etiam <lb></lb>primum acquiſitam ab vſque A, ipſumque iunctum <lb></lb>cum ſecundo. </s> </p> <p type="main"> <s id="s.001344"><emph type="italics"></emph>Concludeſ ne igitur velocitatem tempore<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>acquiſi<lb></lb>tam duplam eſſe velocitatis acquiſitæ toto tempore AD?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001345">Non; ſed acquiſitam toto tempore AE: ita vt tem<lb></lb>pore AD acquiratur vnus velocitatis gradus, & illo <lb></lb>perſeuerante, æquiualentéque duobus, quantum ad <lb></lb>ſpatia ſuperanda tempore æquali attinet, acquiratur <lb></lb>interim alius ſuccedente tempore DE, qui cum eo <lb></lb>iunctus fiat aggregatum, quod ſit ipſius duplum, vt <lb></lb>deductum ſuperiùs eſt. </s> </p> <p type="main"> <s id="s.001346"><emph type="italics"></emph>Hoc certè, ſi conceſſeris, cùm tempora<emph.end type="italics"></emph.end> AD, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> DE <lb></lb><emph type="italics"></emph>ponantur æqualia, neceſſe omnino fuerit, vt etiam spatia <lb></lb>æqualibus illis temporibus emenſa inter ſe ſint, vt velocita<lb></lb>tes: acproinde vt spatium ſecundo tempore<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>decurſum ſpa<lb></lb>tii tempore<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>tranſmißi præcisè ſit duplum: non autem (vt <lb></lb>ſtatuit<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileus) triplum.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001347"><emph type="italics"></emph>Si conceſſero?<emph.end type="italics"></emph.end> inquis, atqui vides vt iam negârim, nec <lb></lb>me negaturum ignoraſſe potes: cùm ab initio vſque <lb></lb>controuerſiæ, & à primis illis Reſponſionis articulis <lb></lb>non alia ratione exhibuerim opinionem intelligen<lb></lb>dam; adeò proinde, vt ſi ipſe proſequi velles vlterius, <lb></lb>argumentando ad hominem, contentus eſſe non de<lb></lb>bueris ſola hac interrogatione, & conceſſionem ſup<lb></lb>ponere, quam iure à me non obtineres: ſed ſuppoſita <lb></lb>negatione, vrgere in me aliquid, quod appoſitum ad <pb pagenum="173" xlink:href="028/01/213.jpg"></pb>rem foret. </s> <s id="s.001348">An verò poſſes iam vrgere dilemm<gap></gap>e eo<lb></lb>dem, quo ego in te vſus ſum? </s> <s id="s.001349">Vt poſſis, obſtat pri<lb></lb>mùm, quòd ego ſecundum membrum manifeſtò reſ<lb></lb>puam, cui tamen inhærere te ex ijs, quæ heic habes, in<lb></lb>telligi poteſt: quódque circa primum videas admitte<lb></lb>re me, & manere primum gradum toto tempore DE; <lb></lb>& manendo non eſſe otioſum, ſed agere aliquid; & <lb></lb>agere duplum illius, qui interim acquiritur; & ex dupla <lb></lb>vnius, & ſimplici alteriùs actione ſuperari tria ſpatia: <lb></lb>ac tu non poſſis ex admiſſo à me triplo ſpatio per tem<lb></lb>pus DE percurrendo, deducere incommodum vllum, <lb></lb>vt ego deduxi ex triente temporis, quo tu debes admit<lb></lb>tere DE pro ſpatio ſumptum percurri. </s> <s id="s.001350">Obſtat ſe<lb></lb>cundò, quòd vt facias, mutare duntaxat terminos <lb></lb>oporteat: hoc eſt, vbi ego tempus tu ſpatium; vbi <lb></lb>ego ſpatium tu tempus debeas dicere, vt factitatum <lb></lb>ſuperiùs eſt, cùm retorquere conatus es, quod ego <lb></lb>obieceram, vt defenderem nullum fuiſſe in Galileo <lb></lb>Paralogiſmum. </s> <s id="s.001351">Scilicet confuſio inde ſequitur, è <lb></lb>qua extricari non liceat, neque rem iam ten<lb></lb>to, vt tempori parcam; tametſi ſaltem videretur circa <lb></lb>ea, quæ ſequuntur, tentanda. </s> <s id="s.001352">Adnoto ergo potius, <lb></lb>quod heic infers <emph type="italics"></emph>fore velocitates, vt ſpatia, & ſpatium tem<lb></lb>pore<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>decur ſum fore duplum, non triplum:<emph.end type="italics"></emph.end> negari tibi <lb></lb>conſequutionem; eò quòd aſſumas, vt rem conceſſam <lb></lb>duos gradus velocitatis, qui reperiuntur in tempore <lb></lb>DE, acquiri ambo per illud tempus: cùm tamen ego <lb></lb>velim vnum tantum acquiri, & alium eſſe permanen<lb></lb>tem, præſtantemque duplum illius, qui acquiritur: <lb></lb>adeò vt, coniuncta vtriuſque actione acquiratur ſpatij <pb pagenum="174" xlink:href="028/01/214.jpg"></pb><emph type="italics"></emph>non duplum, ſed triplum.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001353">At ſi <emph type="italics"></emph>hac ratione conuictus velocitatem toto tempore<emph.end type="italics"></emph.end> DE <lb></lb><emph type="italics"></emph>acquiſitam, alterius toto tempore<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>acquiſitæ duplam eſſe <lb></lb>negaueris; maioremque agnoueris, quod in tuis, & Galilei <lb></lb>decretis admittere cogeris: cur tam acriter reprehendis in <lb></lb>nostris?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001354"><emph type="italics"></emph>Conuictus?<emph.end type="italics"></emph.end> & quomodo tandem? <emph type="italics"></emph>Si duplam ne<lb></lb>gem, ſi ma orem agnoſcam?<emph.end type="italics"></emph.end> Ego verò acquiſitam to<lb></lb>to tempore DE neque duplam, neque maiorem, ſed <lb></lb>omninò æqualem illi, quæ acquiritur toto tempore <lb></lb>AD agnoſco. </s> <s id="s.001355">Indeque eſt illa definitio motus æqua<lb></lb>biliter accelerati, quod, <emph type="italics"></emph>temporibus æqualibus æqualiæ <lb></lb>acquirat velocitatis incrementa:<emph.end type="italics"></emph.end> & hoc ſolum eſt, quod <lb></lb>in meis, & Galilei decretis admittere cogor: ac iure <lb></lb>idcircò reprehendo in tuis, quód cogaris admittere ad<lb></lb>uerſus propriam definitionem, <emph type="italics"></emph>æqualibus spatiis æqua<lb></lb>lia momenta velocitatis non acquiri.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001356"><emph type="italics"></emph>Placet ne verò etiam, vt de velocitate tempore<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>ac<lb></lb>quiſita perpendamus, cuiuſnam alterius velocitatis ſit <lb></lb>æqualis?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001357">Placet; quandò res cordi eſt, & tantopere tibi pla<lb></lb>cet tuum illud de deducendo infra initium initio, ab <lb></lb>ipſo putà S, <gap></gap>nuentum. </s> </p> <p type="main"> <s id="s.001358"><emph type="italics"></emph>Temporibus<emph.end type="italics"></emph.end> AD, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>bifariam diuiſis in<emph.end type="italics"></emph.end> S, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> K, <lb></lb><emph type="italics"></emph>erit adhùc ex tuis, &<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei decretis velocitas acquiſita in<emph.end type="italics"></emph.end><lb></lb>D <emph type="italics"></emph>dupla velocitatis in<emph.end type="italics"></emph.end> S: <emph type="italics"></emph>ſicut velocitas acquiſita in<emph.end type="italics"></emph.end> E <emph type="italics"></emph>dupla <lb></lb>est velocitatis acquiſitæ in<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>& velocitates omnes, ac ſingulæ <lb></lb>inter<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> E <emph type="italics"></emph>deſignabiles, duplæ quoque erunt velocitatis <lb></lb>alterius inter<emph.end type="italics"></emph.end> S, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> D <emph type="italics"></emph>aßignabilis: vt velocitas<emph.end type="italics"></emph.end> KL, <emph type="italics"></emph>me<lb></lb>dia inter<emph.end type="italics"></emph.end> D <emph type="italics"></emph>&<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>dupla erit velocitatis in<emph.end type="italics"></emph.end> VX <emph type="italics"></emph>mediæ<emph.end type="italics"></emph.end><pb pagenum="175" xlink:href="028/01/215.jpg"></pb><emph type="italics"></emph>inter<emph.end type="italics"></emph.end> S, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>& ita de cæteris.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001359">Concedo; hæc enim reuerâ in opinionem, quam <lb></lb>ſequor, quadrant, ſecus ac in tuam, quæ tantoperè <lb></lb>auerſatur progredi adhuc, promouendo comparatio<lb></lb>nem vltra S verſus A, ne initium magis verſus initium <lb></lb>promoueatur. </s> <s id="s.001360">Concedo, inquam, quatenus hæ omnes <lb></lb>velocitates ab A incipiunt, & eandem inter ſe ratio<lb></lb>nem, quam ipſa tempora obſeruant. </s> </p> <p type="main"> <s id="s.001361"><emph type="italics"></emph>Ex quo neceſſariò conſequens eſt, vt tota velocitas acquiſi<lb></lb>ta toto tempore<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>præcisè, & exactè dupla ſit velocitatis <lb></lb>acquiſitæ toto tempore<emph.end type="italics"></emph.end> SD. </s> </p> <p type="main"> <s id="s.001362">Tametſi punctum, à quo incipiunt velocitates, iam <lb></lb>varies: concedo nihilominus, & neque id modò, ſed <lb></lb>etiam velocitatem acquiſitam tempore DE duplam <lb></lb>eſſe acquiſitæ tempore AS, & tempore DK, & tem<lb></lb>pore KE. </s> <s id="s.001363">Nempe acquiſita tempore DE non eſt tota <lb></lb>EH, vt falsò ſupponis, ſed eius dimidium, quod pro<lb></lb>inde duplum eſt non totius DG, quam falsò totam <lb></lb>acquiſitam ſupponis ab S, in D, ſed dimidij eius dun<lb></lb>taxat. </s> <s id="s.001364">Hoc autem cùm æquale ſit acquiſitæ ab A in S, <lb></lb>à D in K, à K in E: ideò acquiſita à D in E, pari modo <lb></lb>eſt earum omnium dupla. </s> </p> <p type="main"> <s id="s.001365"><emph type="italics"></emph>Non autem totius acquiſitæ tempore<emph.end type="italics"></emph.end> AD. </s> </p> <p type="main"> <s id="s.001366">Et quis, cui hoc dixit, acquiſitam tempore DE, du<lb></lb>plam eſſe acquiſitæ tempore AD, niſi ipſe tibi? </s> </p> <p type="main"> <s id="s.001367"><emph type="italics"></emph>Vides igitur in tua quoque, &<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei ſententia perinde, <lb></lb>atque eadem ratione, qua in noſtra, velocitatem ſecunda parte<emph.end type="italics"></emph.end><lb></lb>DE <emph type="italics"></emph>acquiſitam non totius velocitatis acquiſitæ in prima parte<emph.end type="italics"></emph.end><lb></lb>AD <emph type="italics"></emph>duplam eſſe, ſed velocitatis acquiſitæ in vltima eius me<lb></lb>dietate<emph.end type="italics"></emph.end> SD. </s> </p> <pb pagenum="176" xlink:href="028/01/216.jpg"></pb> <p type="main"> <s id="s.001368">Nego, <emph type="italics"></emph>videre me perinde, atque eadem ratione.<emph.end type="italics"></emph.end></s> <s id="s.001369"> Nam <lb></lb>in mea quidem, & Galilei ſententia ſumendo has <lb></lb>parteis DE, AD, SD pro partibus <lb></lb><figure id="id.028.01.216.1.jpg" xlink:href="028/01/216/1.jpg"></figure><lb></lb>temporis, res eſt neceſſaria; at in tua, <lb></lb>ſumendo eaſdem pro partibus ſpatij, <lb></lb>oſtenſum iam eſt velocitatem per DE <lb></lb>debere eſſe duplam velocitatis per AD. <lb></lb></s> <s id="s.001370">Et oſtendetur paulò pòſt non probari <lb></lb>duplam velocitatis per SD, niſi ipſum<lb></lb>met petendo principium. </s> </p> <p type="main"> <s id="s.001371"><emph type="italics"></emph>Eadem quoque ratione cogéris fateri ve<lb></lb>locitatem tertio tempore<emph.end type="italics"></emph.end> EF <emph type="italics"></emph>acquiſitam ve<lb></lb>locitatis primo tempore acquiſitæ triplam ſo<lb></lb>lùm non eſſe, ſed triplo maiorem.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001372">Nempe hoc placet ex abundanti: vide ergo perpe<lb></lb>tuum aduerſus nos paralogiſmum. </s> <s id="s.001373">Nam vt hactenùs <lb></lb>falsò ſuppoſuiſti velle nos totam velocitatem EH, quæ <lb></lb>dupla eſt velocitatis DG, acquiſitam eſſe ſolo tempo<lb></lb>re DE, quam acquiſitam tamen facimus toto tempore <lb></lb>AE, cùm ratiocinatio noſtra conſtans ſit, vt AD, ad <lb></lb>DG, ita AE ad EH; non autem vnquam, vt AD ad <lb></lb>DG, ita DE ad EH: vt hactenus, inquam, id falsò <lb></lb>ſuppoſuiſti; ſic falsò iam ſupponis velle nos totam ve<lb></lb>locitatem FI, quæ tripla eſt eiuſdem velocitatis DG, <lb></lb>acquiſitam eſſe ſolo tempore EF, quam acquiſitam ſta<lb></lb>tuimus toto tempore AF: cùm conſtanter dicamus, vt <lb></lb>AD, ad DG, ita AF ad FI; neque tu oſtendere poſ<lb></lb>ſis dixiſſe vnquam nos, vt AD ad DG, ita EF ad FI. </s> </p> <p type="main"> <s id="s.001374"><emph type="italics"></emph>Deſignata enim ex<emph.end type="italics"></emph.end> D <emph type="italics"></emph>verſus<emph.end type="italics"></emph.end> A <emph type="italics"></emph>tertia parte totius<emph.end type="italics"></emph.end> AD, <lb></lb><emph type="italics"></emph>quæ ſit<emph.end type="italics"></emph.end> DY, <emph type="italics"></emph>ſumptaque ipſi æquali<emph.end type="italics"></emph.end> DZ, <emph type="italics"></emph>erit totum tempus<emph.end type="italics"></emph.end><pb pagenum="177" xlink:href="028/01/217.jpg"></pb>AE <emph type="italics"></emph>treis in parteis ęqualeis diuiſum, ob <expan abbr="eãque">eanque</expan> cauſſam velocitas <lb></lb>in<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>tripla erit velocitatis acquiſitæ in<emph.end type="italics"></emph.end> Y. <emph type="italics"></emph>Sed eadem etiam <lb></lb>ratione velocitas in<emph.end type="italics"></emph.end> F <emph type="italics"></emph>tripla eſt velocitatis acquiſitæ in<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>& <lb></lb>alia quælibet velocitas deſignabilis inter<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> F <emph type="italics"></emph>tripla ſem<lb></lb>per eſt velocitatis alterius inter<emph.end type="italics"></emph.end> Y, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> D <emph type="italics"></emph>acquiſitæ. </s> <s id="s.001375">Tota <lb></lb>igitur velocitas toto tempore<emph.end type="italics"></emph.end> EF <emph type="italics"></emph>acquiſita tripla eſt non to<lb></lb>tius velocitatis toto tempore<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>acquiſitæ, ſed velocitatis ac<lb></lb>quiſitæ ſola parte primi temporis<emph.end type="italics"></emph.end> YD, <emph type="italics"></emph>quæ pluſquam tripla <lb></lb>eſt, totius velocitatis toto tempore<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>acquiſitæ, vt per ſe <lb></lb>notum eſt.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001376">Quid, negato falſo principio, notum per ſe ſit, aut <lb></lb>non ſit; conſtat abundè ex iam dictis. </s> </p> <p type="main"> <s id="s.001377"><emph type="italics"></emph>Habes igitur heic quoque in tua, &<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei ſententia il<lb></lb>lud ipſum, quod tantopere in noſtra inſecturis.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001378">Imò nihil minùs. </s> </p> <p type="main"> <s id="s.001379"><emph type="italics"></emph>Ex quibus, opinor, iam intelligis eadem omnia, quæ tan<lb></lb>quam abſurda, & inter ſe pugnantia nobis obiicis, poſſe in <lb></lb>te pari modo, atque impetu retorqueri. </s> <s id="s.001380">Quid enim prohibet, <lb></lb>vt ego quoque velis, nolis, dicam coniunctum eſſe cum tuis <lb></lb>principiis neceſſariò, vt velocitas acquiſita tempore<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>du<lb></lb>pla ſit velocitatis acquiſitæ tempore<emph.end type="italics"></emph.end> AD, <emph type="italics"></emph>& cùm ea tempora <lb></lb>æqualia ſint, manifestum conſequenter eſſe spatium ſecundo <lb></lb>tempore emenſum, spatij priore tempore emenſi, eſſe præcisè <lb></lb>duplum; ac proinde ex<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei principiis, ac tuis, ſpatia tempo<lb></lb>ribus æqualibus percurri (vt ego contendo) in continua ratione <lb></lb>dupla. </s> <s id="s.001381">Id enim ex ea ſuppoſitione neceßarium est.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001382">Cùm id totum ſit adò falſum, adeóque falsò ſuppo<lb></lb>ſitum, vt ſæpiùs iam oſtenſum eſt: non eſt quòd hanc <lb></lb>tibi gloriationem inuideam. </s> </p> <p type="main"> <s id="s.001383"><emph type="italics"></emph>Quòd ſi fortè nihilominùs reclames, contendaſque veloci-<emph.end type="italics"></emph.end><pb pagenum="178" xlink:href="028/01/218.jpg"></pb><emph type="italics"></emph>tatem per totum tempus<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>acquiſitam totius velocitatis per <lb></lb>totum primum tempus<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>acquiſitæ non eſſe duplam, ſed <lb></lb>eius potiùs veiocitatis, quæ vltima primi illius temporis medie<lb></lb>tate, ſcu tempore<emph.end type="italics"></emph.end> SD <emph type="italics"></emph>acquiſita ſit; tum inſtabo acriùs, teque <lb></lb>pugnantia loqui conteſtabor.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001384">Cùm hanc eſſe meam ſententiam agnoſcas; ipſam <lb></lb>debebas impetere, non ſpuriam aſſingens (vocem con<lb></lb>donabis, quandò tua eſt) euidenter <foreign lang="grc">πα<gap></gap>λογιζ<gap></gap>. </foreign></s> <s id="s.001385">Nunc <lb></lb>verò ſaltem cur non <emph type="italics"></emph>inſtas acrius?<emph.end type="italics"></emph.end> Cur non <emph type="italics"></emph>me pugnan<lb></lb>tia loqui contestaris?<emph.end type="italics"></emph.end> Cur intentaſſe minas ſat eſt? </s> </p> <p type="main"> <s id="s.001386"><emph type="italics"></emph>Et, ſi demonſtrare contendas velocitatem tempore<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>ac<lb></lb>quiſitam velocitatis toto primo tempore<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>acquiſitæ non eſſe <lb></lb>præcisè duplam, ſed dupla maiorem: tantò euidentiorem inde <lb></lb>concludam principiorum tuorum, ac decretorum abſurditatem, <lb></lb>ex quibus tam apertè pugnantia concludantur: cùm fieri non <lb></lb>poßit, vt velocitas acquiſita in<emph.end type="italics"></emph.end> E, <emph type="italics"></emph>velocitatis acquiſitæ in<emph.end type="italics"></emph.end> D <lb></lb><emph type="italics"></emph>ſit dupla, quin velocitas quoque toto tempore<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>acquiſita <lb></lb>velocitatis toto tempore<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>acquiſitæ ſit dupla.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001387">Dicerem heic aliquid, niſi depugnares aduerſus <lb></lb>tuam vmbram. </s> </p> <p type="main"> <s id="s.001388"><emph type="italics"></emph>Quodque amplius eſt, hac tota in re babeo te confitentem <expan abbr="reũ">reum</expan>: <lb></lb>cùm tu rem ita eſſe, ac neceſſariò admittendam eſſe contendas.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001389">Scilicet? </s> </p> <p type="main"> <s id="s.001390"><emph type="italics"></emph>Tuo igitur, opinor, Exemplo admonitus, agnoſces tandem, <lb></lb>ſeu velocitas æqualibus temporibus, ſeu ſpatiis æqualibus æqua<lb></lb>biliter augeri ſupponatur, non modò non abſurdum, aut à recta <lb></lb>ratione abhorrens, ſed prorsùs neceßarium eße, vt velocitas <lb></lb>tota ſecunda parte temporis, aut spatii acquiſita, nunquam <lb></lb>ſit totius velocitatis tota prima parte acquiſitæ præcisè dupla, <lb></lb>ſed potiùs, vt totius velocitatis ſola poſtrema medietate eiuſ-<emph.end type="italics"></emph.end><pb pagenum="179" xlink:href="028/01/219.jpg"></pb><emph type="italics"></emph>dem primæ partis (qualis eſt<emph.end type="italics"></emph.end> SD) <emph type="italics"></emph>acquiſitæ perfectè dupla <lb></lb>reperiatur: & ſimiliter, vt tota velocitas tertia, aut quarta <lb></lb>parte, &c. </s> <s id="s.001391">acquiſita, tripla non ſit, aut quadrupla totius ve<lb></lb>locitatis per primam partem acquiſitæ, ſed eius præcisè veloci<lb></lb>tatis, quæ tertia, aut quarta parte inferiore eiuſdem partis <lb></lb>primæ acquiſita fuerit. </s> <s id="s.001392">Itaque quicquid aduerſus has pro<lb></lb>poſitiones magna tuæ Responſionis parte opponis, aut ex ſup<lb></lb>poſitis earum contrariis colligis, ac concludis, vanum ſine du<lb></lb>bio, atque inane eſt; quamuis apud harum rerunt minùs pe<lb></lb>ritos plauſum inuenire poßint, atque approbationem.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001393">Cuius momenti iſta ſint, expendendum eſt ex hacte<lb></lb>nus dictis. </s> <s id="s.001394">Moneo ſolùm breuiter quatuor, Primum, <lb></lb>velle te <expan abbr="perperã">perperam</expan>, eſſe perin de ſeu ſpatiis, ſeu temporibus <lb></lb>acquiſita velocitatis incrementa exæquentur. </s> <s id="s.001395">Secun<lb></lb>dum, iniuriam à te ſemper fieri miſerando illi dimidio <lb></lb>partis primæ priori: vt cuius rationem <expan abbr="nullã">nullam</expan> vnquam <lb></lb>habeas. </s> <s id="s.001396">Tertium, noſcendum eſſe deinceps quo fru<lb></lb>ctu volueris hæc præoccupata in gratiam eorum, quæ <lb></lb>ſunt dicenda circa articulos ſequenteis. </s> <s id="s.001397">Quartum, ſi <lb></lb>mihi proferre poſſis vel vnum <emph type="italics"></emph>peritum,<emph.end type="italics"></emph.end> qui à tua ſen<lb></lb>tentia ſtet, & apud quem plauſum, approbationemque <lb></lb>inuenias, vltrò me in eandem ſententiam iturum. </s> </p> <p type="main"> <s id="s.001398"><emph type="italics"></emph>Ruit itaque quod iam numero tuæ Responſionis xii. </s> <s id="s.001399">ab<lb></lb>ſurdum infers, & <expan abbr="iterũ">iterum</expan> numero xlii. </s> <s id="s.001400">tangis: futurum ſcilicet, <lb></lb>vt tempore quocumque dato putà vno horæ minuto primo; quo <lb></lb>decurſa ſupponatur deſignati ſpatii pars quæcumque prima, vt<emph.end type="italics"></emph.end><lb></lb>AD, <emph type="italics"></emph>tempus aliud deſignato illi æquale attingt antè non poſ<lb></lb>ſit, quàm ab eodem mobili decurſum fuerit ſpatium infinitum: <lb></lb>Cùm enim abſurdum hoc aliunde non concludas, niſi ex falſa <lb></lb>hypotheſi, quòd ſpatij pars ſecunda dimidio primi temporis,<emph.end type="italics"></emph.end><pb pagenum="180" xlink:href="028/01/220.jpg"></pb><emph type="italics"></emph>& conſequenter tertia & quartapars, tertia, & quarta parte <lb></lb>primi eiuſdem temporis decurrantur: iamque ex tuis etiam <lb></lb>principiis, ea ſuppoſitio falſa, & impoßibilis oſtenſa ſit: <lb></lb>euerſo malè iacto fundamento, tota ſuperexſtructa moles <lb></lb>corruit.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001401">Concluſi ego illud abſurdum ex hypotheſi falſa <lb></lb>quidem, ſed non vt falſa, verùm vt tua; & tu oſtendens <lb></lb>falſam ſeu ex tuis, ſeu ex meis principiis, lucratus nihil <lb></lb>es, lucraturus ſolùm, ſi oſtendere non-tùam potuiſſes. <lb></lb></s> <s id="s.001402">Itaque & ſemper monui, & <expan abbr="iterũ">iterum</expan> moneo moneboque <lb></lb>iterùm, nihil eſſe opus, vt eſſe probes falſum, <emph type="italics"></emph>Partem <lb></lb>ſecundam spatii percurri dimidio temporis, quo primam:<emph.end type="italics"></emph.end> ſed <lb></lb>opus eſſe, vt oſtendas id non eſſe tuum, hoc eſt non ex<lb></lb>preſsè aſſumptum à te vt verum, neceſſariumque prin<lb></lb>cipium, quo Paralogiſmi Galileum argueres; & non <lb></lb>neceſſariò conſequi ex eo, quod defendis velocitates <lb></lb>ſe habere vt ſpatia. </s> <s id="s.001403">Nempe hoc poſterius <emph type="italics"></emph>fundamentum<emph.end type="italics"></emph.end><lb></lb>eſt, quòd vt <emph type="italics"></emph>male iactum euertendum ſit,<emph.end type="italics"></emph.end> ſi contendas qui<lb></lb>dem, vt tam illud <emph type="italics"></emph>abſurdum,<emph.end type="italics"></emph.end> quàm <emph type="italics"></emph>tota ſuperexſtructa mo<lb></lb>les corruat.<emph.end type="italics"></emph.end></s> <s id="s.001404"> Quod interim putas abſurdum euerſum, <lb></lb>non tantùm quatenus obiectum eſt tibi articulo XII. <lb></lb>ſed etiam quatenus obiicitur poſteà articulo xlii. </s> <s id="s.001405">id <lb></lb>haud rectè putas. </s> <s id="s.001406">Siquidem illeic non concluſi ex <lb></lb>hac eadem hypotheſi, ſed ex alia itidem tua, qua nimi<lb></lb>rùm vis accelerationem non ab vſque principio, ſed à <lb></lb>medio vſque duntaxat primæ partis inchoandam eſſe: <lb></lb>adeò vt cùm nihil ad hoc habeas, non ſit cur inuoluas <lb></lb>quod dixi articulo xij. </s> <s id="s.001407">cum eo, quod deinceps articulo <lb></lb>xlii. </s> <s id="s.001408">neque cur etiam illo ruente, iſtud ſic putes corrui<lb></lb>turum, vt ariete nouo non indigeat. </s> </p> <pb pagenum="181" xlink:href="028/01/221.jpg"></pb> <p type="main"> <s id="s.001409"><emph type="italics"></emph>Similiter vanus etiam eſt labor ille tuus, quo numero<emph.end type="italics"></emph.end> 31. <lb></lb><emph type="italics"></emph>ex eadem falſa ſuppoſitione modum alium accelerationis, spa<lb></lb>tiorumque ſingulis temporibus percurrendorum progreſſum <lb></lb>ſcrutaris. </s> <s id="s.001410">Quid enim veri, ac certi ex falſis legitimè con<lb></lb>cluderes?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001411">Heic loci eſt, in quo antè præmonui te loquutu<lb></lb>rum obiter de progreſſu per ſpatia in ratione pluſquam <lb></lb>tripla futuro æqualibus temporibus, quem ego qui<lb></lb>dem & ſcrutarer, & monſtrarem falſum, vt falſitatis <lb></lb><expan abbr="conuincerẽ">conuincerem</expan> hypotheſin, è qua crueretur: tu verò, cùm <lb></lb>deberes oſtendere eandem hypotheſin non deduci ex <lb></lb>tuo principio, ne ipſum quoque ipſa eadem falſitate <lb></lb>inuolueres, ita loquereris de eo progreſſu, quaſi ego <lb></lb>ipſum vt verum ex falſa hypotheſi vano labore per<lb></lb>ſcrutarer. </s> <s id="s.001412">Vnde & iuuit tequærere, <emph type="italics"></emph>Quid veri, ac certi <lb></lb>ex falſis legitimè concluderem?<emph.end type="italics"></emph.end> Quaſi ignorares me con<lb></lb>cludere ipſum falſum: aut neſcires, quod tyrones no<lb></lb>runt, tam verum, quàm falſum poſſe legitimè concludi <lb></lb>ex falſis: ac ſpeciatim demonſtrationem ducentem ad <lb></lb>incommodum (qualis mea fuit argumentatio) non alia <lb></lb>progredi ratione? </s> </p> <p type="main"> <s id="s.001413"><emph type="center"></emph>IN ARTICVLOS XXXIV. XXXV. XXXVI. XXXVII. <lb></lb>XXXVIII. </s> <s id="s.001414">De Tempore, quo R. P. colligit ſingulas <lb></lb>parteis decurſum iri.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001415"><emph type="italics"></emph>Fruſtrà item ſunt, quæ numeris xxxv. </s> <s id="s.001416">xxxvi. </s> <s id="s.001417">xxxvii. <lb></lb></s> <s id="s.001418">ac xxxviii. </s> <s id="s.001419">proſequeris, vt eam propoſitionem refellas, qua <lb></lb>contendo velocitatem tota ſecunda parte<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>acquiſitam <lb></lb>præcisè duplam eſſe totius velocitatis per inferiorem primæ<emph.end type="italics"></emph.end><pb pagenum="182" xlink:href="028/01/222.jpg"></pb><emph type="italics"></emph>partis medietatem<emph.end type="italics"></emph.end> SD <emph type="italics"></emph>acquiſitæ: & ſimiliter velocitatem <lb></lb>per tertiam, & quartam partem, &c. </s> <s id="s.001420">acquiſitam, exactè tri<lb></lb>plam eſſe, ant quadruplam non velocitatis, quæ per totam pri<lb></lb>mam partem<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>acquiſita ſit, ſed eius præcisè velocitatis, <lb></lb>quæ tota tertia, aut quarta parte inferiore eiuſdem primæ par<lb></lb>tis acquiſita fuerit. </s> <s id="s.001421">Nullum enim non moues lapidem, vt <lb></lb>hanc veritatem euertas, quam tamen paulò antè tuis pincipiu <lb></lb>innixam, & ſtabilitam agnouisti; & quam ſi vmquam <lb></lb>eucrteres, tuam quoque, ac<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei ſententiam funditùs euer<lb></lb>teres. </s> <s id="s.001422">Si enim velocitas ſecundo tempore acquiſita velocitatis <lb></lb>primo tempore acquiſitæ eſſet dupla, & fimiliter velocitas ter<lb></lb>tio, & quarto tempore acquiſita eiuſdem velocitatis primæ tri<lb></lb>pla eſſet, & quadrupla, spatia temporibus illis æqualibus de<lb></lb>curſa in eademinter ſe eſſent ratione: nempe in ratione dupla, <lb></lb>tripla, & quadrupla contra<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei mentem, ac tuam.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001423">Hæc iam attinent ad Secundum membrum proba<lb></lb>tionis præcipuæ, qua ſequelam propoſitionis Demon<lb></lb>ſtrationis tuæ confirmas. </s> <s id="s.001424">Miſſum autem facio, quod <lb></lb>ais de mea, & Galilei ſententia, quandò ex paulò antè <lb></lb>deductis adeò manifeſtè intelligitur, fore vt potiùs ma<lb></lb>ri flammam, & terram cælo commiſceas, quàm ex Ga<lb></lb>lilei contextu, aut mea Reſponſione id probes, quod <lb></lb>heic aſſeris, aut euincere valeas cuertere me agnitam à <lb></lb>me veritatem. </s> <s id="s.001425">Quod ſupereſt autem cùm tua ſenten<lb></lb>tia tum verſibus hiſce, tum hactenus toties repetita ſit, <lb></lb><emph type="italics"></emph>velocitatem tota ſecunda parte<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>acquifitam præcisè du<lb></lb>plam eſſe totius velocitatis per inferiorem primæ partis medie<lb></lb>tatem<emph.end type="italics"></emph.end> SD <emph type="italics"></emph>acquiſitæ fimiliterque, &c.<emph.end type="italics"></emph.end></s> <s id="s.001426"> Quæſote primùm, <lb></lb>quomodo nam ipſam hactenùs ſtabiliiſti? </s> <s id="s.001427">Nam ſi <lb></lb>to r<gap></gap>u<gap></gap>ra ſtabiliiſſe probes, fruſtrà ſit omnis meus la-<pb pagenum="183" xlink:href="028/01/223.jpg"></pb>bor: ſi verò non probes, fruſtrà omnis tuus. </s> <s id="s.001428">An ergo <lb></lb>alia ratione probas, quam quæ habetur numero tuæ <lb></lb>Diſſertationis XXXIV. pro ſecunda parte comparata <lb></lb>cum primæ partis inferiore dimidio; & XXXVII. pro <lb></lb>quarta comparata cum triente: ac xxxviij. </s> <s id="s.001429">pro <lb></lb>quarta comparata cum quadrante? </s> <s id="s.001430">Non certe. </s> <s id="s.001431">Ita<lb></lb>que quid id ſit videamus, ac circa partem ſpeciatim ſe<lb></lb>cundam (cùm eadem ſit ratio proportione de cæteris) <lb></lb>nam & tametſi res videatur eſſe iam abundè confecta: <lb></lb>operætamen <expan abbr="pretiũ">pretium</expan> eſt ipſam præſertim heic adnotare. </s> </p> <p type="main"> <s id="s.001432">Aſſumptâ illeic lineâ AB, diuiſa in parteis æqua<lb></lb>leis AD, DE, &c. </s> <s id="s.001433">ac prima parte biſecti in S, <lb></lb><figure id="id.028.01.223.1.jpg" xlink:href="028/01/223/1.jpg"></figure><lb></lb>expreſſa ſententia hiſce verbis exſtat <emph type="italics"></emph>Tota<emph.end type="italics"></emph.end> DE <lb></lb><emph type="italics"></emph>eodem præcisè tempore, quo pars<emph.end type="italics"></emph.end> SD <emph type="italics"></emph>tranſcurritur.<emph.end type="italics"></emph.end><lb></lb>Tum probatio hæc additur, <emph type="italics"></emph>Cùm enim<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>du<lb></lb>pla ponatur ipſius<emph.end type="italics"></emph.end> AS, <emph type="italics"></emph>& ſimiliter<emph.end type="italics"></emph.end> AE <emph type="italics"></emph>dupla ſit <lb></lb>ipſius<emph.end type="italics"></emph.end> AD, <emph type="italics"></emph>neceſſe eſt, vt velocitas in<emph.end type="italics"></emph.end> D, <emph type="italics"></emph>dupla ſit <lb></lb>velocitatis in<emph.end type="italics"></emph.end> S, <emph type="italics"></emph>& velocitas in<emph.end type="italics"></emph.end> E <emph type="italics"></emph>eodem modo du<lb></lb>pla reperiatur velocitatis in D.<emph.end type="italics"></emph.end></s> <s id="s.001434"> Deducis conſe<lb></lb>quenter velocitatem per totam DE eſſe du<lb></lb>plam velocitatis per totam SD: ſed quod caput <lb></lb>eſt, peruideamus. </s> <s id="s.001435">Neceſſe dicis <emph type="italics"></emph>velocitatem in<emph.end type="italics"></emph.end><lb></lb>D, <emph type="italics"></emph>eſſe duplam velocitatis in<emph.end type="italics"></emph.end> S, <emph type="italics"></emph>& velocitatem in<emph.end type="italics"></emph.end> E <lb></lb><emph type="italics"></emph>velocitatis in<emph.end type="italics"></emph.end> D, eo argumento, <emph type="italics"></emph>quòd<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>dupla <lb></lb>ſit ipſius<emph.end type="italics"></emph.end> AS, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> AE <emph type="italics"></emph>ipſius<emph.end type="italics"></emph.end> AD. </s> <s id="s.001436">Quomodo <lb></lb>ergo neceſſitatem huius conſequutionis pro<lb></lb>bas? </s> <s id="s.001437">Nam hoc opus, hic labor eſt. </s> <s id="s.001438">Quomodò, <lb></lb>inquam, ex eo, quòd <emph type="italics"></emph>spatium<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>duplum ſit spatij<emph.end type="italics"></emph.end><lb></lb>AS, <emph type="italics"></emph>ſpatium<emph.end type="italics"></emph.end> AE <emph type="italics"></emph>spatij<emph.end type="italics"></emph.end> AD, ſequi neceſſariò, <emph type="italics"></emph>vt <lb></lb>velocitas in D dupla ſit velocitatis in S, & velocitas in<emph.end type="italics"></emph.end><pb pagenum="184" xlink:href="028/01/224.jpg"></pb><emph type="italics"></emph>E, velocitatis in D?<emph.end type="italics"></emph.end> Id ſanè non probas, ſed ſolùm <lb></lb>ſupponis ex eo vim habere, <emph type="italics"></emph>quòd velocitates ſicut spa<lb></lb>tia ſint.<emph.end type="italics"></emph.end></s> <s id="s.001439"> Atqui hæc ipſa eſt controuerſia, <emph type="italics"></emph>an velocita<lb></lb>tes inter ſe ſicut ſpatia ſint:<emph.end type="italics"></emph.end> neque idipſum, quod opus <lb></lb>eſt, probas, ſed omninò principium petis, ſeu ipſam <lb></lb>quæſtionem, remve controuerſam pro principio aſſu<lb></lb>mis. </s> <s id="s.001440">An verò dices te probaſſe, <emph type="italics"></emph>velocitates eſſe vt ſpa<lb></lb>tia?<emph.end type="italics"></emph.end> Sed quæſo, vbi-nam? </s> <s id="s.001441">Id enim nuſquam de<lb></lb>prehendetur? </s> <s id="s.001442">An vbi voluiſti arguere Galileum Pa<lb></lb>ralogiſmi? </s> <s id="s.001443">At abundè iam <expan abbr="declaratũ">declaratum</expan> eſt te potiùs vſum <lb></lb>paralogiſmo, cùm rurſus nihil aliud, quàm principium <lb></lb>petieris: vt taceam te, ſi quid habuiſti probationis, id<lb></lb>poſteà negaſſe: quando negaſti <emph type="italics"></emph>ſi prima pars spatij per<lb></lb>curratur quadrante, percurri ſecundam dimidio quadrantis,<emph.end type="italics"></emph.end><lb></lb>An vbi demùm protuliſti <emph type="italics"></emph>tuum de Bilance Experimen<lb></lb>tum?<emph.end type="italics"></emph.end> Certè iſta vna probatio fuit tua, neque potes pro<lb></lb>ferre locum, in quo alia ratione probaueris <emph type="italics"></emph>velocitates <lb></lb>ſe habere vt spatia.<emph.end type="italics"></emph.end></s> <s id="s.001444"> Atqui & falſum deprehenſum Ex<lb></lb>perimentum tuum eſt; & quæ germana fuit Experien<lb></lb>tia falſum conuicit <emph type="italics"></emph>velocitates ſe inter ſe habere vt <lb></lb>spatia.<emph.end type="italics"></emph.end></s> <s id="s.001445"> Itaque ex his ſequitur, non modo neceſſe non <lb></lb>eſſe: ſed falſum etiam, atque adeò prorsùs impoſſibile, <lb></lb>vt <emph type="italics"></emph>velocitas in D, dupla ſit velocitatis in S, & velocitas in <lb></lb>E, velocitatis in D.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001446">Cùm ergo non modò probatum non ſit, ſed fal<lb></lb>ſum quoque & impoſſibile ipſa Experientia ſuffra<lb></lb>gante oſtenſum, <emph type="italics"></emph>velocitatem tota ſecunda parte<emph.end type="italics"></emph.end> DE <lb></lb><emph type="italics"></emph>acquiſitam pręcisè duplam eſſe totius velocitatis per inferio<lb></lb>rem primæ partis medietatem<emph.end type="italics"></emph.end> SD, <emph type="italics"></emph>acquiſitæ, ſimiliterque, &c.<emph.end type="italics"></emph.end><lb></lb>Quæſo quî adhûc valeas talem ſententiam defendere, <pb pagenum="185" xlink:href="028/01/225.jpg"></pb>querique, quòd nullum non mouerim lapidem <emph type="italics"></emph>ad euer<lb></lb>tendum hanc veritatem?<emph.end type="italics"></emph.end> Atque ego quidem, quòd ex<lb></lb>inde inferres, <emph type="italics"></emph>Tempus, quo percurritur DE, eſſe præcisè <lb></lb>æquale tempori, quo percurritur SD,<emph.end type="italics"></emph.end> ob duplam nempe <lb></lb>velocitatem, ſicuti ſpatium duplum eſt, huiuſcemodi <lb></lb>lapides, & articulis quidem XXXV. ac XXXVI. moui, I. <lb></lb>fore, vt ſuppoſito tempore, quo percurritur SD, <lb></lb>minutorum v. c. duorum, idem ſpatium SD, <lb></lb>percurreretur ſimùl minuto vno cum triente, ſiue ſe<lb></lb>cundis 80: ac rurſus ſecundis 53, ac iterum 18, iterumque <lb></lb>6, &c. </s> <s id="s.001447">II. </s> <s id="s.001448">Cùm aliunde ſtatuiſſes tempus per SD, bre<lb></lb>uius eſſe tempore per AS, fore tamen ipſi æquale. </s> <s id="s.001449">III. <lb></lb></s> <s id="s.001450">Tempus per DE non æquale fore, ſed ſeſquialterum <lb></lb>temporis per SD. IV. Futurum, vt aut concluderes ni<lb></lb>hil, aut vtereris paralogiſmo, quo Galileum vſum cauſ<lb></lb>ſareris. </s> <s id="s.001451">V. Fore, vt quæuis magnitudo, etiam ſemi<lb></lb>diameter Mundi, tantulo tempore, quantulo SD li<lb></lb>neola percurreretur. </s> <s id="s.001452">Quæ eadem rursus incommoda <lb></lb>proportione deducta ſunt circa partem tertiam com<lb></lb>paratam cum infimo eiuſdem primæ partis triente, ar<lb></lb>ticulo XXXVIII. </s> <s id="s.001453">Quomodo porrò tu excepiſti, reieciſti<lb></lb>ve hos lapides? </s> <s id="s.001454">Scilicet hoc loco dixiſſe contentus, <lb></lb><emph type="italics"></emph>fruſtrà eſſe:<emph.end type="italics"></emph.end> niſi quod iſthæc inſuper habes. </s> </p> <p type="main"> <s id="s.001455"><emph type="italics"></emph>Sed ijſdem quoque numeris multa alia peccas: vt cùm nu<lb></lb>mero xxxvi. </s> <s id="s.001456">ita à diuiſione rationis argumentaris:<emph.end type="italics"></emph.end> Si ſit vt <lb></lb>AE ad AD, ita AD ad AS: erit igitur diuidendo, vt <lb></lb>AS ad SD, ita AD ad AE. <emph type="italics"></emph>Hic enim inferendi modus <lb></lb>non est à diuiſione rationis: & quamuis, vt par eſt, terminos <lb></lb>etiam diſponeres, nihil hac ratione concluderes, niſi priùs ſup<lb></lb>poneres velocitatem per totam<emph.end type="italics"></emph.end> AE <emph type="italics"></emph>duplam eſſe velocitatis<emph.end type="italics"></emph.end><pb pagenum="186" xlink:href="028/01/226.jpg"></pb><emph type="italics"></emph>acquiſitæ per<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>quod falſum eſſe non ignoras.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001457">Nempe ex quinque argumentis, quæ ſunt mox an<lb></lb>tè indigitata, <expan abbr="tertiũ">tertium</expan> delegiſti, de quo (ſi liceat tua pace <lb></lb>dicere) vitilitigares. </s> <s id="s.001458">Quippe <expan abbr="errorẽ">errorem</expan> calami, quo poſtre<lb></lb>mo loco ſcripſi AE pro DE, pro errore mentis habuiſti. <lb></lb></s> <s id="s.001459">Quaſi verò habere oculos oporteat, & <expan abbr="nõ">non</expan> videre <expan abbr="planũ">planum</expan> <lb></lb>ſenſum, quo ſcribere volui <emph type="italics"></emph>vt AS ad SD, ita AD ad DE?<emph.end type="italics"></emph.end><lb></lb>Aut quaſi in huiuſinodi tanta literarum farragine, im<lb></lb>portunaque inculcatione, non vnam pro alia irrepere <lb></lb><expan abbr="humanũ">humanum</expan> ſit? </s> <s id="s.001460">Et cùm volueris ipſe poſteà videri huma<lb></lb>nior, dum legens IC, adnotaſti <emph type="italics"></emph>dicere me voluiſſe HC<emph.end type="italics"></emph.end><lb></lb>(quanqùam dicere nolui HC, ſed ND, tribus inte<lb></lb>gris verſibus, ad illud vſque, <emph type="italics"></emph>vt tu concludis,<emph.end type="italics"></emph.end> qui in ſeheda <lb></lb>fuere, ob idem initium, caſu prætermiſſis) cùm, <expan abbr="inquã">inquam</expan>, <lb></lb>illeic humanior fueris, cur heic quoque eſſe noluiſti? <lb></lb></s> <s id="s.001461">Debuiſti ergo potiùs reſtitutâ literâ D, oſtendere me <lb></lb>impropriè loquutum, quaſi ignorantem diuiſionem <lb></lb>rationis eſſe <emph type="italics"></emph>ſumptionem exceſſus, quo antecedens ſuperat <lb></lb>conſequens, ad ipſummet conſequens:<emph.end type="italics"></emph.end> hoc eſt, <emph type="italics"></emph>eſſe compa<lb></lb>rationem differentiæ terminorum cum ipſorum alterutro.<emph.end type="italics"></emph.end></s> <s id="s.001462"> Sed <lb></lb>ita nimirùm agere fuit cordi, vt dicere poſſes, quamuis <lb></lb>vt par eſt, diſponerentur termini, nihil me hac ratione <lb></lb>concluſurum, niſi prius ſupponerem <emph type="italics"></emph>velocitatem per to<lb></lb>tam<emph.end type="italics"></emph.end> AE <emph type="italics"></emph>duplam eſſe velocitatis acquiſitæ per<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>quod ta<lb></lb>men falſum non ignorarem.<emph.end type="italics"></emph.end></s> <s id="s.001463"> Ego verò falſum <expan abbr="quidẽ">quidem</expan> eſſe, <lb></lb>ſed & tuum eſſe non ignoro: ac ne ex ſuperiùs dedu<lb></lb>ctis argumentum repetam, paucis oſtendo nihil eſſe <lb></lb>hac ſuppoſitione, aut omninò vlla tergiuerſatione <lb></lb>opus. </s> <s id="s.001464">Ex verbis paulò antè ex tua diſſertatione reci<lb></lb>tatis, negare non potes, quin hoc totum tuum ſit: <pb pagenum="187" xlink:href="028/01/227.jpg"></pb><emph type="italics"></emph>vt<emph.end type="italics"></emph.end> AE, <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> AD, <emph type="italics"></emph>ita<emph.end type="italics"></emph.end> AD <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> AS. Quamobrem, aut <lb></lb>neges oportet ratiocinia Geometrica, aut fatearis le<lb></lb>gitimè diuidendo ita concludi, <emph type="italics"></emph>vt<emph.end type="italics"></emph.end> AS, <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> SD; <emph type="italics"></emph>ita<emph.end type="italics"></emph.end> AD <lb></lb><emph type="italics"></emph>ad<emph.end type="italics"></emph.end> DE. </s> </p> <p type="main"> <s id="s.001465"><emph type="italics"></emph>Certè hanc ipſam falſam hypotheſin, eodem numero ſta<lb></lb>tim expreßè aſſumis; ideóque nihil inde concludis: fruſtraque <lb></lb>inſuper laboras, vt originem erroris inquiras, qui nullus eſt, <lb></lb>niſi in falſis ſuppoſitionibus tuis.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001466">Cùm hypotheſes falſæ, ſint; cuius tamen ſint, ad<lb></lb>uerſus quem ſint, quem errorem creent, ſatis iam <lb></lb>apertum. </s> </p> <p type="main"> <s id="s.001467"><emph type="italics"></emph>Atque, vt ingenuè dicam, quod ſentio, in huiuſce contro<lb></lb>uerſiæ penetralia ingreſſus non videris: cùm vbique ferè falſa, <lb></lb>atque ab hac tota materia perquàm aliena ſupponas; & vix <lb></lb>quicquam, niſi ex talibus ſuppoſitionibus concludas. </s> <s id="s.001468">Tuma<lb></lb>ioribus, & melioribus occupatus, leuiora hæc neglexiſſe <lb></lb>videris.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001469">Si hæc ſit ingenuitas tua; beatus es, qui ita de te, ita <lb></lb>de me ſentire poſſis: ac prouidere quid Lectores opi<lb></lb>naturi demùm ſint, vbi cùm te Myſten, me propha<lb></lb>num habuetint, te perſpicacem, me hebetem, te dili<lb></lb>gentem, ac ſedulum, me oſcitantem, & agentem aliud: <lb></lb>requirent tamen vel vnam falſam hypotheſin, quæ <lb></lb>mea ſit; & vel vnam periodum, in qua aliquid ab hac <lb></lb>tota materia tantillùm alienum ſupponam, aut di<lb></lb>cam. </s> </p> <p type="main"> <s id="s.001470"><emph type="italics"></emph>Numero ſequente xxxviij. </s> <s id="s.001471">quicquid concludis, ex du<lb></lb>plici falſa hypotheſi ſimiliter concludis. </s> <s id="s.001472">Vna eſt, quód ve<lb></lb>locitates totæ, atque integræ quibuſlibet partibus acquiſitæ <lb></lb>eam inter ſe rationem obſeruent, quam partes ipſ<gap></gap> quibus<emph.end type="italics"></emph.end><pb pagenum="188" xlink:href="028/01/228.jpg"></pb><emph type="italics"></emph>ſunt acquiſitæ; atque ita, vt quemadmodum<emph.end type="italics"></emph.end> AE <emph type="italics"></emph>dupla eſt <lb></lb>ipſius<emph.end type="italics"></emph.end> AD, <emph type="italics"></emph>ita velocitas acquiſita per totam<emph.end type="italics"></emph.end> AE, <emph type="italics"></emph>præ-<emph.end type="italics"></emph.end><lb></lb><figure id="id.028.01.228.1.jpg" xlink:href="028/01/228/1.jpg"></figure><lb></lb><emph type="italics"></emph>cisè dupla ſit totius velocitatis acquiſitæ per<emph.end type="italics"></emph.end> AD; <lb></lb><emph type="italics"></emph>quod tamen ex tuis, &<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei principijs falſum eſſe <lb></lb>ſuperiùs numero<emph.end type="italics"></emph.end> 6. <emph type="italics"></emph>euici.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001473">Qaid euiceris, & cuiuſ-nam fuerit hypothe<lb></lb>ſis falſa, meminiſſe potes. </s> </p> <p type="main"> <s id="s.001474"><emph type="italics"></emph>Altera ſuppoſitio falſa hæc eſt, quod tanquam ne<lb></lb>ceßarium ducas quaſcumque ſpatij parteis vbicumque <lb></lb>deſignatas eodem tempore percurri, ſi eandem inter <lb></lb>ſe rationem obſeruent. </s> <s id="s.001475">Sic ex eo, quod dico<emph.end type="italics"></emph.end> (in <lb></lb>figura videlicet articuli XXXIV.) IC, <emph type="italics"></emph>& eius <lb></lb>triplam<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>æquali tempore percurri, concludis quo<lb></lb>que partem<emph.end type="italics"></emph.end> QH, <emph type="italics"></emph>& eius triplam<emph.end type="italics"></emph.end> IC (dicere vo<lb></lb>luiſti HC) <emph type="italics"></emph>æquali tempore debere abſolui.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001476">Cuius Suppoſitio falſa fuerit; qua conſequu<lb></lb>tione rem deduxerim; quid dicere voluerim: <lb></lb>citra nauſeam iam repeti non poteſt. </s> </p> <p type="main"> <s id="s.001477"><emph type="italics"></emph>Quod ſanè non faceres, ſi quæ à me ea de redicta ſunt, <lb></lb>ipſamque rei naturam penitiùs inspexiſſes.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001478">Et heic quoque beatus es, qui me æquè à tuis <lb></lb>dictis, & ab ipſa rei natura penitùs inſpiciunda ar<lb></lb>ceas. </s> </p> <p type="main"> <s id="s.001479"><emph type="italics"></emph>Miratus ſum autem etiam non parum, quomodò <lb></lb>paßim à numero Reſponſionis tuæ xxxiij mihi etiam affin<lb></lb>gas, quaſi velim, ac ſtatuam primam partem AD ſex <lb></lb>minutis, poſtremam verò eius medietatem SD, ac ſecun<lb></lb>dam partem DE minutis duobus percurri: cùm ne<lb></lb>que eo loco, quem numero illo xxxiij examinas, neque vſpiam <lb></lb>alibi quidquam tale dixerim; & poſt modum numero xl.<emph.end type="italics"></emph.end><pb pagenum="189" xlink:href="028/01/229.jpg"></pb><emph type="italics"></emph>expreßè profeſſus ſim tempus determinatum totius deſcenſus <lb></lb>à me conſtitui non poſſe, quòd non ſatis notum eſſet tempus, <lb></lb>quo ſpatium<emph.end type="italics"></emph.end> SD <emph type="italics"></emph>tranſcurreretur. </s> <s id="s.001480">Numeris quidem priori<lb></lb>bus, ex aliorum, quos iam <expan abbr="impugnabã">impugnabam</expan> hypotheſi etiam ſuppoſui <lb></lb>primam partem spatij<emph.end type="italics"></emph.end> AB, <emph type="italics"></emph>ſex minutis; poſteriorem verò eius <lb></lb>medietatem<emph.end type="italics"></emph.end> SD, <emph type="italics"></emph>duobus percurri: vt ſcilicet ex eorum prin<lb></lb>cipijs eos erroris reuincerem; at ſagacitas tua aliena cum meis <lb></lb>confundere non debuit, aut mihi tribuere, quod reprebendo in <lb></lb>cæteris. </s> <s id="s.001481">Vide, ſi lubet, Epiſtolæ meæ numerum xxxiij. </s> <s id="s.001482">in quo <lb></lb>ſolo partibus ſpatijparteis quaſdam temporis attribuo, ex mea<lb></lb>ne, an ex aliena ſententia id pronunciem. </s> <s id="s.001483">Ex bac tamen falſa <lb></lb>ſuppoſitione vix credibile eſt, quam-multa mihi abſurda obii<lb></lb>cias, quamque multainter ſe, & cum meis decretis pugnantia <lb></lb>congeras: vno verbo, rem ſic omnem in partem verſas, vt ſi à <lb></lb>me dicta eſſent, quæ mihi affingis, meritò haberi poſſem om<lb></lb>nium hominum ineptißimus. </s> <s id="s.001484">Infinitus ſim, ſi aut recenſere <lb></lb>ſingula, aut ijs ſigillatim ſatisfacere voluero, quæ ex adeò fal<lb></lb>ſa hypotheſi mihi imponis: ſatius ſit ſemel dicere, à numeró <lb></lb>Reſponſionis tuæ xxx. </s> <s id="s.001485">ad finem, vix aliquid à te nobis obiici, <lb></lb>quòd eam hypotheſin non ſupponat, quodque proinde ea ſemel <lb></lb>negata, tanquam euerſo fundamento non corruat.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001486">Miratus es? </s> <s id="s.001487">At <emph type="italics"></emph>Primùm,<emph.end type="italics"></emph.end> is ego non ſum, qui nu<lb></lb>merum ſex minutorum Primæ parti attributorum vltrò <lb></lb>excogitauerim: ipſe es, qui eum induxiſti citato illo <lb></lb>Epiſtolæ, ſeu Demonſtrationis tuæ loco; ac nihil fuit <lb></lb>neceſſe, vt alium, quoties fuit aliquo exemplo vten<lb></lb>dum, ſubſtituerem. <emph type="italics"></emph>Deinde,<emph.end type="italics"></emph.end> licet poſt modum dixe<lb></lb>ris difficile eſſe determinare tempus, quo primum pri<lb></lb>mæ partis dimidium, quo ſecundum percurrerentur: <lb></lb>ego tamen, quòd obſeruarem habere te varia decreta, <pb pagenum="190" xlink:href="028/01/230.jpg"></pb>ac repugnare teipſum tibi; attendi quid foret præcipuè <lb></lb>tuis principiis conſentaneum, & quoniam ſæpè opus <lb></lb>fuit exemplorum illuſtratione, tempus illud ſemper <lb></lb>aſſumpſi iuxta aliquod ex tuis principiis. <emph type="italics"></emph>Tertiò<emph.end type="italics"></emph.end> enim <lb></lb>cùm obſeruâtim, quicquid ipſe aduerſus alios deduce<lb></lb>res partem ſecundam non percurri dimidio temporis, <lb></lb>quo primam: id tamen fuiſſe à te aſſumptum, tan<lb></lb>quam veram hypotheſin, qua paralogiſmi Galileum <lb></lb>conuinceres; & non potuiſſe à te aſſumi, niſi reputan<lb></lb>do partem ſecundam percurri dupla velocitate, ſiue <lb></lb>duobus gradibus, nulla agnita diſtinctione inter ma<lb></lb>nentem, & acquiſitum: idcircò, quia ex prima parte <lb></lb>duo faciebas dimidia, quorum prius ad poſterius ean<lb></lb>dem rationem, quam pars prima ad ſecundam tuere<lb></lb>tur; cenſui ſex minuta à te primæ parti attributa ita di<lb></lb>ſtribuenda in hæc duo dimidia, vt priori quatuor, po<lb></lb>ſteriori duo congruerent. <emph type="italics"></emph>Quartò<emph.end type="italics"></emph.end> verò cùm viderim <lb></lb>te velle aliunde inferius primæ partis dimidium, & ſe<lb></lb>cundam partem æquali tempore percurri: viſum rursùs <lb></lb>eſt deberi ex te duo minuta illi dimidio, tanquam <lb></lb>trientem temporis parti primæ attributi: quoniam <lb></lb>idem triens deberetur ſimiliter ſecundæ parti, iuxta eam <lb></lb>ratiocinationem, quàm ſuperiùs fuſiuſculè circa arti<lb></lb>culum VIII. ex eo contexui, quód eſſe in fine primæ <lb></lb>partis vnum, in fine ſecundæ duos gradus velocitatis <lb></lb>acquiſitos cenſeres. <emph type="italics"></emph>Quintò<emph.end type="italics"></emph.end> proinde, non eſt cur mire<lb></lb>ris ita factum eſſe à me; ſed cur mireris te non vidiſſe id <lb></lb>eſſe cohærens cum principiis tuis, & à me licet admoni<lb></lb>tus, cenſueris tamen diſſimulandum. </s> <s id="s.001488">Nam quod diſ<lb></lb>putàris quidem aduerſus alios, tempus per ſecundam <pb pagenum="191" xlink:href="028/01/231.jpg"></pb>partem, non eſſe dimidium temporis per primam, aſ<lb></lb>ſenſi conſtanter te facere rectè; at ſemper quoque ad<lb></lb>monui te id diſputare aduerſus teipſum: neque tu ocu<lb></lb>los ad hoc ſuſtinuiſti aduertere, & attendere, an aliquis <lb></lb>foret, quo id monſtraſſem, paralogiſmus. <emph type="italics"></emph>Sextò<emph.end type="italics"></emph.end> ex<lb></lb>inde fit manifeſtum, multa me tibi obieciſſe ex falſa <lb></lb>hac ſuppoſitione, non quia falſa, ſed quia tua: neque <lb></lb>ſatis eſſe, vt eam neges, quò quicquid obieci, <emph type="italics"></emph>tanquam <lb></lb>euerſo fundamento corruat,<emph.end type="italics"></emph.end> niſi negando tuam eſſe, oſten<lb></lb>das ſimùl tuam non eſſe (ſeu non eſſe ex tuis principiis <lb></lb>qua neceſſitate viſum eſt, deductam) ac ideò non eſſe, <lb></lb>cur quovſque illud <expan abbr="præſtitũ">præſtitum</expan> à te fuerit, inſultes me id, <lb></lb>quod aſſumo, affingere, imponeréque. </s> <s id="s.001489">Addo <emph type="italics"></emph>Poſtremò,<emph.end type="italics"></emph.end><lb></lb>quod caput eſt, fuiſſe perinde mihi futurum, ſeu hanc <lb></lb>ſeu aliam diſtributionem minutorum ſex, aut cuiuſli<lb></lb>bet temporis alterius, in ea dimidia aſſeruiſſes: ſi modò <lb></lb>ſemper rationem ſpatiorum, ac velocitatum ſuppone<lb></lb>ret eandem: quippe fac iam aliam qualemcumque <lb></lb>voles, quæ ſemper hanc tuam rationem ſupponat; & <lb></lb>ego recipio me eadem abſurda, ac fortè etiam alia lon<lb></lb>gè abſurdiora eſſe obiecturum. </s> </p> <p type="main"> <s id="s.001490"><emph type="center"></emph>IN ARTICVLOS XXXIX. XL. XLI. XLII. </s> <s id="s.001491">De Ra<lb></lb>tione continuò dupla, qua ſpatia decurri temporibus <lb></lb>æqualibus R. P. concludit.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001492"><emph type="italics"></emph>Quæris autem numero xxxv. </s> <s id="s.001493">& numero item xl. </s> <s id="s.001494">Quid<lb></lb>nam cauſſæ eſſe poßit, cur Progreßionem accelerationis in <lb></lb>deſcenſu grauium non à primo ſpatij decurrendi puncto<emph.end type="italics"></emph.end> A, <emph type="italics"></emph>ſed <lb></lb>à puncto primi spatii medio<emph.end type="italics"></emph.end> S, <emph type="italics"></emph>incipiam; cùm ratio velocitatis<emph.end type="italics"></emph.end><pb pagenum="192" xlink:href="028/01/232.jpg"></pb><emph type="italics"></emph>per totum ſpatium decurrendum, non autem per parteis eius <lb></lb>aliquas inquiratur. </s> <s id="s.001495">Nam, inquis,<emph.end type="italics"></emph.end> qua ratione biſecuiſti par<lb></lb>tem AD, in S, biſecare etiam potuiſti partem AS, ac ſu<lb></lb>periores ſimilieer cæteras. <emph type="italics"></emph>Potui certè, ſed ſtandum tandem <lb></lb>fuit alicubi, cùm diuiſio infinita eſſe non potuerit. </s> <s id="s.001496">Quid ni igitur <lb></lb>iam primùm, in ea parte conſiſtamus, ex qua totius motus ac<lb></lb>celerati ratio perfectè intelligatur? </s> <s id="s.001497">Sed ne putes tamen, ſi <lb></lb>pars ſuperior<emph.end type="italics"></emph.end> AS <emph type="italics"></emph>mente, & cogitatione diuiſibilis intelligatur <lb></lb>infinitas in parteis, conſequens proptereà eſſe, vt per illas par<lb></lb>teis omneis mente confictas acceleratio varietur: motus enim, <lb></lb>eiuſque acceleratio effectus Phyſicus est, qui proptereà (vt in <lb></lb>cæteris rebus Phyſicis accidit) per parteis ſenſibileis, eaſque <lb></lb>pro ratione ponderis, & reſiſtentiæ medij, maiores, aut mino<lb></lb>res metiendus videatur. </s> <s id="s.001498">Accedit, quòd tecum, & cum<emph.end type="italics"></emph.end> G<emph type="italics"></emph>a<lb></lb>lileo non ſentio corpus graue deſcendens ſtatim à quiete, atque <lb></lb>in omnibus, ac ſingulis indiuiſibilibus momentis accelerare <lb></lb>motum.<emph.end type="italics"></emph.end> C<emph type="italics"></emph>uius rei cauſſa eſt, quòd acceleratio omnis à ſolo <lb></lb>medio eſt; vnde deſcenſus in vacuo ſui ſemper ſimilis, atque <lb></lb>vniformis exſiſteret: ſicut tunc quoque tota cauſſa deſcenſus, <lb></lb>nempe grauitas, ſemper eadem, ac ſui ſimilis perſeueraret. <lb></lb></s> <s id="s.001499">Igitur, cùm graue quodcumque per aërem, aut aliud medium <lb></lb>deſcendit, talis deſcenſus à ſolagrauitate inchoatur, etiam me<lb></lb>dio plus, aut minùs reſiſtente, prout ipſum grauius, aut leuius <lb></lb>eſt, & faciliùs, aut difficiliùs diuiditur: nec priùs acceleratur <lb></lb>motus deſcendentis corporis, quàm à medij accurrentis, ſéque <lb></lb>à tergo claudentis motu, eóque iam notabili, medii reſiſtentia <lb></lb>ſupereretur, & grauitatis niſus, natiuaque velocitas Phyſicè <lb></lb>augeatur: ad quod ſine dubio requiritur pars temporis, ac spa<lb></lb>tii non Mathematicè minima, ſed Phyſicè notabilis, quæ cùm <lb></lb>pro grauium diuerſitate, & varia reſiſtentia mediorum modò.<emph.end type="italics"></emph.end><pb pagenum="193" xlink:href="028/01/233.jpg"></pb><emph type="italics"></emph>maior ſit, modò minor: heinc eſt, cur accelerationis ratio à <lb></lb>primo spatii percurrendi puncto minùs tutò inchoetur. </s> <s id="s.001500">Hæc <lb></lb>porrò, ſi cum tuis, ac<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei decretis minùs fortè conueniant; <lb></lb>principiis certè Phyſicis aptè congruunt. </s> <s id="s.001501">Sed reliqua breuiùs <lb></lb>percurramus.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001502">Peruentum iam eſt ad Phſiycæ tuæ Demonſtratio<lb></lb>nis Concluſionem: quæ quoniam eſt eadem cum ipſo <lb></lb>conſequente Propoſitionis, idcircò elicienda fuit vi <lb></lb>conſequutionis qua illud dependet ab antecedente. <lb></lb></s> <s id="s.001503">Quod porrò notas quæſiiſſe me; quanto, amabò, iure <lb></lb>quæſiuii: cùm <expan abbr="ſtupendũ">ſtupendum</expan> ſit te ab vſque initio definiſſe <lb></lb>motum æquabiliter acceleratum, qui æqualibus ſpatiis <lb></lb>æqualia celeritatis augmenta acquireret; ac ſpatia illa <lb></lb>æqualia ſemper & habuiſſe, & ſic expreſſiſſe per lineas <lb></lb>in parteis æqualeis diuiſas, vt eſſet in iis vna prima, vna <lb></lb>ſecunda, &c. </s> <s id="s.001504">nunc autem rem ſic perturbare, vt pars <lb></lb>prima vna æqualium non ſit; vt primum primæ dimi<lb></lb>dium pro nihilo ſit, vt reliquum pro tota ſit: vt motus <lb></lb>æquabiliter acceleratus non incipiat, cùm incipit; vt <lb></lb>incipiat, poſtquam incepit, & alia id genus, quæ ob<lb></lb>iecta ſunt, quæque repetere iam piget? </s> <s id="s.001505">Cùm deduxe<lb></lb>rim verò incommoda varia ex eo, quòd liceat <expan abbr="dimi-diũ">dimi<lb></lb>dium</expan> prius in duo alia dimidia ſubdiuidere, & prius iſto<lb></lb>rum in duo alia, & ſic conſequenter: quid tu ad ea om<lb></lb>nia? </s> <s id="s.001506">Nempe <emph type="italics"></emph>poſſe quidem id dimidium ſubdiuidi: verùm <lb></lb>eſſe tandem alicubi ſtandum: cùm diuiſio eſſe infinita non poſ<lb></lb>ſit.<emph.end type="italics"></emph.end></s> <s id="s.001507"> Age itaque peruideamus quid hac reſponſione ef<lb></lb>ficias. </s> <s id="s.001508">Dicis <emph type="italics"></emph>eſſe tandem alicubi ſtandum, quòd diuiſio eſſe <lb></lb>infinita non poßit:<emph.end type="italics"></emph.end> igitur per te licebit non ſtare, quo vſ<lb></lb>que diuiſio finita non erit, ac partes ſupererunt, per <pb pagenum="194" xlink:href="028/01/234.jpg"></pb>quas progredi diuidendo liceat? </s> <s id="s.001509">Igitur tumerit neceſ<lb></lb>ſariò ſtandum, cùm ſic finita erit diuiſio, vt exhauſtis <lb></lb>partibus, nulla ampliùs fieri ſubdiuiſio poſſit. </s> <s id="s.001510">Quando<lb></lb>nam verò id continget? </s> <s id="s.001511">An-non cùm tota pars AD <lb></lb>tantula erit, & ſic diuiſa in duo dimidia AS, & SD, vt <lb></lb>AS non habeat ampliùs duo dimidia, ac ſit indiuiſibilis <lb></lb>pars? </s> <s id="s.001512">An-non proinde cùm l inea AD contexta erit <lb></lb>ex duobus punctis? </s> </p> <p type="main"> <s id="s.001513">Prouidens tu quæ poſſent exinde iure vrgeri in<lb></lb>commoda, præoccupaſti, <emph type="italics"></emph>partem AS accipiendam eſſe <lb></lb>vt quid Phyſicum, quod mente quidem, ſeu Mathematicè <lb></lb>diuiſibile in parteis infinitas ſit: ſed non ita tamen, vt accelera<lb></lb>tio variari ſecundum eas poßit; quippe quæ effectus Phyſi<lb></lb>cus cùm ſit, non-niſi per parteis ſenſibileis metienda videa<lb></lb>tur.<emph.end type="italics"></emph.end></s> <s id="s.001514"> Aequiuocatio eſſe quædam poſſet circa vocem <lb></lb><emph type="italics"></emph>ſenſibileis;<emph.end type="italics"></emph.end> verùm ſic accipio, quaſi tu per illam intelle<lb></lb>xeris parteis <emph type="italics"></emph>Phyſicas,<emph.end type="italics"></emph.end> hoc eſt reuerâ exſiſtenteis in <lb></lb>rerum natura; nempe vt opponantur Mathematicis, <lb></lb>ſiue iis, quas mente confictas dixiſti. </s> <s id="s.001515">Nam ſi alioquin <lb></lb>diceres <emph type="italics"></emph>ſenſibileis,<emph.end type="italics"></emph.end> quaſi ſenſu perceptibileis, notum eſt <lb></lb>naturam non eſſe metiendam in ſuis adeò ſubtilibus <lb></lb>operationibus iuxta ſenſus captum. </s> <s id="s.001516">Neque enim in <lb></lb>compingendo v. g. animalculo acari noſtrum ſenſum <lb></lb>conſulit, qui ipſum habet quaſi punctum, ſiue rem viſu <lb></lb>minimam; ſed ſeipſam potiùs, prout illud texit ex <lb></lb>innumeris myriadibus partium infra omnem ſenſus <lb></lb>acutiem exſiſtentium, & neceſſariarum tamen, vt rem <lb></lb>faciat perſe mobilem, ac vegetationis, ſenſus, appeti<lb></lb>tus capacem. </s> <s id="s.001517">Vt præteream ſenſum haberi regulam <lb></lb>pluſquàm Leſbiam, propter diuerſitatem ſenſuum acu-<pb pagenum="195" xlink:href="028/01/235.jpg"></pb>tiorum, hebetiorumque, & adiumentorum, quibus <lb></lb>poſſunt ſubtiliora omnibus rebus antè perceptis per<lb></lb>cipere; & ſine ſpe tamen, vt vnquam naturæ ſubtilita<lb></lb>tem aſſequantur. </s> <s id="s.001518">Itaque, vt in hac diſtinctione hærea<lb></lb>mus: tunc igitur erit finita diuiſio, ſeu <expan abbr="peruentũ">peruentum</expan> erit ad <lb></lb>eam diuiſionem, vltra <expan abbr="quã">quam</expan> ſubdiuidere in duo dimidia <lb></lb>non liceat, cùm AS erit non Mathematicè quidem, <lb></lb>ſed Phyſicè tamen indiuiſibilis: atqui ſi AS ſit Phyſi<lb></lb>cè indiuiſibilis: erit igitur & pars SD indiuiſibilis, tan<lb></lb>quam ipſi AS æqualis? </s> <s id="s.001519">An ergo, ſi pars SD ſit in<lb></lb>diuiſibilis Phyſicè, diſtingues in ea trientem, quadran<lb></lb>tem, & cæteras Phyſicas parteis iis temporibus percur<lb></lb>rendas, quæ menſuræ ſint conſequentium, hoc eſt ipſi <lb></lb>AD æqualium? </s> <s id="s.001520">Cùm non poſſis: vide quàm fruſtrà <lb></lb>eò confugeris, vt <emph type="italics"></emph>ſtandum alicubi ſit, quòd diuiſio eſſe infi<lb></lb>nita non poßit.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001521">Hanc iterùm difficultatem quaſi præſentiens, præ<lb></lb>uenienſque, <emph type="italics"></emph>quid ni,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>iam primùm in ea parte con<lb></lb>ſiſtamus, ex qua totius motus accelerati ratio perfectè intelli<lb></lb>gatur?<emph.end type="italics"></emph.end> Dicere ergo vis, non eſſe exſpectandum, ad <lb></lb>hoc vt conſiſtamus, quovſque ad eam diuiſionem per<lb></lb>uenerimus, ex qua partes AS, & SD ſint duo puncta <lb></lb>Phyſica, ſeu duæ Phyſicè indiuiſibiles partes: ſed in illa <lb></lb>ſtandum, in qua tam AS, quàm SD conſtent adhùc ex <lb></lb>tot Phyſicis partibus, <emph type="italics"></emph>vt ex ijs ratio accelerati motus per<lb></lb>fectè intelligatur.<emph.end type="italics"></emph.end></s> <s id="s.001522"> At imprimis, ſi ita ſit, fruſtrà ergo <lb></lb>dicis alicubi ſtandum, <emph type="italics"></emph>quòd diuiſio eſſe infinita non poßit:<emph.end type="italics"></emph.end><lb></lb>cùm etiam diuiſione exſiſtente non infinita, progredi <lb></lb>adhûc vlteriùs liceat: atque idcircò vigent adhûc in<lb></lb>commoda omnia, quæ obiecta ſunt: quandò poteſt <pb pagenum="196" xlink:href="028/01/236.jpg"></pb>adhûc pars AS, ſubdiuidi in plura, pluraque dimidia. <lb></lb></s> <s id="s.001523">Deinde, cùm in dimidio SD, tot requiris parteis, vt <lb></lb><emph type="italics"></emph>ex ipſis ratio accelerati motus perfectè intelligatur:<emph.end type="italics"></emph.end> quot<lb></lb>nam quæſo ſunt, quas requiris? </s> <s id="s.001524">An aliquot pauculas, <lb></lb>v. c. ſex, quas nempe recenſes, dum rationem motus <lb></lb>accelerati explicas per trientem, quadrantem, per quin<lb></lb>tam, perque ſextam parteis tantum? </s> <s id="s.001525">Sanè vel neſciens <lb></lb>tot requiris, vt innumerabiles ſint; & tum abſis longiſ<lb></lb>ſimè ab eo, vt cauſſeris ſtandum, quòd <emph type="italics"></emph>diuiſio eſſe infinita <lb></lb>non poßit,<emph.end type="italics"></emph.end> quaſi vel in fine, vel certe non longè à fine <lb></lb>conſiſtendum ſit: tum etiam ab eo, vt ex cognitis par<lb></lb>tibus <emph type="italics"></emph>ratio motus intelligatur.<emph.end type="italics"></emph.end></s> <s id="s.001526"> Rem vt experiamur, ac<lb></lb>cipiamus, ecce, caſum globi ferrei (quod tuum poſteà <lb></lb>exemplum eſt) ex cælo Lunæ in centrum terræ: atque <lb></lb>in ipſo talem partem, <emph type="italics"></emph>in qua iam primum,<emph.end type="italics"></emph.end> vt ais, <emph type="italics"></emph>conſiſta<lb></lb>mus.<emph.end type="italics"></emph.end> Cùm tuo ex decreto, menſura durationis om<lb></lb>nium partium iſti primæ æqualium ſit æqualis duratio <lb></lb>totidem minutiorum partium ſigillatim acceptarum <lb></lb>in inferiore eius dimidio: ergo inferius eius dimidium <lb></lb>diuiſibile eſt in tot parteis, non Mathematicas, men<lb></lb>teve confictas, ſed Phyſicas, ſiue in ipſa rerum natura <lb></lb>exſiſtenteis, quot partes ſunt à cælo Lunæ, vſque in <lb></lb>centrum terræ, ipſi AD æquales. </s> <s id="s.001527">Hæ verò partes quot<lb></lb>nam ſunt? </s> <s id="s.001528">Certè, cùm aſſumendo pedes (vt facis) pro <lb></lb>Galilei cubitis, admittas à Luna in centrum nonagies <lb></lb>octies mille myriadas pedum: oportebit, etiam ſi pri<lb></lb>mam partem AD, non minorem pede habeas, vt di<lb></lb>cas dimidium illius inferius, ſeu ſemi-pedem totidem <lb></lb>pati diuiſiones, & continere totidem parteis Phyſicas <lb></lb>non mente confictas. </s> <s id="s.001529">Quid verò ſi acceperis partem <pb pagenum="197" xlink:href="028/01/237.jpg"></pb>pedis milleſimam, quippe quæ non modò ſenſibilis, ſeu <lb></lb>viſu perceptibilis ſit, ſed microſcopicis etiam vitris, ex <lb></lb>quam plurimis texi obſeruetur: an non tribus additis <lb></lb>cyphris, <expan abbr="erũt">erunt</expan> iam nouies mille, & octingentæ myriades <lb></lb>mytiadum partium? </s> <s id="s.001530">Quid ſi caſus foret ex Sole, vicies <lb></lb>ſaltem diſtantiore, quam Luna? </s> <s id="s.001531">Quid ſi ex firmamen<lb></lb>to diſtantiore ſaltem ducenties quinquagies? </s> <s id="s.001532">Tantam <lb></lb>igitur partium multitudinem eſſe vis in inferiore di<lb></lb>midio SD, vt ratio motus accelerati poſſit perfctè <lb></lb>intelligi: tantam, in ſuperiore AS, vt cenſeamus illam <lb></lb>non poſſe vlteriùs in duo ſubdiuidi dimidia. </s> <s id="s.001533">Videſ-ne <lb></lb>ergo quàm procùl abſit à diuiſionum fine ea pars, <emph type="italics"></emph>in <lb></lb>qua iam primùm,<emph.end type="italics"></emph.end> vt ais, <emph type="italics"></emph>conſistamus?<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001534">Subiicis, <emph type="italics"></emph>non ſentire te cum<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileo, & me, graue <lb></lb>deſcendens, statim à quiete, atque in omnibus, ac ſingulis mo<lb></lb>mentis accelerare motum.<emph.end type="italics"></emph.end></s> <s id="s.001535"> Quot ergo putas momenta, <lb></lb>ſeu Phyſicas temporis parteis abſque acceleratione <lb></lb>tranſiri? </s> <s id="s.001536">Tot certè, quot ſunt innumerabiles illæ par<lb></lb>tes, quæ ſunt <expan abbr="nõ">non</expan> in priore minùs, quàm in poſteriore di<lb></lb>midio diſtinctæ: neque enim illæ, niſi ſucceſſiuè, & vna <lb></lb>poſt aliam, atque adeò diſtinctis temporis partibus per<lb></lb>curruntur. </s> <s id="s.001537">Vide igitur per quot parteis, & per quot <lb></lb>momenta temporis diſtincta inefficacem facias cauſ<lb></lb>ſam Phyſicam, quam aduocas ſtatim. </s> <s id="s.001538">Videlicet <emph type="italics"></emph>cauſ<lb></lb>ſam accelerationis<emph.end type="italics"></emph.end> decernis <emph type="italics"></emph>eſſe ſolum medium, v. c. aërem: <lb></lb>neque enim prius accelerari motum à grauitate inchoatum, <lb></lb>quàm à medii accurrentis, ſeque à tergo claudentis motu, eó<lb></lb>que iam notabili reſiſtentia ſuperetur.<emph.end type="italics"></emph.end></s> <s id="s.001539"> Quo loco rursùs <lb></lb>æquiuocatio in nomine <emph type="italics"></emph>notabilis.<emph.end type="italics"></emph.end> Nam <emph type="italics"></emph>notabilem<emph.end type="italics"></emph.end> intel<lb></lb>ligis aut naturæ, aut nobis. </s> <s id="s.001540">Et nobis quidem <emph type="italics"></emph>notabilem<emph.end type="italics"></emph.end><pb pagenum="198" xlink:href="028/01/238.jpg"></pb>non debes intelligere: cùm natura noſtræ <emph type="italics"></emph>notationi<emph.end type="italics"></emph.end> non <lb></lb>alligetur; & priuſquam noſtra perſpicacia <emph type="italics"></emph>notare<emph.end type="italics"></emph.end> quic<lb></lb>quam valeat, natura iam tranſierit per innumerabi<lb></lb>leis parteis. </s> <s id="s.001541">Si ergo naturæ; quæro quot partes in mo<lb></lb>tu neceſſariæ ſint, vt natura progreſſa eſſe <emph type="italics"></emph>notabiliter<emph.end type="italics"></emph.end><lb></lb>reputetur? </s> <s id="s.001542">An-non ſaltem myrias deberet eſſe ſatis? <lb></lb></s> <s id="s.001543">An-non ſaltem decem, centum, & mille myriades? </s> <s id="s.001544">An<lb></lb>non ſaltem <expan abbr="myriadũmyrias">myriadummyrias</expan>; a<gap></gap> ſaltem decem, <expan abbr="centũ">centum</expan>, <lb></lb>mille myriades myriadum? </s> <s id="s.001545">Stupendum iſta non eſſe <lb></lb>ſatis, ſed deinceps adhûc multiplicanda eſſe, <expan abbr="priuſquã">priuſquam</expan> <lb></lb>numerus <emph type="italics"></emph>notabilis<emph.end type="italics"></emph.end> ſit, & cauſſa tua Phyſica euadere ef<lb></lb>ficaxpoſſit. </s> <s id="s.001546">Sed de hac quidem Phyſica cauſſa dicen<lb></lb>dum erit inferiùs: quæro heic ſolùm, an putes aërem <lb></lb>ſeſe à tergo claudere, cùm iam ſuperatur, vel ſtatim ac <lb></lb>ſuperata à fronte eſt pars ſpatij prima, vnaque ex illis <lb></lb>innumerabilibus, an non? </s> <s id="s.001547">Si dicas ſe non claudere; <lb></lb>igitur ſpatium illud à tergo vacuum remanet; quod <lb></lb>non es ſanè admiſſurus. </s> <s id="s.001548">Si ſe claudere, ergo cum ſe <lb></lb>claudendo agat (neque enim alia ratione putas hanc <lb></lb>cauſſam agere) ab ea vſque parte agit aliquid: ergo ab <lb></lb>initio vſque grauitatem iuuat: ergo & motum accele<lb></lb>rat: ergo exſpectandæ non ſunt tam innumerabiles <lb></lb>partes, vt motus notabilis ſit, & acceleratio incipiat. <lb></lb></s> <s id="s.001549">Quod <emph type="italics"></emph>cauſſam hanc<emph.end type="italics"></emph.end> verò dicis <emph type="italics"></emph>neceſſariam, vt reſiſtentia <lb></lb>ſuperetur:<emph.end type="italics"></emph.end> vides quàm non ſit neceſſarium, cùm graui<lb></lb>tate ſola agente ſuperatam iam facias, priuſquàm aër <lb></lb>aliquid agat, ſiue mobili iam promoto per totum ſupe<lb></lb>rius dimidium ſuperueniat, ac ſeſe claudat. </s> <s id="s.001550">Vtcum<lb></lb>que autem eſſe debeat <emph type="italics"></emph>notabilis<emph.end type="italics"></emph.end> pars; ſic cine probas <lb></lb>platicè ſubtilem determinationem in primæ partis me-<pb pagenum="199" xlink:href="028/01/239.jpg"></pb>dio? </s> <s id="s.001551">Quaſi non poſſit motus <emph type="italics"></emph>notabilis<emph.end type="italics"></emph.end> eſſe paulò antè <lb></lb>medium, aut non-niſi paulò pòſt medium? </s> <s id="s.001552">Eſt ne <lb></lb>aliquod argumentum, quo probes iſtam tuam cauſſam <lb></lb>nihil omninò agere, nihil ſuperare reſiſtentiæ, per tot <lb></lb>illas partium ſpatij, temporiſque myriadas, quæ toti <lb></lb>priori dimidio tribuuntur, ſtatim autem ac mobile at<lb></lb>tigit primam poſterioris, incipere & agere, & reſiſten<lb></lb>tiam ſuperare? <emph type="italics"></emph>Requiritur,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>pars temporis, ac spa<lb></lb>tii non Mathematicè minima, ſed Phyſicè notabilis.<emph.end type="italics"></emph.end></s> <s id="s.001553"> Aduer<lb></lb>ſatiuam hanc non capio: cùm videretur debere pars <lb></lb>dici, aut <emph type="italics"></emph>Mathematicè notabilis,<emph.end type="italics"></emph.end> aut <emph type="italics"></emph>Phyſicè minima:<emph.end type="italics"></emph.end> ſed <lb></lb>quicquid ſit, vis eam Phyſicè notabilem eſſe; quid inde <lb></lb>concludis? <emph type="italics"></emph>Heinc eſt,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>cur accelerationis ratio à <lb></lb>primo ſpatii percurren li puncto non tutò inchoetur.<emph.end type="italics"></emph.end></s> <s id="s.001554"> Non <lb></lb>tutò inchoetur? </s> <s id="s.001555">Imò, vnde tutiùs inchoetur, quàm <lb></lb>vnde eſt periculi nihil? </s> <s id="s.001556">Nam tibi quidem meritò ef<lb></lb>ficiuntur omnia ſuſpecta, cùm viâ regiâ ſemel relictâ, <lb></lb>non valeas ecce, niſi per dumos, ſalebraſque incedere; <lb></lb>at verò illis, qui viam tenent, ſimile nihil timendum eſt. <lb></lb></s> <s id="s.001557">Sed nempe platicè aſſumenti, platicè perinde conclu<lb></lb>dendum fuit. </s> <s id="s.001558">Sperandum quippe fuerat, vt conclu<lb></lb>deres, cur ante primæ partis medium, ſeu alicubi per <lb></lb>totum prius dimidium, acceleratio non inchoaretur; at <lb></lb>tu intereà de medio, totove priore dimidio nihil: ſed <lb></lb>ſolùm, <emph type="italics"></emph>accelerationem à primo puncto non tutò inchoari.<emph.end type="italics"></emph.end><lb></lb>Quod autem addis, <emph type="italics"></emph>ſi iſta cum meis, &<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei decretis <lb></lb>non fortè conueniant, principiis certè Phyſicis aptè congruere;<emph.end type="italics"></emph.end><lb></lb>cedò ſolùm, Quibus? </s> </p> <p type="main"> <s id="s.001559"><emph type="italics"></emph>Ex his igitur nunc habes, quod numero xl. </s> <s id="s.001560">quæris, cur<lb></lb>rationem accelerationis à primo spatii decurrendi puncto non<emph.end type="italics"></emph.end><pb pagenum="200" xlink:href="028/01/240.jpg"></pb><emph type="italics"></emph>deducam: quamvis iam etiam aliunde id haberes; ex eo nimi<lb></lb>rùm, quod diuiſo, vt libet, in parteis æqualeis tempore, aut <lb></lb>ſpatio, ſemper impoßibile ſit, vt velocitas ſecundæ partis præ<lb></lb>cisè dupla ſit totius velocitatis per priorem partem acquiſitæ: <lb></lb>quod ex tuis etiam principiis anteà numero<emph.end type="italics"></emph.end> 17. <emph type="italics"></emph>euidenter de<lb></lb>monſtratum eſt.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001561">Et ſæpe repetij, & repetere ſæpiùs cogis me, quæ<lb></lb>ſtionem non eſſe, an impoſſibile ſit velocitatem per <lb></lb>ſecundam partem eſſe præcisè duplam velocitatis per <lb></lb>primam: ſed id-ne ſequatur ex admiſſo principio, quòd <lb></lb>velocitates vt ſpatia ſe habeant. </s> <s id="s.001562">Ego enim ſemper id <lb></lb>ſequi conteſtatus ſum: tu non ſequi probaſti nun<lb></lb>quam; & perinde ſemper procedis, ac ſi id habendum <lb></lb>eſſet nihili; quod ipſum tamen eſt rei caput. </s> <s id="s.001563">An, & <lb></lb>quomodo aliquid ex meis principijs demonſtraueris; <lb></lb>nihil eſt quam obrem heic repetatur. </s> </p> <p type="main"> <s id="s.001564"><emph type="italics"></emph>Cæterùm hoc etiam loco erras non mediocriter, dum ex <lb></lb>eo, quòd partes NC, & CD eodem tempore percurrun<lb></lb>tur, talem gradum velocitatis acquiri concludis ab N in <lb></lb>C, qualis acquiritur à C, in D: tunc enim velocitates eſſe <lb></lb>vt spatia neceſſe eſt.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001565">Quàm egregiè elaberis? </s> <s id="s.001566">Ego enim cætera inter, <lb></lb>quæ non attigiſti, ex eo, quòd priùs admiſiſſes, pro<lb></lb>pter progreſſionem Arithmeticam, duorum graduum <lb></lb>acquiſitorum in D, vnum acquiſitum ab A, in C, alte<lb></lb>rum à C, in D, concluſi te velle velocitatem acquiſi<lb></lb>tam ab N in C, eſſe æqualem acquiſitæ à C, in D, <lb></lb>quandoquidem tum velles ipſam CD tanto tempore, <lb></lb>quanto NC, cuius eſſet dupla, percurri. </s> <s id="s.001567">Et quia vi<lb></lb>deris non attendiſſe ad conſequutionem, quæ ſatis <pb pagenum="201" xlink:href="028/01/241.jpg"></pb>tamen inſinuabatur in duobus conſectariis, ecce quo<lb></lb>modò ea probetur. </s> <s id="s.001568">NC, & CD debent, per <lb></lb><figure id="id.028.01.241.1.jpg" xlink:href="028/01/241/1.jpg"></figure><lb></lb>te, eſſe æquales; quoniam vtraque, per te, de<lb></lb>bet eſſe æqualis lineæ AC: quare &, ſi æquali <lb></lb>percurrantur tempore, æquali percurrentur ve<lb></lb>locitate. </s> <s id="s.001569">Et de æqualitate quidem lineæ CD, <lb></lb>cum AC, non eſt dubium; probo de NC, AC, & <lb></lb>NC eadem velocitate ſecundum ſe totas per<lb></lb>curruntur, ex te; Ergo ſunt inter ſe æquales. </s> <s id="s.001570">Pro <lb></lb>batur antecedens. </s> <s id="s.001571">Ad velocitatem acquiſitam <lb></lb>per totam AC, addita quæ acquiritur per CD, <lb></lb>facit velocitatem in D duplam velocitatis in <lb></lb>C; ad volocitatem acquiſitam per totam NC, <lb></lb>addita quæ acquiritur per eandem CD, facit <lb></lb>itidem velocitatem in D, velocitatis in C du<lb></lb>plam; & vtrumque quidem per te. </s> <s id="s.001572">Igitur per te <lb></lb>AC, & NC, ſecundum ſe totas velocitate ea<lb></lb>dem percurruntur; ſuntque idcircò inter ſe <lb></lb>æquales. </s> <s id="s.001573">Tu ergo vim conſequutionis ex inte<lb></lb>gro antecedente diffimulans, infers ſolùm ex <lb></lb>duplo ſpatij, & temporis æqualitate, velocitates <lb></lb>eſſe vt ſpatia: ac retices quod intereſt, quodque <lb></lb>ſubnotatum fuit, cùm ſubiunxi, <emph type="italics"></emph>conſequi, vt <lb></lb>velocitates per AC, & NC, acquiſitæ ſint prorſus <lb></lb>æquales: ac proinde vt AC, & NC, hoc est totum, & <lb></lb>pars eodem tempore percurrantur, &c.<emph.end type="italics"></emph.end></s> <s id="s.001574"> Sequitur. </s> </p> <p type="main"> <s id="s.001575"><emph type="italics"></emph>Numero xli. </s> <s id="s.001576">etiam peccas; cùm, vt impugnes conſtitu<lb></lb>tam à me cæterarum partium toto spatio decurrendo deſigna<lb></lb>tarum respectum ad analoga primæ partis ſegmenta, non ſo<lb></lb>lùm earumdem partium reſpectum ad parteis temporis exigis,<emph.end type="italics"></emph.end><pb pagenum="202" xlink:href="028/01/242.jpg"></pb><emph type="italics"></emph>quas neque tu, neque alius quiſquam aßignare poteſt, ſed <lb></lb>tempora etiam illis adſcribis, quæ nullo modo ipſis conuenire <lb></lb>non ignoras. </s> <s id="s.001577">Vis enim primi ſpatij partem dimidiam dimidia <lb></lb>parte eius temporis percurri, quo totam primam partem ab<lb></lb>ſolui ſupponis; & tertiam partem tertia parte, quartam <lb></lb>quartaparte eiuſdem temporis: cùm ex tuis, &<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alilei prin<lb></lb>cipiis dimidia parte prima temporis, quarta pars tantum spatij <lb></lb>ſuperior decurratur, & reliqua dimidia parte temporis tres <lb></lb>inferiores ſpatij quadrantes abſoluantur. </s> <s id="s.001578">Vide ergo quid ex <lb></lb>tam abſurda hypotheſi concludere poßis.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001579">Cùm nihil ſit, quod prodat magis decretorum <lb></lb>incohærentiam, quàm reductio ad calculos; ex eo eſt, <lb></lb>cur potiſſimùm ſupputationes auerſeris. </s> <s id="s.001580">Id autem hoc <lb></lb>loco præſertim probatur. </s> <s id="s.001581">Admiſiſti poſſe diſtingui <lb></lb>in motu grauium decidentium plura æqualia tempora: <lb></lb>at cùm planum foret, vt ſpatio diuiſo in parteis æqua<lb></lb>leis, primum tempus attribueretur primæ huiuſcemodi <lb></lb>partium, ac deinde explicaretur quota eius temporis <lb></lb>parte percurrerentur cæteræ; & in qua ipſarum ſecun<lb></lb>dum tempus æquale deſineret, in qua tertium, &c. </s> <s id="s.001582">di<lb></lb>uertiſti nihilominus, & pro primo tempore accipien<lb></lb>dum voluiſti id, quo decurreretur eiuſdem primæ par<lb></lb>tis non prius, ſed poſterius dimidium; & tum voluiſti <lb></lb>ſecundam partem, quæ eſſet dupla huius dimidii, æqua<lb></lb>li cum eo tempore percurri: tum tertiam æquali cum <lb></lb>eo, quo triens eiuſdem primæ partes infimus; quartam <lb></lb>æquali cum eo, quo quadrans, &c. </s> <s id="s.001583">tum <expan abbr="ſecundũ">ſecundum</expan> tem<lb></lb>pus æquale primo eſſe id, quod debetur ſecundæ parti <lb></lb>ſoli: tertium, quod tertiæ, & quartæ ſimùl: quartum, <lb></lb>quod quintæ, ſextæ, ſeptimæ, octauæ: quintum, quod <pb pagenum="203" xlink:href="028/01/243.jpg"></pb>octo ſequentibus: ſextum, quod ſexdecim ſuccedenti<lb></lb>bus, atque ita porrò. </s> <s id="s.001584">Ego itaque oſtenſurus, vt hæc ſe <lb></lb>probè non haberent, cætera inter argumenta, rem ex<lb></lb>primendam numeris cenſui, ac aſſumpſi <expan abbr="primũ">primum</expan> ipſum <lb></lb>tempus, quod dimidio illi poſteriori attribueres, veluti <lb></lb>aſſem, eiuſque proinde parteis duodecim quaſi vncias, <lb></lb>ſiue mauis minuta habui. </s> <s id="s.001585">Debueras tu procedere dein<lb></lb>ceps per parteis æqualeis huic dimidio: quo caſu ſe<lb></lb>cundæ parti fuiſſent attributa minuta ſex, ſiue <expan abbr="dimidiũ">dimidium</expan> <lb></lb><expan abbr="tẽporis">temporis</expan> (ob duplicatam velocitatem) & tertiæ quatuor, <lb></lb>ſiue triens (ob triplicatam) & quartæ tria, ſiue quadrans <lb></lb>(ob quadruplicatam) &c. </s> <s id="s.001586">& quia tamen duplum di<lb></lb>midij vſurpandum eſſe vbique cenſuiſti, vt partes ſe<lb></lb>cunda, tertia, quarta, &c. </s> <s id="s.001587">fierent vbique toti primæ <lb></lb>æquales: ideò effectum eſt, vt ſecundæ parti non dimi<lb></lb>dium, ſeu ſex minuta, ſed omninò tantumdem, ſeu duo<lb></lb>decim tribueris, & tertiæ beſſem, ſiue octo: quartæ di<lb></lb>midium, ſiue ſex. </s> <s id="s.001588">Ipſe proinde, vtcumque rationem <lb></lb>dupli prætermiſerim (& quam tamen iam interſeren<lb></lb>dam cenſui) declarare volui, vt hæc tempora non con<lb></lb>gruerent ſpatiis vtravis ratione aſsuptis. </s> <s id="s.001589">Et de ſecundo <lb></lb><expan abbr="quidẽ">quidem</expan> conſtitit, ob illud, quod duplicato quidem con<lb></lb>ueniret tempus primo æquale, ſeu minutorum duode<lb></lb>cim, at ſimplici non niſi dimidium, ſeu minuta ſex: de <lb></lb>fuccedentibus autem iuxta aggregationem tuam, ob id, <lb></lb>quòd neque ſimplicibus, neque duplicibus conueniret <lb></lb>vnquam tempus æquale primo, ſeu minutorum duo<lb></lb>decim, ſed vel in ſimplicibus ſemper deficeret, vel in <lb></lb>duplicibus ſemper abundaret: cùm deberet tamen ſal<lb></lb>tem in duplicibus ſemper exæquari, vt exæquatum <pb pagenum="204" xlink:href="028/01/244.jpg"></pb>fuerat in ipſa ſtatim ſecunda parte. </s> <s id="s.001590">Quid tu ad iſta <lb></lb>igitur? </s> </p> <p type="main"> <s id="s.001591">Dicis me, <emph type="italics"></emph>non ſolùm reſpectum partium ad parteis <lb></lb>temporis exigere, quas neque ego, neque alius quiſquam aßi<lb></lb>gnare poßit: ſed tempora etiam illis adſcribere, quæ nullo <lb></lb>modo ipſis conuenire non ignorem.<emph.end type="italics"></emph.end></s> <s id="s.001592"> Verumtamen, quæ<lb></lb>ſtio non eſt de eo, quod ego, aut alius præſtare poſſi<lb></lb>mus, aut non poſſimus, in aſſignandis temporibus, quæ <lb></lb>partibus quibuſque conueniant: quanquam Galileum <lb></lb>quidem imitatus, ſumpto quocumque tempore primæ <lb></lb>parti debito, aſſignaui tempus, quod exigitur ad ſecun<lb></lb>dam, & quod ad vtrumque primæ partis dimidium, <lb></lb>paratus idem prorsùs præſtare circa quælibet tempora, <lb></lb>quarumcum que voles partium cætetarum, iuxta gene<lb></lb>rale ſcilicet Effatum, quod articulo <expan abbr="Reſpõſionis">Reſponſionis</expan> XXXVI. <lb></lb>retuli, & in quod nihil fuit, quod à te obiiceretur. <lb></lb></s> <s id="s.001593">Non item eſt quæſtio, an tempora quæ partibus adſcri<lb></lb>bo, ipſis nullo modo conuenire ignorem, an ſciam (ſcio <lb></lb>enim eſſe longè alià, prout ex citato moxloco intelligi <lb></lb>poteſt) ſed an ea adſcribam iuxta tua principia. </s> <s id="s.001594">Quo<lb></lb>nam verò modo id non fieri probas? <emph type="italics"></emph>Vis enim,<emph.end type="italics"></emph.end> inquis, <lb></lb><emph type="italics"></emph>primi ſpatij partem dimidiam dimidia parte eius tem<lb></lb>poris percurri, quo totam primam partem, & tertiam <lb></lb>tertia, quartam quarta,<emph.end type="italics"></emph.end> &c. </s> <s id="s.001595">Sperâram, vt aliò querela <lb></lb>tua vergeret. </s> <s id="s.001596">Quia enim iuxta ante-dicta defendis te <lb></lb>nolle dimidium inferius primæ partis percurri dimidio <lb></lb>eius temporis, quo ſuperius: procliue mihi videbatur, <lb></lb>vt querereris tibi affingi tempora à te pernegata. </s> <s id="s.001597">Sed <lb></lb>videlicet, animaduertiſti me commiſiſſe tuæ libertati, <lb></lb>vt dares quodcumque demùm velles tempus pro infe-<pb pagenum="205" xlink:href="028/01/245.jpg"></pb>riore dimidio: fore enim me idem oſtenſurum. </s> <s id="s.001598">Vnde <lb></lb>& animi ſolùm gratiâ, & conſonanter ad ſuperiora, <lb></lb>aſſumpſi pro partis primæ tempore numerum trigin<lb></lb>ta ſex, vt inferiori dimidio attribueretur numerus com<lb></lb>modiſſimus duodecim. </s> <s id="s.001599">Et ſanè heic non quærebatur, <lb></lb>quota portio eſſet hoc tempus temporis totius per pri<lb></lb>mam inſumpti: ſed ſolùm, quodcumque illud eſſet, ex <lb></lb>quibus ſui partibus cenſeri poſſet integrum, vt alia ipſi <lb></lb>æqualia deinceps adnumerarentur. </s> <s id="s.001600">Quidnam verò eſt, <lb></lb>quod ſubiungis? </s> <s id="s.001601">Iſtud nimirùm: <emph type="italics"></emph>cùm ex tuis, &<emph.end type="italics"></emph.end> G<emph type="italics"></emph>a<lb></lb>lilei principiis dimidia parte primi temporis quarta pars tan<lb></lb>tum spatii ſuperior decurratur, & reliqua dimidia parte tem<lb></lb>poris tres inferiores spatii quadrantes abſoluantur.<emph.end type="italics"></emph.end></s> <s id="s.001602"> Sed <lb></lb>quæſtio heic non eſt, quid Galileus, & ego ſentiamus: <lb></lb>ea de re enim ſatis iam conſtat: verùm, an quod tibi <lb></lb>obiicio, ſit tuum, ſiue iuxta tua decreta, an non? </s> <s id="s.001603">Cùm <lb></lb>non fuerit, quod reſponderes, his tamen verbis con<lb></lb>cluſiſti, <emph type="italics"></emph>Vide ergo, quid ex tam abſurda hypotheſi conclu<lb></lb>dere poßis.<emph.end type="italics"></emph.end></s> <s id="s.001604"> Ego verò, <emph type="italics"></emph>Imò tuvide,<emph.end type="italics"></emph.end> inquam, <emph type="italics"></emph>quid ex hypo<lb></lb>theſi tam abſurda, cum tua ſit, concluſerim, & ad concluſio<lb></lb>nem reſponde, ſi poßis.<emph.end type="italics"></emph.end></s> <s id="s.001605"> Pergis. </s> </p> <p type="main"> <s id="s.001606"><emph type="italics"></emph>Vt verò etiam numero xlij. </s> <s id="s.001607">augmentum velocitatis in <lb></lb>ratione dupla conſtitutum impugnes, inter alia aſſumis pari <lb></lb>iure, ac modo ſtatui poſſe idem augmentum etiam procedere in <lb></lb>quacumque alia<emph.end type="italics"></emph.end> G<emph type="italics"></emph>eometrica ratione, in tripla ſcilicet, in qua<lb></lb>drupla, in decupla &c. </s> <s id="s.001608">exemplumque profers in tripla. </s> <s id="s.001609">Et pri<lb></lb>mùm quidem obiter mihi affingis, quòd velim partem AN, <lb></lb>& eius triplam ND eodem tempore percurri.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001610">Ego verò nihil affinxi; ſed idipſum fuit, quod de<lb></lb>duxeram articulo XL. ea parte, quam non attigiſti: <pb pagenum="206" xlink:href="028/01/246.jpg"></pb>oſtendendo videlicet, cùm CN foret duorum minu<lb></lb>torum, & CD illius dupla, ſimiliter minutorum <lb></lb><figure id="id.028.01.246.1.jpg" xlink:href="028/01/246/1.jpg"></figure><lb></lb>duorum, atque ideò tota ND, minutorum qua<lb></lb>tuor: forè vt AN ex tuis principiis minutorum <lb></lb>quatuor, & eius tripla ND, tempore eodem <lb></lb>percurrerentur. </s> </p> <p type="main"> <s id="s.001611"><emph type="italics"></emph>Sed cùm iis partibus omißis, rectè compares<emph.end type="italics"></emph.end> XC <lb></lb><emph type="italics"></emph>vltimum trientem ſupremæ partis<emph.end type="italics"></emph.end> AC <emph type="italics"></emph>cum tertia <lb></lb>parte<emph.end type="italics"></emph.end> DE: <emph type="italics"></emph>non rectè conſequenter hanc tertiam par<lb></lb>tem comparas cum tribus ſequentibus<emph.end type="italics"></emph.end> EH, <emph type="italics"></emph>quæ non <lb></lb>eodem tempore, aut æquali cum tertia parte<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>ſed <lb></lb>tempore longiore percurruntur. </s> <s id="s.001612">At rectiùs cum ea<lb></lb>dem tertia parte<emph.end type="italics"></emph.end> DE <emph type="italics"></emph>compararentur ſeptima, octa<lb></lb>ua, & nona, nempe<emph.end type="italics"></emph.end> HL: <emph type="italics"></emph>ſed talis progreßio per to<lb></lb>tum ſpatium decurrendum continua non eſt, vt vides: <lb></lb>interrupta enim primùm eſt inter<emph.end type="italics"></emph.end> XC, <emph type="italics"></emph>&<emph.end type="italics"></emph.end> DE, <emph type="italics"></emph>& <lb></lb>inde ab<emph.end type="italics"></emph.end> E <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> H: <emph type="italics"></emph>& ſi vlteriùs procedendum eſſet, tum <lb></lb>à nona parte interrumperetur vſque ad decimam octa<lb></lb>uam, & ita deinceps: progreßio autem in ratione dupla <lb></lb>ſola per totum spatium continua eſt.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001613">Id ſatis peruidi, ſed & ſimùl agnoui, quàm <lb></lb>operoſo ſimùl, <expan abbr="irritõque">irritonque</expan> conamine mentem ad <lb></lb>iſta aduerteres; ea videlicet ſuperexſtruens la<lb></lb>baſcentibus ſponte fundamentis. </s> <s id="s.001614">Labaſcentibus, <lb></lb>inquam, primùm, quatenùs falſum eſt, velocitates eſſe <lb></lb>inter ſe ſicut ſpatia: quod tamen fuit tibi fundamen<lb></lb>tum primarium, ipſumque eodem Experimento, quo <lb></lb>id ſtabilieras, euerſum. </s> <s id="s.001615">Deinde quatenus nihil eſſe <lb></lb>videtur poſſe abſurdius, quàm primum primæ partis <lb></lb>dimidium nullo poſſe habere loco in progreſſione <pb pagenum="207" xlink:href="028/01/247.jpg"></pb>Geometrica, & eius tamen comparatione eam <expan abbr="pro-greſſionẽ">pro<lb></lb>greſſionem</expan> ſtabilire; <expan abbr="quã">quam</expan> ex fragmentis poſterioris dimi<lb></lb>dij durationem quærere innumerabilium partium con<lb></lb>ſequent<gap></gap><expan abbr="ũ">um</expan>: quàm cogi ad <expan abbr="comminiſcendũ">comminiſcendum</expan>, quæ in ipſa te<lb></lb>tam malè cohæreant, vt quod commentum ſemel pla<lb></lb>cuerit, cohætere poſſe videatur. </s> <s id="s.001616">Tandem, quatenus <lb></lb>etiam iuxta progreſſionem in ratione dupla, quam ſo<lb></lb>lam vis eſſe continuam, repugnes tibi neceſſe eſt, cùm <lb></lb>indefinite aiens <emph type="italics"></emph>æqualibus temporibus spatia decurri ma<lb></lb>iora ſemper, ac maiora in ratione dupla,<emph.end type="italics"></emph.end> neceſſe ſit eandem <lb></lb>rationem euertas, quotieſcumque aſſumpſeris tempo<lb></lb>ra aſſumptis maiora, & ipſa tamen inter ſe æqualia. <lb></lb></s> <s id="s.001617">Quippe cùm in tuo, v. c. de caſu ex Luna exem<lb></lb>plo aſſumpſeris primo tempore decurri pedes 100, ſe<lb></lb>cundo 200, tertio 400, quarto 800, quinto 1600, <lb></lb>ſexto 3200, &c. </s> <s id="s.001618">conſtatſi deinceps duo tempora pri<lb></lb>ma pro vno aſſumas, duo ſequentia pro alio, duo <lb></lb>item ſequentia pro alio: aut ſi tria quidem prima pro <lb></lb>vno, tria ſuccedentia pro alio, &c. </s> <s id="s.001619">conſtat, inquam, <lb></lb>fore omnia tempora inter ſe æqualia; & abfutura ta<lb></lb>men, quæ interim decurrentur ſpatia, à ratione dupla: <lb></lb>cùm binis temporibus aſſumptis pro ſingulis, futura <lb></lb>ſint ſpatia in ratione quadrupla, vt putà primo tem<lb></lb>pore 300, ſecundo 1200, tertio 4800: & aſſum<lb></lb>ptis ternis, futura ſint in ratione octupla, vt puta pri<lb></lb>mo tempore 700, ſecundo 5600, tertio 44800, <lb></lb>atque ita de cæteris. </s> <s id="s.001620">Dicerem heic de Incommodo, <lb></lb>in quod te recidiſſe conſequenter obieci, <emph type="italics"></emph>de nunquam <lb></lb>abſoluendo tempore ſecundo,<emph.end type="italics"></emph.end> aut <emph type="italics"></emph>percurrendis ſaltem ſpatijs <lb></lb>infinitis,<emph.end type="italics"></emph.end> ſi progreſſio ſpatiorum fieret temporibus ęqua-<pb pagenum="208" xlink:href="028/01/248.jpg"></pb>libus in ratione continuò dupla. </s> <s id="s.001621">Sed cùm tu nihil am<lb></lb>pliùs habeas, quàm quod te obiter attigiſſe memora<lb></lb>tum ſuperiùs eſt; ideò nihil eſt addendum ad ea, quæ in. <lb></lb></s> <s id="s.001622">Reſponſione leguntur. </s> </p> <p type="main"> <s id="s.001623"><emph type="center"></emph>IN ARTICVLOS XLIII, & XLIV. </s> <s id="s.001624">De Tempore, <lb></lb>quo globum ferrcum caſurum ex Luna in <lb></lb>Terram contendit.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001625"><emph type="italics"></emph>Quod autem numero xliij, & xliv. </s> <s id="s.001626">incredibilem putas <lb></lb>celeritatem, qua globus ferreus à Luna ad terram deſcende<lb></lb>ret in continua ratione dupla: non ſufficienter probat eam ex <lb></lb>natura rei tantam eſſe non debere: ac tecum ego quoque arbi<lb></lb>tror eam adeò immenſam reipsâ eſſe non poſſe, quantumvis id <lb></lb>natura exigeret: quod medium tantam, adeóque celerem par<lb></lb>tium diuiſionem, ac rarefactionem pati poſſe non videatur: <lb></lb>quod ſatis à me inſinuatum non ignoras.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001627">Peracta Concluſione, fuit tibi, quaſi illuſtre quod<lb></lb>dam Exemplum prolixus huiuſmodi caſus, vt in ip<lb></lb>ſo exprimeres, quanta eſſetvis progreſſionis in ratione <lb></lb>continuò dupla. </s> <s id="s.001628">Quòd ego porrò celeritatem, qua tu <lb></lb>ſtatuiſti globum ferreum caſurum ex Luna in terram <lb></lb>minutis non omninò duobus, tantam non eſſe ex rei <lb></lb>natura, abundè ſatis probauerim: vel ex eo conſtat, <lb></lb>quòd monſtratum ſit, eam non eſſe iuxta progreſſum, <lb></lb>quem natura in motu grauium decidentium inſtituit: <lb></lb>& euerſum ſit fundamentum, cui ipſam ſuperſtruxeras, <lb></lb>ratio ſcilicet eadem ſpatiorum, ac velocitatum; idque <lb></lb>non modò Experimentis aliis, ſed illo etiam, quod à <lb></lb>te vſurpatum, deprehenſum eſt, ſecus ſe habere, & ſecus <pb pagenum="209" xlink:href="028/01/249.jpg"></pb>probare, quàm ipſe putâris. </s> <s id="s.001629">Ne memorem rapiditatem, <lb></lb>qua ille globus ciendus foret, oſtenſam fuiſſe adeò <gap></gap><lb></lb>manem, adeò, vt loquuntur, inſanam, vt te etiam <lb></lb>iam cogat ad abnegationem ſui: tametſi rem lenias, <lb></lb>dum naturam quidem id exigere, ſed medij tamen <lb></lb>conditionem obſtare dicis. </s> </p> <p type="main"> <s id="s.001630"><emph type="center"></emph>IN ARTICVLOS XLV. XLVI. XLVII. </s> <s id="s.001631">De quodam <lb></lb>lapſu emendando circa cauſſam Phyſicam <lb></lb>accelerati grauium Motus.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001632">Cum nihil habeas circa alios, qui heinc ad con<lb></lb>eſuſionem vſque interſeruntur, articulos, & ego in ip<lb></lb>ſis, occaſione Phyſicæ cauſſæ, de qua te dicturum alio <lb></lb>loco, temporéque receperas, inſinuâtim lapſum, à quo <lb></lb>non ſatis caueram, in priore Epiſtolatum de Motu im<lb></lb>preſſo à motore tranſlato (imò & in Epiſtola ante duos <lb></lb>annos ad te data) eam ob rem heic locus erit opportu<lb></lb>nus, vt rem paulò fuſiùs deducam, ac memetipſum cor<lb></lb>rigam, dicturus ſimùl de Phyſica cauſſa, quam tu pla<lb></lb>cere tibi dixiſti in articulum XXXV. Itaque, cùm ego <lb></lb>demirarer illam accelerati motus progreſſionem ſe<lb></lb>cundum ſeriem numerorum ab vnitate imparium, Ra<lb></lb>tiocinatus ſum imprimis, lapidem v.g. non habere ex <lb></lb>ſe huiuſmodi motum; quoniam ſi ſolus lapis non ex<lb></lb>ſiſtente Mundo foret, aut aliàs in vacuo ſic conſtitue<lb></lb>retur, vt nihil cum Mundo communicaret; non eſſet <lb></lb>prorsùs, quamobrem eò, quò iam mouetur tenderet; <lb></lb>vnde & concluſi cauſſam huiuſmodi motus eſſe debe<lb></lb>re extrinſecam, ipſamque aut impellentem, aut attra-<pb pagenum="210" xlink:href="028/01/250.jpg"></pb>hentem, aut vtramque ſimùl. </s> <s id="s.001633">Secundò, viſum mihi <lb></lb>eſt aſſumi poſſe aërem, qui infernè preſſus, reſilienſ<lb></lb>que ad latera, in locum poſterum ſuccederet, ſuperné<lb></lb>que inſtaret, pro cauſſa impellente; & magneticam Ter<lb></lb>ræ vim, quæ hamulorum, catenularumque inſtar, in<lb></lb>fernè pelliceret, pro cauſſa trahente. </s> <s id="s.001634">Tertiò viſum eſt <lb></lb>aërem non poſſe inchoare motum, quatenus ſi nulla <lb></lb>eſſet Terra, & ſolus aër in vniuerſo, & ipſe quidem in<lb></lb>finitè fuſus, vnaque lapis intra ipſum, tunc lapis in <lb></lb>hanc potiùs partem, quàm in aliam non moueretur: <lb></lb>quare & motum lapidis videri debere ab attractione <lb></lb>incipere, ac tum poſſe ab aëre ſuccedente adiutari. <lb></lb></s> <s id="s.001635">Quartò, cùm fuiſſem ratiocinatus motum ſemel im<lb></lb>preſſum futurum perpetuum, & æquabilem, niſi eſſet <lb></lb>cauſſa, quæ illum aut retundendo minueret, aut vrgen<lb></lb>do acceleraret; concluſi motum lapidis accelerari, quòd <lb></lb>ſtatim à prima attractione, & quaſi poſt primum <expan abbr="ictũ">ictum</expan>, <lb></lb>ſuccederent continuò ictus alij, qui impreſſione facta, <lb></lb>manenteque facerent motum celeriorem. </s> <s id="s.001636">Quintò vi<lb></lb>ſum eſt neque attractionem ſolam, neque impulſio<lb></lb>nem ſolam, neque vllam aliam ſimplicem cauſſam ſuf<lb></lb>ficere ad memoratam progreſſionem: quia cùm hoc <lb></lb>modo ictus continenter facti progreſſuri eſſent ſecun<lb></lb>dum vnitatum ſeriem, conſentaneum videbatur, vt & <lb></lb>velocitatis gradus acquirerentur, & ſpatia quoque per<lb></lb>currerentur ſecundum eandem ſeriem: ſicque in fine <lb></lb>cuiuſque momenti ſpatia aggregata non forent vt <lb></lb>quadrata temporum, vnum, quatuor, nouem, ſex de<lb></lb>cim, & quadrata cætera; ſed vt vnum tria, ſex, decem, <lb></lb>& conſequentia aggregata. </s> <s id="s.001637">Sextò viſum eſt ergo <pb pagenum="211" xlink:href="028/01/251.jpg"></pb>potiùs vtramque cauſſam ſic coniungendam, vt pri<lb></lb>mo momento ſola Terra vi attractice ageret, vnumque <lb></lb>ictum imprimeret: vnde & vnus gradus velocitatis im<lb></lb>primeretur, quo mobile certum ſuperaret ſpatium: ſe<lb></lb>cundo autem momento tum Terra attrahere pergeret, <lb></lb>tum aër pellere inciperet; ſicque duo, ex duobus velut <lb></lb>ictibus, noui eſſent velocitatis gradus, qui cum primo <lb></lb>manente eſſent tres, vnde & tria ſpatia primo æqualia <lb></lb>percurrerentur; & ita porrò continenter. </s> <s id="s.001638">Poſtremò, <lb></lb>cùm mihi viderer cauſſam dicere, quamobrem ſpatia <lb></lb>percurrerentur ſecundum ſeriem numerorum ab vni<lb></lb>tate imparium, & aggregata ſpatiorum eſſent ſicut <lb></lb>quadrata temporum; rem totam ſic expoſui, repetito <lb></lb>iam aliquoties triangulo, vt partes æquales alterutrius <lb></lb>cturum pro momentis, ſeu partibus æqualibus temporis <lb></lb>habens, intercepta <lb></lb><figure id="id.028.01.251.1.jpg" xlink:href="028/01/251/1.jpg"></figure><lb></lb>illa ipſi triangula <lb></lb>per interductas li<lb></lb>neas partim baſi, <lb></lb>partim cruribus pa<lb></lb>rallelas creata, ha<lb></lb>beri poſſe ſimùl <lb></lb>cenſuerim, & pro <lb></lb>partibus æquali<lb></lb>bus ſpatij decurſi; <lb></lb>& pro æqualibus <lb></lb>gradibus veloci<lb></lb>tatis acquiſitæ. </s> </p> <p type="main"> <s id="s.001639">Iam lapſus fuit, quatenus proinde velocitates vt <lb></lb>ſpatia habere ſe admiſi imprudens. </s> <s id="s.001640">Quia enim non <pb pagenum="212" xlink:href="028/01/252.jpg"></pb>ſatis attendi velocitatis gradum primo momento ac<lb></lb>quiſitum ita integrum manere in ſecundo, vt ad ſu<lb></lb>perandum duo ſpatia valeret, ipſumque ita habui, qua<lb></lb>ſi valeret ſolùm ad ſuperandum vnicum; ideò cùm vi<lb></lb>derem ſecundo momento tria ſuperari ſpatia, exiſti<lb></lb>maui facilè ita vnum ſuperari per gradum manentem, <lb></lb>vt duo alia deberent per duos alios, interim acquiſitos <lb></lb>ſuperari. </s> <s id="s.001641">Pari autem ratione quinque ſpatia tertio <lb></lb>ſuperari momento agnoſcens, ſic putaui treis gradus <lb></lb>ſuperiores manere, vt ſingula per ſingulos ſuperaren<lb></lb>tur ſpatia, ac interim acquirerentur duo alij, quibus <lb></lb>duo alia ſuperarentur: non ſatis attendens duos tan<lb></lb>tum gradus prius acquiſitos, manenteiſque eſſe, quo<lb></lb>rum vtrique deberentur duo ſpatia; ſicque ambobus <lb></lb>quatuor; ac neceſſarium rursùs eſſe vnicum duntaxat <lb></lb>acquiri, cui ſpatium quintum deberetur. </s> <s id="s.001642">Pari etiam <lb></lb>ex ſpatiis ſeptem quarto momento ſuperatis, quin que <lb></lb>retuli ad gradus quinque, quos habui iam acquiſitos, <lb></lb>ac manenteis, & duo ad duos, qui acquirerentur in<lb></lb>tereà: non attendens ipſos eſſe treis duntaxat, quorum <lb></lb>tamen ſingulis deberentur duo ſpatia; vnde & per illos <lb></lb>ſuperarentur ſex, ac ideò eſſe ſolùm neceſſe, vt tum ite<lb></lb>rùm acquireretur vnicus, quo ſeptimum ſuperaretur; <lb></lb>atque ita de cæteris. </s> <s id="s.001643">Itaque, quam primùm animum <lb></lb>aduerti, diſplicuit rem ſic expoſuiſſe, vt velocitates ita <lb></lb>ſe habere viderentur, quemadmodum ſpatia, & non <lb></lb>modò ſpatiorum, ſed etiam velocitatum aggregata <lb></lb>perinde ſe habere, vt quadrata temporum: quod mi<lb></lb>hi quidem viſum eſt ipſi naturæ repugnare; ſecundum <lb></lb>quam potiùs doberent velocitates eſſe quemadmo-<pb pagenum="213" xlink:href="028/01/253.jpg"></pb>dum tempora, & aggregata ſpatiorum ſola ſe habere <lb></lb>vt temporum (aut velocitatum proinde) quadrata. <lb></lb></s> <s id="s.001644">Quare & retento eodem Schemate, ſic omnia con<lb></lb>gruere mihi viſa ſunt, vt partes illæ cturum æquales ro<lb></lb>præſentarent ſemper æqualeis parteis temporis: lineæ <lb></lb>verò parallelæ ex vno crute in aliud ductæ, & ſtatim <lb></lb>à prima in parteis æqualeis diuiſæ, gradus æqualeis ve<lb></lb>locitatis; intercepta autem illa, æqualiaque triangula, <lb></lb>æqualeis parteis ſpatii; ac denique ex triangulis impari <lb></lb>numero ſub vnoquoque <expan abbr="momẽto">momento</expan> contentis, aſſumpta <lb></lb>bina, & quadrangulos conſtituentia triangula, repræ<lb></lb>ſentarent ſpatia per gradus manenteis decurſa; & quod <lb></lb>impar ſupereſſet, repræſentaret ſpatium gradu interim <lb></lb>acquiſito decurſum. </s> <s id="s.001645">Atque hoc quidem modo ſen<lb></lb>tentiam expreſſi partim in Reſponſione, partim etiam <lb></lb>ſuperiùs circa explicandum Controuerſiæ ſtatum. </s> <s id="s.001646">Cæ<lb></lb>terùm vt animaduerti ſingulos, non binos velocitatis <lb></lb>acquiri gradus; ſic facile fuit animaduertere ſingulos, <lb></lb>non binos quouis momento impingi ictus. </s> <s id="s.001647">Quam<lb></lb>obrem peruidi me in eo fruſtrà laboraſſe, vt Phyſi<lb></lb>cam cauſſam accelerati motus requirens, excogitarem <lb></lb>denique duas, quarum vna inchoaret motum, & pri<lb></lb>mo momento ſola ageret, ſingularemque ictum im<lb></lb>primeret: ac deinde in ſecundo momento geminæ eſ<lb></lb>ſent, quæ & ſimul agerent, & geminatis ictibus accele<lb></lb>rarent æquabiliter motum: quippe cùm non modò <lb></lb>non fuerit duplex cauſſa neceſſaria, ſed ne potuerit <lb></lb>quidem eſſe, niſi vna. </s> <s id="s.001648">Quam-nam verò, putas, ex dua<lb></lb>bus retinui; quam-nam eliminandam cenſui? </s> <s id="s.001649">Scilicet <lb></lb>retinui attractricem Terræ, vt quæ poſſet ſola non <pb pagenum="214" xlink:href="028/01/254.jpg"></pb>modò inchoare motum, ſed & ipſum quoque accele<lb></lb>rare æquabiliter: vt putà per gradus ab vſque initio <lb></lb>tum manenteis, tum acquiſitos, eo modo, quo decla<lb></lb>ratum eſt. </s> <s id="s.001650">Abieci verò impellentem attributam aëri, <lb></lb>vt quæ non modò inefficax inchoando motui videre<lb></lb>tur, ſed illius etiam promotioni, ſeu accelerationi offi<lb></lb>ciens; tantum abeſt, vt ad ipſam procurandam quic<lb></lb>quam conferret. </s> <s id="s.001651">Atque hæc quidem cauſſa eſt, quam<lb></lb>obrem quidpiam videatur ſimùl de tua opinione di<lb></lb>cendum, quatenus partim conſentit cum ea, quæ mihi <lb></lb>priùs animo inſedit, partim diſſentit ab ea, quæ iam in<lb></lb>ſidet. </s> <s id="s.001652">Quippe, vt ego quidem priùs, ſic tu agnoſcis du<lb></lb>plicem cauſſam; & vnam quidem penitùs candem, <lb></lb>aërem putà impellentem; alteram verò nomine diuer<lb></lb>ſam, ſed effectu eandem, inſitam putà grauitatem (cui <lb></lb>ego attractricem Terræ <expan abbr="ſubſtituendã">ſubſtituendam</expan> cenſueram) qua<lb></lb>tenus tu eam retinens, ipſi quoque tribuis incœptio<lb></lb>nem motus. </s> <s id="s.001653">Cùm verò ipſe ſolam iam attractricem <lb></lb>retineam, à qua continenter agente, & impreſſione non <lb></lb>pereunte, acceleratio motus fiat; opinatis tu grauita<lb></lb>tem ad accelerationem nihil facere: ſed inalteratam ſic <lb></lb>perſeuerare, vt ex ſe motum vniformem, & æquabilem <lb></lb>faciat: ſolum autem aërem ſeſe à tergo concludentem <lb></lb>eſſe accelerationis cauſſam. </s> <s id="s.001654">Heinc nempe ſuperiùs tua <lb></lb>hæc verba fuerunt. <emph type="italics"></emph>Acceleratio omnis à medio ſolo eſt: vn<lb></lb>de deſcenſus in vacuo ſui ſemper ſimilis, atque vniformis <lb></lb>exſiſteret: ſicut tunc quoque tota cauſſa deſcenſus, nempe graui<lb></lb>tas, ſemper eadem, ac ſui ſimilis per ſeueraret.<emph.end type="italics"></emph.end></s> <s id="s.001655"> Itaque cùm <lb></lb>diſſenſus ſit circa tuam vtramque cauſſam, ecce de <lb></lb>vtraque pauca hæc attingo. </s> </p> <pb pagenum="215" xlink:href="028/01/255.jpg"></pb> <p type="main"> <s id="s.001656">Et ab Aëre quidem vt incipiam, non immanifcſtum <lb></lb>videtur ipſum nihil poſſe ad accelerationem conferre; <lb></lb>quin-etiam potiùs officere, tantum abeſt, vt aër ſolus <lb></lb>ſit accelerationis cauſſa. </s> <s id="s.001657">Ipſe certè cùm priùs illum in <lb></lb>aliquam partem admittens, varia energiæ ipſius argu<lb></lb>menta conquiſiui (auſus etiam ad cum ex parte referre <lb></lb>adactionem retrorsùm factam tormentariæ machinæ, <lb></lb>dum globus prorsùm exploditur; idque, vt iam reor, <lb></lb>iniutiâ, quòd potiùs ille totus effectus ad vnum ignem <lb></lb>pertineat) ſubieci ſtatim eas rationes, ob quas meritò <lb></lb>de mea aëris aſſumptione dubitaretur. </s> <s id="s.001658">Vt verò iam <lb></lb>vel vnicam aduerſum te heic repetam, quæſo ex te, <lb></lb>qui ſieri valeat, vt lapidi deorsùm tendenti ad celeri<lb></lb>tatem aër conferat, non conferat tendenti ſurſum? </s> <s id="s.001659">Ni<lb></lb>mirùm vt aër lapide cadente infernè abſcedit, ſupernè <lb></lb>ſuccedit: ſic ſursùm adacto ſupernè abſcedit, infernè <lb></lb>ſuccedit, &, tuo verbo vt <expan abbr="dicã">dicam</expan>, ſe à tergo claudit. </s> <s id="s.001660">Non<lb></lb>ne ergo, ſi deſcendendo iuuat aër impetum à grauitate <lb></lb>impreſſum: neceſſe eſt, vt aſcendendo iuuet impetum <lb></lb>impreſſum à manu? </s> <s id="s.001661">Et quia impetus à manu impreſ<lb></lb>ſus fortior illo eſt, qui à grauitate imprimitur, ſiquidem <lb></lb>illum ſuperat, eóque ne quicquam reſiſtente, lapis ni<lb></lb>hilo min ùs ten dit ſurſum: quid eſt, cur aſcendendo non <lb></lb>magis, quam exſcendendo iuuet? </s> <s id="s.001662">Nonne clauditur <lb></lb>à tergo rapidiùs, ſtatim ac manum lapis deſeruït, quàm <lb></lb>dum lapis initio cadit? </s> <s id="s.001663">Nonne ſaltem deberet tune <lb></lb>accelerationis quidpiam facere, non verò pati diminu<lb></lb>tionem? </s> <s id="s.001664">Nonne & quandiù grauitate d<gap></gap>uicta, infe<lb></lb>rioreque exſiſtente, aër à tergo velociùs occurrit? </s> <s id="s.001665">Sed <lb></lb>& quæſo te, nonne ipſe fateris reſiſtere aërem? </s> <s id="s.001666">Dixiſti <pb pagenum="216" xlink:href="028/01/256.jpg"></pb>videlicet <emph type="italics"></emph>motum, eiuſque accelerationem effectum eſſe <lb></lb>Phyſicum, qui per parteis maiores, aut minores pro ratione <lb></lb>ponderis, & reſiſtentia medij metiendus videatur.<emph.end type="italics"></emph.end></s> <s id="s.001667"> Igitut <lb></lb>aër non tantum reſiſtit ſupernè, vt omnes admittunt, <lb></lb>ſed etiam infernè, vt tu quoque admittis (& certè vi<lb></lb>detur tantò maior eſſe debere infernè reſiſtentia, quan<lb></lb>tò aër craſſior eſt, & propter terram ſuppoſitam diffici<lb></lb>liùs diffundi, ac dilabi poteſt; ſed hoc parùm eſt.) Aut <lb></lb>ergo reſiſtentia aëris infernè eſt maior, quàm impulſio <lb></lb>ſupernè, aut æqualis, aut minor. </s> <s id="s.001668">Si dicas maiorem; <lb></lb>igitur motus rei cadentis non accelerationem ab aëre, <lb></lb>ſed retardationem patietur. </s> <s id="s.001669">Si æqualem; igitur motus <lb></lb>non acecl<gap></gap>rabitur, ſed vno ſemper tenore erit. </s> <s id="s.001670">Si mi<lb></lb>norem, igitur cum tota vis aëris ſupernè impellens ſit <lb></lb>ab ipſa vi lapidis infernè aërem vtgentis, erit effectus <lb></lb>potentior cauſſa; & exſiſtente aëre, quaſi flagello, quo <lb></lb>lapis ſeipſum quaſi verberet, fiet flagelli adactio, <lb></lb>quam intentatio rapidior; &, vt verbo dicam, mouebi<lb></lb>tur aër velociùs à tergo, quàm refugiat à fronte; ſic<lb></lb>que neceſſariò relinquet locum in medio vacuum: <lb></lb>quod vt repugnat, ſic clarum eſt, non poſse aerem ve<lb></lb>lociùs accedere, quàm abſcedat: cùm etiam ex ſe tantò <lb></lb>moueatur ſegniùs, quantò longiùs ab<gap></gap>t à cauſſa mo<lb></lb>uente. </s> <s id="s.001671">Ac vt præteream, ſi id dicas, idem prorsùs fo<lb></lb>re dicendum de aere, dum lapis ſeu ſurſum, ſeu alior<lb></lb>ſum compellitur: prætereo quoque non fore quam<lb></lb>obrem cauſſemur aerem ſuâ reſiſtentiâ retardare tan<lb></lb>tillum motum, cùm illum potiùs ſit promoturus; ne<lb></lb>que quamobrem concludamus aerem quicquam re<lb></lb>ſiſtere, cùm nullum ſit reſiſtentiæ ipſius futurum indi-<pb pagenum="217" xlink:href="028/01/257.jpg"></pb>cium: eo modo, quo agnoſcere non licet corpus ali<lb></lb>quod frigefacere, quando calor eſt ita potentior fri<lb></lb>gore, vt ſolus ipſius effectus ſentiatur. </s> <s id="s.001672">Sic non eſt <lb></lb>quare iam excuſes non poſſe globum ferreum ex Luna <lb></lb>eadentem moueri tam perniciter, quàm prædixeris, <lb></lb>ob conditionem medij, cùm reſiſtentia ſit ſemper ipſa <lb></lb>impulſione futura minor. </s> <s id="s.001673">Et quod ais <emph type="italics"></emph>aërem demùm <lb></lb>neque tam celeriter diuidi, neque tam citò rarefieri, & <lb></lb>accurrere ad replendum vacuum naturaliter poſſe:<emph.end type="italics"></emph.end> idipſum <lb></lb>probat non minorem in reſiſtendo, <expan abbr="quã">quam</expan> in accurren do <lb></lb>vim eſſe; cùm & vacuum ex eo metuendum à tergo <lb></lb>non ſit, quòd non aër immediate antrorsùm pulſus ille <lb></lb>ſit, qui retrorsùm concluditur, verùm ille, qui priùs <lb></lb>ad latera pulſus, & à ſuccedente compulſus, eò iam ac<lb></lb>ceſſit. </s> <s id="s.001674">Ex his itaque, aliiſque id genus argumentis <lb></lb>fieri videtur, vt aër à tergo accurrens minùs poſſit ad <lb></lb>compellendum, quàm occurrens à fronte ad reſiſten<lb></lb>dum: aut ſaltem, vt compenſatio fiat, & dici ad ſum<lb></lb>mum valeat, tantum aërem à tergo concluſum ad pel<lb></lb>lendum iuuare, quantum à fronte diuiſum ad proce<lb></lb>dendum reſiſtere. </s> <s id="s.001675">Vnde & efficiatur, vt aër non mo<lb></lb>dò non ſola, ſed ne vlla quidem cauſſa ſit accelera<lb></lb>tionis. </s> </p> <p type="main"> <s id="s.001676">De Grauitate verò, quod ſit qualitas inſita, & ab <lb></lb>attractione diſtincta, cuius effectus ſit motus deorsùm, <lb></lb>& ille quidem aëre, alióve quovis medio ſecluſo, ſem<lb></lb>per idem, ſimiliſve ſui, aut æquabilis, videtur mihi dici <lb></lb>non poſſe. </s> <s id="s.001677">Ac vt illa quidem præteream, quæ mox <lb></lb>ſunt de aëre, & nomine aëris vniuersè de medio dicta; <lb></lb>dicamus igitur de vacuo, in quo ais <expan abbr="grauiũ">grauium</expan> deſcenſum <pb pagenum="218" xlink:href="028/01/258.jpg"></pb>futurum æquabilem, ob grauitatem ſemper eandem. <lb></lb></s> <s id="s.001678">Nihil autem eſt neceſſe admoneam, quod ſatis in Epi<lb></lb>ſtolis antè memoratis expreſſi: lapidi nempe, exſiſtenti <lb></lb>in vacuo, perinde eſſe penitùs, ac ſi Mundus prorsùs <lb></lb>non foret: quippe niſi perinde foret, habere igitur de<lb></lb>beret colligationem quampiam cum Mundo, aliqua<lb></lb>ve parte ipſius, ſiue per contactum corporeum, ſiue per <lb></lb>defluxum, atque tranſmiſſionem aut aliquorum cor<lb></lb>puſculorum, aut qualitatum, accidentiumve, non ſine <lb></lb>ſubiecto corporeo, fulcien eque prætermeantium: <lb></lb>quo caſu non eſſet lapis in vacuo, ſed in ſpatio cor<lb></lb>poribus, ſubſtantiave corporea pleno. </s> <s id="s.001679">Quamobrem <lb></lb>nihil penitùs cum ipſo Mundo communicans, perinde <lb></lb>ſe habere debet, ac ſi Mundus foret redactus in ni<lb></lb>hilum, aut procul in immenſitatem imaginariorum <lb></lb>ſpatiorum tranſlatus. </s> <s id="s.001680">Supponamus itaque Deum ſic <lb></lb>feciſſe vacuam regionem hanc elementar<gap></gap>m, vt à <lb></lb>concauo Lunæ orbe ad Terræ vſque ſuperficiem facta <lb></lb>ſit penitùs inanis, & lapis vno ſtadio ſupra ſuperfi<lb></lb>ciem Terræ conſtitutus. </s> <s id="s.001681">Interim verò dum lapis per ſe <lb></lb>æquabiliter deſcendet, & vbi iam vnum, alterumve <lb></lb><expan abbr="paſsũ">paſsum</expan> ſuo motu confecerit, ſupponamus iterùm Deum, <lb></lb>qua potentia eſt, ſic emouere totum Mundum, & cum <lb></lb>ipſo Terram in eadem ſemper diſtantia cum cælo cir<lb></lb>cùm perſeuerantem, vt ipſum circa lapidem, quaſi cir<lb></lb>ca quoddam centrum circumducat, quovſque per<lb></lb>acto circutionis dimidio ita illum ſiſtat, vt Terra iam <lb></lb>ſit è regione loci, in quo fuerit, & lapis ipſam habeat <lb></lb>ad oppoſitam partem: quæro quid-nam tunc lapidi <lb></lb>cuenturum ſit? </s> <s id="s.001682">Si perrecturum moueri dicas, igitur <pb pagenum="219" xlink:href="028/01/259.jpg"></pb>quapræditus erit grauitate ſurſum aſcend<gap></gap>t quoniam <lb></lb>à centro non modò Terræ, verùm etiam Mundi r<gap></gap>ce<lb></lb>det. </s> <s id="s.001683">Si dicas mutaturum viam, & petiturum ipſam Ter<lb></lb>ram; ergo ſentiet Mundum mutatum, eo modo, quo <lb></lb>ferrum magnetem ſibi circumductum? </s> <s id="s.001684">Ergo per quan<lb></lb>dam vim tranſmiſſam, cuius interuentu cum Mundo <lb></lb>communicet, ſicque in puro vacuo non ſit: quod eſt <lb></lb>contra ſuppoſitionem. </s> <s id="s.001685">Si demùm conſtiturum dicas; <lb></lb>ergo carebit grauitate, qua & deſcendat per vacuum, <lb></lb>& æquabiliter deſcendat. </s> <s id="s.001686">Prætereo heic, quæ ad hanc <lb></lb>fententiam quaſi conſequenter ediſſerüi, cùm ante <lb></lb>duos annos reſcribens ad te, declararem tum grauita<lb></lb>tem non eſſe qualitatem quandam ipſi lapidi inhæren<lb></lb>tem: tum motum illum primum, quo lapis à quiete <lb></lb>recedit, quique deinceps acceleratur, non ab huiuſmo<lb></lb>di grauitate, ſed ab ipſa terræ attractione eſſe: tum <lb></lb>ſi deinceps talis motus æquabilis perſeueraret, fore, vt <lb></lb>primo momento, quo intelligeretur fieri, ſuppoſito <lb></lb>eſſe vno horæ minuto, ex ijs quæ decima vocant: vt <lb></lb>(inquam) lapis, ſiue per vacuum, ſiue per plenum mo<lb></lb>ueretur, non caderet ex laqueari ad tabulatum (hoc eſt <lb></lb>orgyis duabus) ne per annorum quidem quinquagies <lb></lb>centena millia, aliaque huiuſmodi. </s> <s id="s.001687">Addo heic ſolùm <lb></lb>grauitatem, quæ aliquid agat in primo momento, <expan abbr="dũ">dum</expan> <lb></lb>motum inchoando lapidem adigit deorſum, aut agere <lb></lb>etiam aliquid in ſecundo, & conſequentium quolibet, <lb></lb>aut nihil. </s> <s id="s.001688">Poſterius non dices, quoniam ſecluſo pri<lb></lb>mo momento grauitatem faceres otioſam, ac nullam, <lb></lb>& lapis conquieſceret, neque poſſes dicere, quam<lb></lb>obrem ipſi vno momento, non quolibet alio, in quo <pb pagenum="220" xlink:href="028/01/260.jpg"></pb>agere non prohiberetur, non competeret actio. </s> <s id="s.001689">At ſi <lb></lb>dicas prius; aut impetus prima actione, & qualibet con<lb></lb>ſequente impreſſus euaneſcit, aut manet. </s> <s id="s.001690">Si euaneſcit, <lb></lb>ergo debet pari ratione euaneſcere, qui ſecundo mo<lb></lb>mento, & conſequente quolibet ab aëre imprimitur; <lb></lb>neque enim potior eſt ratio de vna cauſſa, quàm de <lb></lb>alia (imò neque vlla ratio de vtravis eſt; cùm & dici <lb></lb>non valeat quid perire impetum faciat, &, ſi quid di<lb></lb>catur, probaturum ſit, quicquid vnico ictu à nobis per<lb></lb>cellitur, eo ſolo momento, quo percellitur, moueri, ne<lb></lb>que vel tan tillum perſeuerare poſſe in motu, tanquam <lb></lb>impetu illicò pereunte) quare & aëre nequicquam <lb></lb>pellente perſeuerabit nihilominus conſtitutus à te <lb></lb>æquabilis motus. </s> <s id="s.001691">Sin manet: ergo impetus primi mo<lb></lb>menti additusimpetui ſecundi, & quilibet anteceden<lb></lb>tes additi conſequentibus motum efficient celeriorem. <lb></lb></s> <s id="s.001692">Itaque motus à grauitate ſola non ſic elicietur, vt ſit <lb></lb>ſemper ſui ſimilis, atque vniformis; neque grauitas <lb></lb>ſemper eadem, ſimiliſque ſui, & inalterata (hoc eſt, quæ <lb></lb>à me ſimplex dicta eſt, ſine appellata adiectitia) per<lb></lb>ſeuerabit. </s> </p> <p type="main"> <s id="s.001693"><emph type="center"></emph>IN RESPONSIONIS CONCLVSIONEM.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001694"><emph type="italics"></emph>Et hæc, Clarißime<emph.end type="italics"></emph.end> G<emph type="italics"></emph>aſſende, præcipua ſunt, quæ tibi <lb></lb>neceſſariò pro me, & pro veritate reſcribenda putaui; tum <lb></lb>vt, ſi fieri poteſt, eam tibi, quam ignotam acrius impugnas, <lb></lb>veritatem, maiore luce illuſtratam aperiam: tum vt, ne ſal<lb></lb>tem apud eos, qui Responſionem tuam viſuri ſunt, adeò de<lb></lb>formis, & abſurdus appaream, quàm me deformem, & ab-<emph.end type="italics"></emph.end><pb pagenum="221" xlink:href="028/01/261.jpg"></pb><emph type="italics"></emph>ſurdum effingis. </s> <s id="s.001695">Equidem mihi planè perſuadeo, non alio <lb></lb>animo id à te factum, quàm ſtudio veritatis; ſed quia tamen <lb></lb>aliter factum eſt, quàm intenderes, spero tibi non ingratu<gap></gap><lb></lb>fore, ſi quam quæſiisti, atque optaſti veritatem, eam tibi ab <lb></lb>errore vindicatam exhibeam.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001696">Ego verò, Religioſſime Vir, ita habeo me, vt <lb></lb>exiſtimem licere per tuam æquitatem, habere ipſam <lb></lb>tui cauſſam, à veritatis cauſſa ſeiunctam. </s> <s id="s.001697">Nam te <lb></lb>quidem ſemper eo loco habeo, vt reputem virum non <lb></lb>modò piiſſimum, optimumque, & mei amantiſſi<lb></lb>mum: ſed etiam peritiſſimum, ſolertiſſimum, ſtudio<lb></lb>ſiſſimum veritatis. </s> <s id="s.001698">Veritatem autem eo loco habeo, <lb></lb>vt Eius amore, qui ſeipſum eſſe Veritatem dixit, ſan<lb></lb>ctiſſimum reputem, ipſam, quantum agnoſcitur, nulli <lb></lb>rei non præhabere, & à conditione perſona (aliunde <lb></lb>licet cariſſimæ, ac venerabiliſſimæ, quæ eius poſſeſſio<lb></lb>nem ſibi vendicet) quaſi ſepoſitam ſpectare. </s> <s id="s.001699">Ac <lb></lb>tu quidem nunquam voluiſti, opinor, vt quia plurimi <lb></lb>tuam virtutem, amicitiamque facerem: eapropter, ſi <lb></lb>quidquam tibi videretur, quaſi tabulas vnà obſigna<lb></lb>rem; & in tuam iurans ſententiam, quicquid diceres, <lb></lb>indubium haberem; tuaque permotus authoritate, non <lb></lb>hærerem, quin veritas planè, prorsúmque à te ſtaret. <lb></lb></s> <s id="s.001700">Quare iniurium haud-quaquam fuit, habere te vnum <lb></lb>ex iis viris doctis, qui quapiam in re falli poſſint, & <lb></lb>cùm habeant ſe homines, alienum non putent à ſe, vt <lb></lb>errare poſſe, ſic poſſe ab aliis ſecus ſentientibus mone<lb></lb>ri. </s> <s id="s.001701">Ego itaque, non quòd ſim profeſſus eſſe eum m<gap></gap><lb></lb>qui docere te veritatem aliquam poſſem, ſed quòd te <lb></lb>veritatem ſequi tuâ doctrinâ non eſſem perſuaſus, <pb pagenum="222" xlink:href="028/01/262.jpg"></pb>propoſui tibi candidè quas ſubdubitandi rationes ha<lb></lb>berem. </s> <s id="s.001702">Vnde non mirari, quod ais, non poſſum, <emph type="italics"></emph>fuiſſe <lb></lb>te deformem, atque abſurdum à me effictum:<emph.end type="italics"></emph.end> quippe in eo <lb></lb>ſemper incubui vt de re dicens quod |opinarer, de te <lb></lb>reuerenter ſentirem. </s> <s id="s.001703">Sed nimirùm ex eo, quòd ipſe <lb></lb>cauſſam tuam non aliam eſſe, quàm veritatis exiſtimes, <lb></lb>videris id, quod de re dixi, ita accepiſſe de te, vt ex eo, <lb></lb>quod poſſit opinio deformis, atque abſurda apparere, <lb></lb>ipſemet deformis, & abſurdus appareas; ac illa attingi <lb></lb>non debeat, ne ipſe quoque attingaris. </s> <s id="s.001704">Quanquam <lb></lb>&, quæſo, apud quoſnam effingere te, qualem putas, <lb></lb>volui? </s> <s id="s.001705">Videlicet apud te ſolùm, ad quem res eſt pri<lb></lb>uatim miſſa, & per quem ſtetit, vt aut quaſcumque <lb></lb>velles lituras duceres: aut quicquid id eſſet, ſupprimi <lb></lb>iuberes. </s> <s id="s.001706">Cùm neutrum volueris, ſed potiùs rem <lb></lb>euulgandam cenſueris, confiſus, quod ais, <emph type="italics"></emph>te hiſce Vin<lb></lb>dicijs ignotam mihi, impugnatamque, & maiore iam luce <lb></lb>illuſtratam veritatem aperire:<emph.end type="italics"></emph.end> ac mihi gratum fore ſperans, <lb></lb><emph type="italics"></emph>quòd à me quæſitam, optatamque mihi ab errore iam vindi<lb></lb>catam exhiberes:<emph.end type="italics"></emph.end> non debui ſanè genium fraudare, & <lb></lb>reluctante conſcientia, mancipiique more aſſentari, <lb></lb>applauderéque, annuendo eſſe mihi apertam, exhibi<lb></lb>tamque veritatem, quam nullam planè perſpicerem. </s> </p> <p type="main"> <s id="s.001707"><emph type="italics"></emph>Illud certè mihi perquàm gratum accidit, quòd accu<lb></lb>ratiore experientia globorum decidentium momenta expen<lb></lb>dens, nouam veritati lucem attuliſti: ſpem enim magnam in<lb></lb>de feciſti, futurum breui, vt huius lucis beneficio quæſitam <lb></lb>hactenus veritatem certiùs inueniamus: quam ego ſemper <lb></lb>vbicumque inuentam pari plauſu excipiam, eadęmque ſua<lb></lb>uitate amplexabor.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="223" xlink:href="028/01/263.jpg"></pb> <p type="main"> <s id="s.001708">Quæſo te verò, optime Vir, quomodò putes iſta <lb></lb>cum iis, quæ mox dixiſti, cohærere? </s> <s id="s.001709">Nam ſi ego qui<lb></lb>dem meâ experientiâ nouam veritati lucem attuli, quî <lb></lb>ergo tu mihi veritatem ignotam, ac maiori luce il<lb></lb>luſtratam aperuiſti? </s> <s id="s.001710">An tuâ illâ experientiâ, cui mea <lb></lb>fuit oppoſita? </s> <s id="s.001711">At ſi mea quidem veritati lucem, tua <lb></lb>ipſi tenebras fecit. </s> <s id="s.001712">An adhibito à te ratiocinio? </s> <s id="s.001713">At cùm <lb></lb>id non fuerit aliunde, quàm ex iis tenebris deductum; <lb></lb>quomodo rem mihi aperuit, quæ coram allata à me <lb></lb>luce euanuit? </s> <s id="s.001714">Spem factam ais, vt huius lucis à me al<lb></lb>latæ beneficio veritatem quæſitam certiùs inueniamus. <lb></lb></s> <s id="s.001715">Et quomodo ergo tu ſic eam habuiſti, vt à me quæſi<lb></lb>tam mihi ab errore vindicatam iam exhibueris? </s> <s id="s.001716">An <lb></lb>forte, quia iuxta lucem à me allatam es ratiocinatus? <lb></lb></s> <s id="s.001717">Non ſanè: quin potiùs conſtitiſti ſemper in illis iiſdem <lb></lb>tenebris, hoc eſt hæſiſti ſemper principiis ex tua illa <lb></lb>falſa Experientia ductis. </s> <s id="s.001718">Ac laudabiliſſimum quidem, <lb></lb>quod profiteris te veritatem, vbicumque inuenta fue<lb></lb>rit, perquàm grate, & cum plauſu, ſuauitateque ample<lb></lb>xaturum: ſed cùm ſit quidem quæſtio de ea, quam <lb></lb>profiteris ſimul te mihi aperuiſſe, exhibuiſſeque: quo<lb></lb>modo, amabò, vis iſta excipiam? </s> </p> <p type="main"> <s id="s.001719"><emph type="italics"></emph>At cæteris in rebus tam acutè non vidiſti, & tam certò <lb></lb>in illis deceptus es, quàm auſpicatò tibi, ac fœliciter illud <lb></lb>ceßit.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001720">Ipſe verò hebetem me neque neſcio, neque diffi<lb></lb>teor; at magno tamen deſiderio acutè videndi non <lb></lb>careo. </s> <s id="s.001721">Vnde & cùm in cæteris rebus non ſim aliunde <lb></lb>ratiocinatus, quàm iuxta eam lucem, quæ per factam à <lb></lb>me experientiam allata eſt, vellem oſtenderes quid <pb pagenum="224" xlink:href="028/01/264.jpg"></pb>prauè, ea vſus luce, viderim; & cùm me certò deceptum <lb></lb>ais, peruellem apertam deceptionem faceres, & aut fal<lb></lb>ſitatem principij, aut incohærentiam conſequutionis <lb></lb>manifeſtares. </s> <s id="s.001722">Nam ſi mihi quidem id Experimentum, <lb></lb>de quo loqueris, auſpicatò, ac fœliciter ceſſit; non vi<lb></lb>deo huc vſque quid-nam fuerit illi aut à me <expan abbr="repugnãs">repugnans</expan>, <lb></lb>aut à te conſentaneum admiſſum. </s> </p> <p type="main"> <s id="s.001723"><emph type="italics"></emph>Ego ſanè, cùm in rebus longé obſcurioribus, magiſque <lb></lb>incertis ſatis diù multumque verſatus fuerim, vnus tamen ha<lb></lb>ctenus inuentus es, qui meis in aſſertionibus, ac decretis pu<lb></lb>gnam, contrarietatémque non dicam inuenerit, ſed aliquando <lb></lb>etiam obiecerit: vt mirum tibi videri non debeat, ſi rei noui<lb></lb>tate perculſus, ea, quæ à me in re apertiore decreta, & conſti<lb></lb>tuta ſunt, à tam fœda diſſenſione vindicanda putauerim.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001724">At noſti certè me eum non eſſe, qui vltrò me aſſer<lb></lb>tionibus, decretiſque tuis immiſcuerim. </s> <s id="s.001725">Non eram ea <lb></lb>fœlicitate, vt vel te noſſem, vel nomen meum eſſe tibi <lb></lb>notum putarem, cùm ea fuit humanitas tua, vt me <lb></lb>prior interpellâris, & tum ea improbaueris, quæ con<lb></lb>ſcripta eſſent à me: tum non modò priuatim, ſed pu<lb></lb>blicè etiam teſtatus dolorem, ob fidem à me principiis <lb></lb>falſis, erroneiſque adhibitam, tua vt certiora ſubſtitue<lb></lb>ris, <emph type="italics"></emph>quibus intrepidè<emph.end type="italics"></emph.end> (tua fuit hæc vox) præberem aſ<lb></lb>ſenſum. </s> <s id="s.001726">Neque id modò; verùm etiam conſtituiſti me <lb></lb>publicè eorum arbitrum, iudicemque: ac prouocaſti <lb></lb>adeò, vt quid videretur de ipſis eſſe ſentiendum, ſigni<lb></lb>ficarem. </s> <s id="s.001727">Vtinam verò ipſe me non ita ſponte ſollici<lb></lb>taſſes; longiſſimè enim abfuiſſem, ab omni tuorum <lb></lb>aſſertorum, decretorumque inquiſitione. </s> <s id="s.001728">Quippe <lb></lb>ſatis conſcius, quàm-multa reprchendi in me valeant, <pb pagenum="225" xlink:href="028/01/265.jpg"></pb>is non ſum, qui alijs roprehendendis inhiem; & licere <lb></lb>exiſtimans, vt quiſque ſuo ſenſu ſapiat, in eo ſolùm <lb></lb>ſum, vt ſi roger, quid ſentiam aliqua de re, illud ex<lb></lb>plicem bona fide. </s> <s id="s.001729">Vtinam ſaltem incidiſſes in al<gap></gap>m, â <lb></lb>quo is haberi potuiſſes, Qui gloriaretur ſe in hac tanta <lb></lb>& obſcuritate naturæ, & imbecillitate humani ingenij, <lb></lb>habere decreta, atque aſſertiones; nec duceret eſſe <lb></lb>abunde, ſi quaſpiam veriſimiles coniecturas nanciſ<lb></lb>ceretur Qui conſonantiæ decretorum, aſſertionumque <lb></lb>ſic foret certus, vt ſi à quopiam obſeruaretur, aut obii<lb></lb>ceretur pugna, contrarietaſve aliqua; tum quaſi ad <lb></lb>rem inſolentem ſtupore quodam percelleretur: Qui ſic <lb></lb>videretur ſibi comparatus, vt non quandoque dormi<lb></lb>tar<gap></gap>t; ſemper nimirùm adeò vigil, prouidus, atque <lb></lb>perſpicax, vt nihil rerum cum decretis ſeu cohæren<lb></lb>tium, ſeu repugnantium latere mentem vn quam poſſet: <lb></lb>Qui veluti ſtomachabundus notaret illum, à quo pri<lb></lb>mo interturbata fœlicitas eiuſce de ſe opinionis foret, <lb></lb>ac labor creatus monſtrandi conſtantem ſui cum ſe ip<lb></lb>ſo conſenſum. </s> <s id="s.001730">Me quod attinet, tale nihil vnquam <lb></lb>ſentire aut potui, aut volui de re; ipſe præſertim ſatius <lb></lb>ducens viuere, quod aiunt, in diem, ac poſſe, ſi quid <lb></lb>manè ſenſi, ipſo veſpere recantare. </s> <s id="s.001731">Ac non requiro <lb></lb>quidem, quæ ſint illa obſcuriora, magiſque incerta, in <lb></lb>quibus ais tua decreta tantam tueri conſtantiam; quan<lb></lb>dò videor tibi ne in huius quidem longè clarioris, <lb></lb>certioriſque de Motu controuerſiæ ingreſſus penetra<lb></lb>lia; teſtor tamen me longè eſſe, vt in illa vnquam in<lb></lb>quiram, qui etiam, iſta quod attinet, ſi forte præmo<lb></lb>nuiſſes me, quid rei tibi cordi foret, non adulatus <pb pagenum="226" xlink:href="028/01/266.jpg"></pb>ſanè fuiſſem, ne aduerſus meam mentem loqueter: ſed <lb></lb>neque quicquam reſcrip ſiſſem, ne videri poſſem quam <lb></lb>tu heic appellas fœdam diſſenſionem (quaſi diceres <lb></lb>Camarinam) mouere. </s> </p> <p type="main"> <s id="s.001732"><emph type="italics"></emph>Cæterùm quantalibet aut decretorum meorum inter ſe, <lb></lb>aut pro veritate inter nos pugna, & contentio interceſſerit, <lb></lb>ſumma tamen, vt spero, perſeuerabit ſemper animorum <lb></lb>conſenſio, nec minùs vnquam futurus ſum Tuus ad omnia<emph.end type="italics"></emph.end><lb></lb>PETRVS CAZRÆVS. <emph type="italics"></emph>Metis,<emph.end type="italics"></emph.end> 6. <emph type="italics"></emph>Eid. April.<emph.end type="italics"></emph.end><lb></lb>M. DC. XLV. </s> </p> <p type="main"> <s id="s.001733">Ego verò ſanctè affirmo, nihil me vnquam remiſ<lb></lb>ſurum neque de ſumma veneratione, qua te proſe<lb></lb>quor, neque de ſincero affectu, quo toto ex corde ſum <lb></lb>Tuus. </s> <s id="s.001734">Vale. </s> <s id="s.001735">Pariſijs, Non. Maij, M. DC. XLV. <lb></lb><figure id="id.028.01.266.1.jpg" xlink:href="028/01/266/1.jpg"></figure></s> </p> <pb pagenum="227" xlink:href="028/01/267.jpg"></pb> <figure id="id.028.01.267.1.jpg" xlink:href="028/01/267/1.jpg"></figure> <p type="main"> <s id="s.001736">EPISTOLA TERTIA, <lb></lb>QVAM, TAMETSI TEMPORE <lb></lb>primam, viſum eſt tamen poſt-ponere, quòd <lb></lb>præter argumentum cum ſuperioribus com<lb></lb>mune, contineat etiam explicationem plu<lb></lb>rium aliarum difficultatum, quæ fuerant in <lb></lb>Epiſtolas, <emph type="italics"></emph>De Motu impreſſo a Motore tranſ<lb></lb>lato,<emph.end type="italics"></emph.end> objectæ. <lb></lb><gap desc="hr tag"></gap></s> </p> <p type="main"> <s id="s.001737"><emph type="italics"></emph>AD MODVM REVERENDO, <lb></lb>& Religivſißimo, Doctißimóque Viro,<emph.end type="italics"></emph.end> P. <lb></lb>PETRO CAZRÆO, <emph type="italics"></emph>Societatis<emph.end type="italics"></emph.end> IESV, <lb></lb><emph type="italics"></emph>Diuionenſis Collegij Rectori ſapient ißimo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.001738"><emph type="center"></emph>PETRVS GASSENDVS S.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001739">EXIMIA profectò humanitas tua, vt im<lb></lb>perâris tibi patientiam percurrendi, co<lb></lb>gnoſcendique quicquid illud fuit mearum <lb></lb>ineptiarum; méque ſimul adeò ſolerti, ele<lb></lb>gantique diſquiſitione cohoneſtandum cenſueris. </s> <s id="s.001740">Et <lb></lb>dies quidem ſunt aliquot, ex quo illam cum literis no-<pb pagenum="228" xlink:href="028/01/268.jpg"></pb>biliſſimi Son at o<gap></gap>is M<gap></gap>i oct <gap></gap>uo Eidus datis accepi: <lb></lb>ſed vix iam demùm ruente menſe aggredior quid<lb></lb>piam reſcribere; quòd nunc ſolùm inualetudo, quæ me <lb></lb>per dies complurcis habuit, vacare ſcriptioni non-nihil <lb></lb>permittat. </s> <s id="s.001741">Teſtatus ſum nuper reuerendis illis, opti<lb></lb>miſque Patribus Furnerio, & Burdino, cùm dignati <lb></lb>fuiſſent inuiſere me, & ſuauiſſima de tua virtute inci<lb></lb>diſſetmentio, quantum ægrè ferrem non licere mihi <lb></lb>aliquid ſtatim reponere: nempe tu magis me deuinxi<lb></lb>ſti, quàm vt omninò poſſim, aut debeam videri tacen<lb></lb>do ingratus. </s> <s id="s.001742">Quare & nunc occupationes, quibus <lb></lb>aliunde incumbentibus vrgeri me ſentio, ſepono, ni<lb></lb>hilique earum detrimentum habeo; ſimodò iſto erga <lb></lb>te merito officio defungar. </s> <s id="s.001743">Cogito porrò aliquid cir<lb></lb>ca ſingula capita <foreign lang="grc">τ<gap></gap>ς <gap></gap>υξητήσεως</foreign> attingere; tum ne non <lb></lb>ſatis gratam habuiſſe, aut obiter ſolùm legiſſe eam vi<lb></lb>dear: tum vt rationem reddere, quam depoſcere viſus <lb></lb>es, diſtinctiorem ſimul, & pleniorem poſſim. </s> </p> <p type="main"> <s id="s.001744"><emph type="center"></emph><emph type="italics"></emph>Nondum obſeruatum, qui Galileo obiicitur, Paralogiſmum; <lb></lb>& Neutram duarum virium à Motore tranſlato <lb></lb>impreſſarum imminui ab alterutra.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001745">II. </s> <s id="s.001746">Cùm tu igitur duas illas <emph type="italics"></emph>de Motu impreſſo à Motore <lb></lb>tranſlato<emph.end type="italics"></emph.end> à me conſcriptas Epiſtolas reuocaueris in exa<lb></lb>men; poſtquàm exhibuiſti inſignia ſingularis bene<lb></lb>uolentiæ, & comitatis teſtimonia: tum explicare ag<lb></lb>greſſus es, quæ improbaſti circa Priorem. </s> <s id="s.001747">Imprimis <lb></lb>verò, quòd comprobârim illud Galilei decretum, <lb></lb><emph type="italics"></emph>Motum corporum decidentium ſic accelerari, vt ſuperatæ<emph.end type="italics"></emph.end><pb pagenum="229" xlink:href="028/01/269.jpg"></pb><emph type="italics"></emph>æqualibus temporibus spatia increſcant, ſicut numeri ab vni<lb></lb>tate impares,<emph.end type="italics"></emph.end> dicis me, <emph type="italics"></emph>Si illud quidem decretum in examen <lb></lb>adduxiſſem, perſpecturum fuiſſe & falſum, & Paralogiſmo <lb></lb>euidente confirmatum.<emph.end type="italics"></emph.end></s> <s id="s.001748"> Ego verò neque inficior hallu<lb></lb>cinari potuiſſe me; neque me habeo adeò ſolertem, vt <lb></lb>Paralogiſmum à te inſinuatum etiamnùm pervideam. <lb></lb></s> <s id="s.001749">Peruelle proinde ipſum oſtendiſſes, atque adeò ſubin<lb></lb>dicaſſes, qua ergo alia proportione accelerationem de<lb></lb>cidentium fieri, aut experiundo notaueris, aut deduxe<lb></lb>ris demonſtrando. </s> <s id="s.001750">Certè non ſatis intelligo quam<lb></lb>obrem cenſueris, <emph type="italics"></emph>ſiue hæc proportio, ſiue alia ſit, eam nihil <lb></lb>referre ad meum inſtitutum:<emph.end type="italics"></emph.end> quippe ſi alia fuerit, quàm <lb></lb>quæ ſuppoſita à me eſt, fruſtrà eſt tota ratiocinatio. <lb></lb></s> <s id="s.001751">Quod ad experientiam porrò attinet, obſeruationes à <lb></lb>Galileo recitatas prætereo: ad meas quod ſpectat, quot<lb></lb>quot mihi licuit, & quantum licuit peragere, illam pro<lb></lb>portionem ſemper exhibuerunt. </s> <s id="s.001752">Potiſſimæ fuere, cùm <lb></lb>rem præſtiti, adnotatis ſpatiis, tam in prolixiore ſex<lb></lb>decim orgyis pariete, quàm in tubo vitreo inclinato <lb></lb>prolixiore duabus; ac ſociis ſimul adhibitis, quorum <lb></lb>ſinguli ad ſingula ſpatia, eorumque notas attenderent, <lb></lb>vt tam decidente globo <expan abbr="ſecundũ">ſecundum</expan> parietem, quàm dela<lb></lb>bente per tubum, dicere poſſent, ecquo momento ex <lb></lb>numeratis (& alta voce pronunciatis) æqualibus, glo<lb></lb>bus pertranſiret vnamquamque notam. </s> <s id="s.001753">Nempe ex<lb></lb>inde conſtitit, quale ſpatium fuiſſet primo momento <lb></lb>ſuperatum vnum, talia deinceps ſuperata fuiſſe ſecundo <lb></lb>momento tria, tertio quinque, quarto ſeptem: adeò vt <lb></lb>illa aggregando reperirentur ſuperata in fine primi <lb></lb>momenti vnum, in fine ſecundi quatuor, in fine tertij <pb pagenum="230" xlink:href="028/01/270.jpg"></pb>nouem, in fine quarti ſexdecim & c. ſicque aggregata <lb></lb>ſpatiorum ſe vt temporum quadrata haberent. </s> <s id="s.001754">Quod <lb></lb>ad rationem; quia nondum perſpexi, quem ipſe te ais <lb></lb>perſpexiſſe Paralogiſmum: ideo <foreign lang="grc">έπέχω</foreign>, expectoque, <lb></lb>quouſque eximias lucubrationes vulgaueris, quas pol<lb></lb>liceris aduerſus ea, quæ à Galileo de Motu ediſſeruntur <lb></lb>Dialogo tertio. </s> </p> <p type="main"> <s id="s.001755">III. Deinde, cùm ipſe elicio, <emph type="italics"></emph>Vim impellentem mobils <lb></lb>ſurſum, non modò non deſtrui, ſed ne vlla quidem ratione im<lb></lb>minui à vi impellente in latus,<emph.end type="italics"></emph.end> dicis, <emph type="italics"></emph>Me non inuenturum <lb></lb>fidem apud harum rerum peritos, apud quos receptum eſt, Mo<lb></lb>bile quodcumque duobus motibus in diuerſas partes actum, <lb></lb>tantò ſegniùs deferri in vnum terminum, quantò fortiùs is <lb></lb>alterum tendit.<emph.end type="italics"></emph.end></s> <s id="s.001756"> Ego verò, cui cordi eſt, non tam peri<lb></lb>tis quid perſuadere, quàm addiſcere ab ijs aliquid; id <lb></lb>expeto ſolùm, vt perſpicuè doceant, quod poſſim ca<lb></lb>pere perſpicuè. </s> <s id="s.001757">Et, quod ſpectat quidem ad tuum <lb></lb>Effatum, ſi dum Mobile reipsâ mouetur, diſiunctum<lb></lb>que eſt à motore, veluti lapis per aërem, ſuperueniat <lb></lb>vis aliqua, vt venti, aut manus, quæ ipſum deflectat: <lb></lb>agnoſco eo caſu vim primò impreſſam imminutum iri, <lb></lb>& mobile, ad quem terminum deſtinabatur, non per<lb></lb>uenturum. </s> <s id="s.001758">At ſi noui nihil interueniat ab ipſo vſque <lb></lb>proiectore, in quo & visipſius propria, & vis corporis <lb></lb>ipſum transferentis in vnam coierint: non video quî <lb></lb>debeat recipi Effatum; cùm mobile non tam agatur <lb></lb>duabus viribus, quarum vna alteri obſtet, quàm vnâ, <lb></lb>eáque ſic compoſitâ, vt ad vnicum terminum, ſcilicet <lb></lb>obliquum, contendat. </s> <s id="s.001759">Neque enim manus, dum à <lb></lb>naui transfertur, lapidem reuerâ ſurſum proiicit (vt-<pb pagenum="231" xlink:href="028/01/271.jpg"></pb>cúmque ijs, qui eadem naui conuchuntur appareat) ſed <lb></lb>proiicit reuerà obliquè, quatenus & ipſa obliquè mo<lb></lb>uetur, dum agi ſurſum creditur, deflexa putà à motu <lb></lb>nauis. </s> <s id="s.001760">Et quia proinde vis propria manus, & tranſla<lb></lb>titia nauis ſibi non repugnant, ſed ſeſe veluti inten<lb></lb>dunt, vnam que totalem, fortioremque, quàm ſi ſigilla<lb></lb>tim eſſent, conſtituunt: heinc fieri videtur, vt ſe ſe non <lb></lb>deſtruant, ſed vna euadant, quæ tantum ſit alterutrâ <lb></lb>fortior, quantum altera fortis eſt. </s> <s id="s.001761">Quare & cùm lapis <lb></lb>non tendat directè ſurſum, vt ſi à ſola manu proiicere<lb></lb>tur: neque directe ſecundùm horizontem, vt ſi vehere<lb></lb>tur, agereturve à ſolanaui; verùm feratur motu miſto, <lb></lb>obliquóve, & deſcribat per aërem, quaſi arcum (ſiue <lb></lb>potiùs lineam, quam dicunt parabolicam) cuius chorda, <lb></lb>ſeu baſis ſecundum horizontem eſſe intelligatur; & ſa<lb></lb>gitta, ſeu axis ſecundum perpendiculum (prout medium <lb></lb>eſt inter aſcenſum, & deſcenſum) Exinde eſt, cur lapis <lb></lb>neque minùs altùm, quàm ſi à ſola manu proiiceretur, <lb></lb>perueniat: neque minus ptorsùm, quàm ſi à ſola agere<lb></lb>tur naui, quatenus prolixitas lineæ eſt quidem maior, <lb></lb>quàm ſimplex aſcenſus, deſcenſuſque ad perpendicu<lb></lb>lum; ſed ad hoc vim ſuppletimpreſſio à naui: & pro<lb></lb>lixior quoque, quàm ſimplex ſecundum horizontem <lb></lb>progreſſio; ſed ad hoc vim ſupplet impreſſio à manu. <lb></lb></s> <s id="s.001762">Idem verò dicendum eſt de ſemi parabolica linea: vt <lb></lb>dum lapis è carcheſio non proiectus, ſed dimiſſus, ad <lb></lb>pternam perinde cadit, vt ſi nauis quieſceret: ſiqui<lb></lb>dem ipſi grauitati lapidem adacturæ ſecundùm perpen<lb></lb>diculum, accedit vis nauis, qua manus dimittens inte<lb></lb>rim transfertur, quæque tantumdem impetus addit, <pb pagenum="232" xlink:href="028/01/272.jpg"></pb>quantum eſt neceſſe ad prolixitatem ſemiparaboles, <lb></lb>quàm perpendiculi, maiorem. </s> <s id="s.001763">Heinc mirabilis quidem <lb></lb>eſt ea, quam obiicis, <emph type="italics"></emph>ſemiparabolarum plurium decuplò <lb></lb>etiam, aut centuplò contractiorum, apertiorumque æqui tem<lb></lb>poranea deſcriptio:<emph.end type="italics"></emph.end> ſed videtur tamen apertè deduci ex <lb></lb>minore, & maiore vi, quæ alteri, vt per axem, perpendi<lb></lb>culumve duntaxat acturæ, ſuperadditur. </s> <s id="s.001764">Et <emph type="italics"></emph>poſtularet <lb></lb>quidem ratio,<emph.end type="italics"></emph.end> quemadmodum ais, <emph type="italics"></emph>vt idem mobile non <lb></lb>tranſmitteretur ad eandem altitudinem, aut diſtantiam in pro<lb></lb>iectoris quiete, aut motu, eodem tempore. </s> <s id="s.001765">ſi foret ab eadem vis<emph.end type="italics"></emph.end><lb></lb>ſed conſtat vim non eſſe eandem, quatenus proiectoro <lb></lb>moto eſt tantumdem adauctior, quanta eſt ipſa vis <lb></lb>tranferentis. </s> <s id="s.001766">Ad illud quod habes de <emph type="italics"></emph>Reſistentia medij:<emph.end type="italics"></emph.end><lb></lb>ſi illud quidem vniforme ſit, nihil videtur prorsùs ob<lb></lb>ſtare, quatenus tantum proiicienti, transferentique, <lb></lb>quantum proiectili reſiſtit, pergitve potiùs reſiſtere: <lb></lb>quod idem dicendum de vento, ſi ſecundùm eundem <lb></lb>nauis curſum, & æquabilisfuerit: ſin verò aut medium <lb></lb>inæquabile ſit, aut ventus obliquus, vel variabilis, at<lb></lb>que ade ò ſit inæquabilis reſiſtentia; tunc videtur pro<lb></lb>fectò poſſe non-nihil deſciſcere à parabolico ſuo curſu, <lb></lb>& à termino, in quem contendebat: ſed nempe hic ipſe <lb></lb>eſt caſus, de ſuperueniente vi, ob quam dixi poſſe Effa<lb></lb>tum admitti. </s> </p> <p type="main"> <s id="s.001767">IV. </s> <s id="s.001768">Quòd <emph type="italics"></emph>experimenta deſideras alia,<emph.end type="italics"></emph.end> facillimum im<lb></lb>primis eſt, quod vel tuo iuſſu peragi ab Equite poteſt. <lb></lb></s> <s id="s.001769">Si is enim pluribus lapillis ad manum aſſumptis, & <lb></lb>manu ita protenſa, vt ſit in perpendiculo, quod pedem <lb></lb>proximè præter-radat, lapillum vnum primò dïmittat <lb></lb>quieſcente equo; tum alium equo pedetentim, & paſſu <pb pagenum="233" xlink:href="028/01/273.jpg"></pb>ſolito incedente; & rurſus alium gradiente concitatiùs; <lb></lb>ac poſteà alium moderatè currente; denique & alium <lb></lb>præteruolante tum ocyùs, tum ocyſſimè: eueniet ſanè, <lb></lb>vt lapilli omnes præter-radant ſemper eandem pedis <lb></lb>partem, omneſque appareant ipſi equiti ad perpendi<lb></lb>culum cadere: & quia tamen omnes eiuſmodi caſus, <lb></lb>præter illum, qui quaſi axis equo quieſcente factus fue<lb></lb>rit, ſemiparabolicæ erunt lineæ, eæque ſemper tantò <lb></lb>apertiores, quantò tranſlatio fuerit velocior: fiet, vt ſi <lb></lb>ipſe è regione fueris, illaſque adnotaueris, deſideraturus <lb></lb>non ſis luculentiora <expan abbr="experimẽta">experimenta</expan>. </s> <s id="s.001770">Poteris verò ipſe quo<lb></lb>que ſimile quidpiam experiri, ſi pilam manu ſuſtentâ<lb></lb>ris, ac dimiſeris, dum per aulam, aut pergulam nunc len<lb></lb>to paſſu, nunc concitato, nunc etiam currendo incedes. <lb></lb></s> <s id="s.001771">Nam vt pila tibi ſemper apparebit ad perpendiculum <lb></lb>cadere: ita agnoſces ab ea deſcribi ſemiparabolen nunc <lb></lb>contractam, nunc apertam, nunc apertiorem. </s> <s id="s.001772">Quod <lb></lb>conſequenter verò depoſcis <emph type="italics"></emph><expan abbr="experimentũ">experimentum</expan> in globo ſursùm, <lb></lb>& ſecundum mali nunc quieſcentis, nunc moti longitudinem <lb></lb>areu-baliſta emiſſo:<emph.end type="italics"></emph.end> id tanta facis vrbanitate, vt volentiſ<lb></lb>fimus recipiam me, cum fauente Numine in Prouin<lb></lb>ciam rediero, & ad mare acceſſero, rem in tui gratiam <lb></lb>præſtiturum. </s> <s id="s.001773">Intereà verò res probari vel tuo iuſſu <lb></lb>poterit, ſi quiſpiam è curru prope parietem quieſcente, <lb></lb>& arcu-baliſtâ lateri currus illigatâ emittat ſurſum glo<lb></lb>bulum; ac deinde curru præter eundem parietem, quan<lb></lb>tacumque voles pernicitate abrepto, globulum iterum <lb></lb>emittat, & ſit alius quis è regione, qui vtroque caſu <lb></lb>adnotet altitudinem, ad quam vſque globulus pertin<lb></lb>get. </s> <s id="s.001774">Spondere enim auſim haud inæqualem altitu-<pb pagenum="234" xlink:href="028/01/274.jpg"></pb>dinem adnotatum iri: ita mihi huc-vſque ſucceſſere <lb></lb>multa experimenta haud abſimilia. </s> <s id="s.001775">Dico autem arcu<lb></lb>baliſtam eſſe debere illigatam; quoniam ſi manu con<lb></lb>tineatur, poterit linea directionis aut perpendicularis <lb></lb>non eſſe, aut ſi à perpendiculari deflexerit, non per<lb></lb>inde vno, atque alio caſu deflecti: ob quam eandem <lb></lb>cauſſam agi currus debet per complanatiſſimum lo<lb></lb>cum; ne, ſi ſubſultârit, linea illa nutet. </s> <s id="s.001776">Prætereo au<lb></lb>tem, ſi tot illis, quæ congeſſi, experimentis quæſitam <lb></lb>fidem aliquam putes primatio illi Theoremati, <emph type="italics"></emph>Si id <lb></lb>corpus, cui innitimur, transferatur, motus omneis noſtros, re<lb></lb>rumque à nobis mobilium perinde fieri, appareréque, ac ſi il<lb></lb>lud quieſceret:<emph.end type="italics"></emph.end> quæſitam ſimul eſſe <emph type="italics"></emph>Paradoxo,<emph.end type="italics"></emph.end> quod <lb></lb><emph type="italics"></emph>magnum<emph.end type="italics"></emph.end> appellas, <emph type="italics"></emph>de aſſurgente mobili ad parem altitudi<lb></lb>nem, ſeu moueatur, ſeu quieſcat motor, qui id emiſerit pari <lb></lb>vi;<emph.end type="italics"></emph.end> alioquin certè motus rerum à nobis mobilium pa<lb></lb>ri modo haud apparerent. </s> <s id="s.001777">Quanquam & Paradoxum <lb></lb>dicis ob id ſolùm, quòd res prima fronte adeò admi<lb></lb>rabilis ſit, vt niſi quis expertus fuerit, fidem facilè ha<lb></lb>bere non poſſit. </s> <s id="s.001778">Quòd denique tibi hæret ſcrupulus <lb></lb><emph type="italics"></emph>de globo tormentario, qui caſu perpendiculari recidens in ter<lb></lb>ram, & in eam directe emiſſus, parem percußionis effectum <lb></lb>ſortiri poſſe non videatur,<emph.end type="italics"></emph.end> is, quandò ratio non ſufficit, <lb></lb>experimento eſt <emph type="italics"></emph>lege<emph.end type="italics"></emph.end> eximendus. </s> <s id="s.001779">Quan quam ego quidem, vt <lb></lb>fatear, ſatis hucuſque fœlix non fui, vt rem piſtoleto, <lb></lb>moſquetóque explorare volens, obſeruare potuerim <lb></lb>caſum (adeò pernix efficitur recidentis prope terram <lb></lb>motus: adeó que difficile eſt declinationem tantulam <lb></lb>à perpendiculo cauere, quæ in altitudine tanta para<lb></lb>bolen creet cum diſtentione crurum inſigni, & verſus <pb pagenum="235" xlink:href="028/01/275.jpg"></pb>eam partem, quam ſuſpicari facile non ſit, vt ad <lb></lb>ipſam locus caſus inquiratur; ne etiam cauſer ventum, <lb></lb>agitationemve ſuperioris aëris) ac fortè etiam Gali<lb></lb>leus eatenus hæſit hac de re; quatenus ipſe paris fuit <lb></lb>inter experiundum infœlicitatis. </s> </p> <p type="main"> <s id="s.001780"><emph type="center"></emph><emph type="italics"></emph>Poſſe varias Sectas veritatis studio tentari; ac Poſſe ani<lb></lb>malis inceſſum præ ſaltatione, & globi volutionem <lb></lb>præ adactione, dici naturalem.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001781">V. </s> <s id="s.001782">Seligis conſequenter nonnulla, quæ dicis <emph type="italics"></emph>me <lb></lb>nimia facilitate admittere, quæque viris eruditis, ac pijs minùs <lb></lb>placitura videantur.<emph.end type="italics"></emph.end></s> <s id="s.001783"> Quo ſanè loco, ſi aliquid ex ijs, quæ <lb></lb>admitto, pietati repugnet, id prorsùs deuoueo; vt <lb></lb>quod imprudenti, neque repugnantiam intelligenti <lb></lb>ſeſe obtrudat; agnoſcóque te ſummopere lenem, dum <lb></lb><emph type="italics"></emph>nimiam<emph.end type="italics"></emph.end> potiùs <emph type="italics"></emph>facilitatem,<emph.end type="italics"></emph.end> quàm <emph type="italics"></emph>temeritatem,<emph.end type="italics"></emph.end> aut aliud <lb></lb>quid dicis: quanquam quid tale hactenus, mihi acci<lb></lb>derit, non peruideo. </s> <s id="s.001784">Ad cætera, quæ merè ſùnt na<lb></lb>turalia, quod attinet; non nego quidem ea me phi<lb></lb>loſophari libertate, vt non vni alicui Sectæ erudito<lb></lb>rum, vt vocas, hæreſcam: ſed ſi quid alij aut dicant, <lb></lb>aut dicere poſſe videantur, quod magis probabile ſit, <lb></lb>id veluti magis probabile ſequar: at quoniam ſolo <lb></lb>veritatis amore ita comparor, non eſt, cur verear, <emph type="italics"></emph>ne <lb></lb>quid nimis.<emph.end type="italics"></emph.end></s> <s id="s.001785"> Neque verò is ſum, qui Platonis, Ariſtote<lb></lb>liſque (aut ſi quos putas eſſe illis eruditiores) ſannis <lb></lb>mouear: ac præſertim, cùm ipſi me voce, factóque do<lb></lb>cuerint, <emph type="italics"></emph>Rem ſanctam eſſe, nihil habere ſtudio veritatis an<lb></lb>tiquius.<emph.end type="italics"></emph.end></s> <s id="s.001786"> Non ſanè, quòd ego proptereà ſequi me <pb pagenum="236" xlink:href="028/01/276.jpg"></pb>ipſam veritatem, tanquam à me certò arreptam, pro<lb></lb>ſitear: ſed quòd omnibus exploratis, & ſequutus id, <lb></lb>quod ſimilitudinem maiorem cum ipſa habere mihi <lb></lb>viſum eſt, tum videar mihi cumulatè eo defunctus of<lb></lb>ficio, quod exigit ipſa eius reuerentia. </s> <s id="s.001787">Ex quo pro<lb></lb>inde ſit, vt ſi illi quidem, quos eruditos intelligis, ip<lb></lb>ſam veritatem facerent apertam, nemo me citiùs non <lb></lb>pedibus modò, ſed manibus quoque, & corpore toto <lb></lb>iret, prorueretque in eorum ſententiam: verùm quia <lb></lb>dum ſuis inhærent principiis, nihilo nobis veritatem <lb></lb>reuclatiorem faciunt: quid diſpliceat, ſi à me aliæ, at<lb></lb>que aliæ pulſentur fores? </s> <s id="s.001788">Aut nunquam enim veritas <lb></lb>(intelligo veram, proximamque cauſſam operum na<lb></lb>turæ cuiuis occurrentium) innoteſcet hominibus, quod <lb></lb>mihi penè perſuaſum eſt; aut non vna eſt via ad eius <lb></lb>receſſum hactenus incompertum, tentanda. </s> <s id="s.001789">Quod <lb></lb>ad me ſpectat, agnoſco ſatis nihil aliud me, quàm <lb></lb>balbutire; longéque abſum, vt ex meis nugis <emph type="italics"></emph>famam<emph.end type="italics"></emph.end><lb></lb>aliquam aut quæram, aut ſperem; tuque es nimis bo<lb></lb>nus, dum ſupponis me aliquam adeptum, qui nullam <lb></lb>promereor. </s> <s id="s.001790">Non ſum verò tamen ita ſcrupuloſus, <lb></lb>quin exigentibus amicis, propalatas aliquas faciam; ac <lb></lb>eo fine potiſſimùm, vt eruditos excitem, ad quidpiam <lb></lb>melius comminiſcendum. </s> </p> <p type="main"> <s id="s.001791">VI. </s> <s id="s.001792">Improbas primùm quod dixerim, <emph type="italics"></emph>eſſe inceſſum <lb></lb>animalis præ ſaltatione naturalem:<emph.end type="italics"></emph.end> ſed non vis ſanè, quan<lb></lb>tum opinor, litigare de nomine. </s> <s id="s.001793">Vides me circa mo<lb></lb>tus rerum concretarum ſic diſtinxiſſe, vt reputârim <lb></lb>quemlibet motum aliqua ratione eſſe naturalem, ali<lb></lb>qua ratione violentum: ac id proinde nec de Inceſſu, <pb pagenum="237" xlink:href="028/01/277.jpg"></pb>nec de Saltatione fuiſſe negaturum; & fateris ipſe, me <lb></lb>poſteà aduertere quandam in Inceſſu violentiam ex <lb></lb>laſſitudine demonſtraram. </s> <s id="s.001794">Vides aliunde me illeic <lb></lb>loci nihil aliud requirere, quàm commodam quan<lb></lb>dam vſurpationem nominum, qua ſi quis aliam attu<lb></lb>lerit commodiorem, ſim complexurus. </s> <s id="s.001795">Et quia is mo<lb></lb>tus mihi eſt viſus dici poſſe <emph type="italics"></emph>naturalis,<emph.end type="italics"></emph.end> qui aut ſponte fit, <lb></lb>aut ſine repugnantia; is <emph type="italics"></emph>violentus,<emph.end type="italics"></emph.end> qui præter naturam, <lb></lb>aut cum aliqua repugnantia: heinc eſt, cur <emph type="italics"></emph>Inceſſum na<lb></lb>turalem<emph.end type="italics"></emph.end> dixerim, quatenus nempe ſponte fit; & <emph type="italics"></emph>Salta<lb></lb>tionem violentam,<emph.end type="italics"></emph.end> quatenus quadam cum repugnantia. <lb></lb></s> <s id="s.001796">Non quod Inceſſus quoque non fiat cum repugnantia <lb></lb>aliqua, propter ipſum pondus membrorum: aut Salta<lb></lb>tio non fiat ſponte, ſiue ab eodem principio interno, <lb></lb>hoc eſt anima: ſed quòd neque Inceſſus fiat cum ſenſi<lb></lb>bili adeò repugnantia, tantoque connixu ad eam ſu<lb></lb>perandam, vt Saltatio; neque Saltatio ſit perinde ſpon<lb></lb>tanea, incogitatáque, ac ipſe Inceſſus; vt proinde cum <lb></lb>vterque motus aliqua ratione naturalis ſit, aliqua ra<lb></lb>tione violentus; Inceſſus tamen magis naturalis ſit, & <lb></lb>Saltatio magis violenta; cùm & id probetur ex eo, <lb></lb>quòd Inceſſus ſit incomparabiliter æquabilior, durabi<lb></lb>lior, minuſque fatigans, quàm ipſa Saltatio. </s> <s id="s.001797">Neque <lb></lb>verò ſi ad eos ipſos, quos tu inſinüas, eruditos prouo<lb></lb>care lubuerit, non potero memet tueri Principis eo<lb></lb>rum authoritate, qui etiam in ijs, quæ à ſe mouentur, <lb></lb>cuiuſmodi ſunt animalia, motus alios <foreign lang="grc">φύσ<gap></gap></foreign> <emph type="italics"></emph>naturá,<emph.end type="italics"></emph.end><lb></lb>alios <foreign lang="grc">ω<gap></gap>ὰ φύσιν</foreign> <emph type="italics"></emph>præter naturam,<emph.end type="italics"></emph.end> pro varietate Poſi<lb></lb>tionum, modorumque, fieri agnoſcit. </s> <s id="s.001798">Quod autem <lb></lb>concludis <emph type="italics"></emph>vtrumque motum eſſe partim naturalem, partim<emph.end type="italics"></emph.end><pb pagenum="238" xlink:href="028/01/278.jpg"></pb><emph type="italics"></emph>violentum: neutrum abſolutè naturalem, neutrum abſolutè <lb></lb>violentum:<emph.end type="italics"></emph.end> non ego ſanè oppoſitum cenſui, aut ex ijs, <lb></lb>quæ dixi, cenſere ſum viſus; tametſi cenſens illum præ <lb></lb>iſto eſſe maximè naturalem, iſtum præ illo maximè <lb></lb>violentum, dixi videri illum mihi cenſeri poſſe natu<lb></lb>ralem, iſtum cenſeri poſſe violentum, vtrumque nem<lb></lb>pe <foreign lang="grc">κα<gap></gap> <gap></gap>χ<gap></gap>ὺ. </foreign></s> </p> <p type="main"> <s id="s.001799">VII. </s> <s id="s.001800">Idem porrò dicendum eſt circa id, quod miraris <lb></lb><emph type="italics"></emph>de volutione globi ſupra planum.<emph.end type="italics"></emph.end></s> <s id="s.001801"> Neque enim dixi il<lb></lb>lam eſſe abſolutè naturalem, quaſi nullo modo ab alio <lb></lb>ſit: ſed ſolùm comparatione motus, quo globus per <lb></lb>aërem tranſadigitur, quique ſit præſertim dicendus <lb></lb>violentus. </s> <s id="s.001802">Scilicet globus, quà globus eſt, ſeu ex figuræ <lb></lb>ſuæ natura, ad volutionem eſt comparatus, imò com<lb></lb>paratiſſimus; volutionem, inquam, quæ peragitur non <lb></lb>modò in loco, ſeu ſupra axem ſuſtentantem, vt Ariſto<lb></lb>teles admittit: ſed maximè etiam per locum, ſeu ſu<lb></lb>pra planum horizontale, quod & ſuſtentat, & nihil <lb></lb>reſiſtit; cùm aliunde tamen ex eodem Ariſtotele, nul<lb></lb>lum ſit corpus globo ineptius ad motum <foreign lang="grc">εἰς <gap></gap> ω<gap></gap>ὲν</foreign><lb></lb><emph type="italics"></emph>antrorſum,<emph.end type="italics"></emph.end> & qualis eſt eorum, quæ per ſe mouentur. <lb></lb></s> <s id="s.001803">Heinc proinde ſit, vt de globo ſupra planum conſtitu<lb></lb>to liceat dicere, illum ad motum ſupra planum, ſeu ad <lb></lb>volutionem ita propendere, vt minimo pulſu, ac ve<lb></lb>luti nutu talem motum ſubeat, ipſoque ita afficiatur, <lb></lb>vt depoſiturus illum nunquam ſit, niſi planum defece<lb></lb>rit, aut facta aliunde fuerit reſiſtentia. </s> <s id="s.001804">Niſi verò ille <lb></lb>motus non eſt dicendus maximè ſecundum mobilis <lb></lb>naturam, qui ſemel inditus, ſit ex ſe perpetuus, ac præ<lb></lb>tereà æquabilis, vniuſque tenoris? <emph type="italics"></emph>At,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>natu-<emph.end type="italics"></emph.end><pb pagenum="239" xlink:href="028/01/279.jpg"></pb><emph type="italics"></emph>ralis nondicitur motus, niſi ab interno principio, ipſaque rei <lb></lb>natura effectiuè procedat.<emph.end type="italics"></emph.end></s> <s id="s.001805"> Sed quid-ni ille quoque di<lb></lb>catur, qui ab externo eſt, effectiuéque ab alio eſt; ſi mo<lb></lb>dò <expan abbr="ſecundũ">ſecundum</expan> mobilis <expan abbr="naturã">naturam</expan>, ac diſpoſitionem, non ve<lb></lb>rò contra illam ſit; & quaſi fiat, quod dicitur, <foreign lang="grc"><gap></gap>σοντ<gap></gap><lb></lb>ὀτ<gap></gap>ω<gap></gap><gap></gap>ν</foreign>; <emph type="italics"></emph>inſtigare iam feſtinantem?<emph.end type="italics"></emph.end> Et nonne ipſe <lb></lb>fateris cum Ariſtotele motum rerum grauium eſſe na<lb></lb>turalem, quem ille tamen vult ab externo, non ab in<lb></lb>terno eſſe principio? </s> <s id="s.001806">Et nonne proinde eius verba <lb></lb>ſunt, <foreign lang="grc">τ<gap></gap> ἐπ̓ ἄλλου χινουμ<gap></gap>όων, τὰ μ̄́̓ φύσ<gap></gap>, τὰ δ<gap></gap><lb></lb><gap></gap>ὰ φύσιν χίν<gap></gap></foreign>; <emph type="italics"></emph>eorum, quæ ab alio mouentur, alia qui<lb></lb>dem naturâ, alia verò prater naturam moueri?<emph.end type="italics"></emph.end> Ac ad<lb></lb>uerti quidem, imò expreſsè dixi, <emph type="italics"></emph>alias globi parteis deor<lb></lb>ſum tendere, alias ſurſum:<emph.end type="italics"></emph.end> ſed & hoc ipſum eſt, quod fa<lb></lb>cere cenſui ad æquabilitatem motus; vt dum globus <lb></lb>non ampliùs ſurſum, quàm deorsùm, nec deorsùm, <lb></lb>quàm ſursùm fertur, motusinterim abſque vlla aut ac<lb></lb>celeratione, aut retardatione perſeueret. </s> <s id="s.001807">Quod inter<lb></lb>ſeris verò <emph type="italics"></emph>de corporum cæleſtium motu,<emph.end type="italics"></emph.end> quaſi dicendum <lb></lb>conſequenter fuerit, <emph type="italics"></emph>moueri eorum ſingula à ſingulis ſui<gap></gap><lb></lb>formis, ſeu naturis;<emph.end type="italics"></emph.end> id licet recipiam, non video ecquid<lb></lb>nam incommodi ſit: cùm & graues Doctores ſint, qui <lb></lb>motrices illas Ariſtotelis Intelligentias reſpuant; & <lb></lb>Ariſtoteles ipſe, non modò fateatur moueri cælum à <lb></lb>ſeipſo, ſcilicet tanquam <foreign lang="grc">ἔμφυχὸν</foreign> <emph type="italics"></emph>animatum,<emph.end type="italics"></emph.end> atque <lb></lb>adeò habens in ſe motus ſui principium: ſed etiam <lb></lb>contendat Separatam ſubſtantiam non mouere cælum <lb></lb>vt Efficientem, ſed vt Finem, ac <emph type="italics"></emph>instar rei, quæ appeti<lb></lb>tur,<emph.end type="italics"></emph.end> <foreign lang="grc">ὡς ὁ<gap></gap>εχτὸν</foreign>, quod nunc dicimus <foreign lang="grc">μ<gap></gap>φ<gap></gap>ιχ<gap></gap></foreign><lb></lb>mouere. </s> <s id="s.001808">Atque id quidem, vt præteream, commodius <pb pagenum="240" xlink:href="028/01/280.jpg"></pb>longè eſſe videri, ſi, quod eſt dictum de motu perpe<lb></lb>tuo globi ſupra planum ex facto ſemel vno impulſu, <lb></lb>aſſerat quis cælum continuò, æquabiliterque moueri, <lb></lb>quia in ſui à Deo creatione eam impulſionem acce<lb></lb>perit, qua cœptus tunc motus etiam-num perduret. </s> </p> <p type="main"> <s id="s.001809"><emph type="center"></emph><emph type="italics"></emph>Incredibilem fore motus corporum decidentium ſegnitiem, ſi <lb></lb>vt incipit, ita pergeret: & Non ſolùm accelerationem, <lb></lb>ſed ipſum quoque initium motus eſſe à principio <lb></lb>externo.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001810">VIII. </s> <s id="s.001811">Dicis poſteà, <emph type="italics"></emph>forè, vt mihi Eruditi omnes conce<lb></lb>dant accelerationem eſſe violentam, ſi illam, vt quid ſuper<lb></lb>ueniens, mente ſecernamus ab ipſo deſcenſu.<emph.end type="italics"></emph.end></s> <s id="s.001812"> Non eſt porrò <lb></lb>cur dubites, quin ipſe quoque mente ſecernam motum <lb></lb>illum ſimplicem, quo lapis fertur deorſum, quemque <lb></lb>tu deſcenſum appellas, ab omnibus, qui ſuperueniunt, <lb></lb>giadibus accelerationis. </s> <s id="s.001813">Quippe id abunde expreſſi, <lb></lb>cùm dixi <emph type="italics"></emph>eum motum, ſecluſa acceleratione, fore ex ſe æqua<lb></lb>bilem, ſed imperceptibilem tamen, ob incredibilem ſegnitiem.<emph.end type="italics"></emph.end><lb></lb>Non eſt proinde etiam, cur hæreas, quin illum eſſe na<lb></lb>turalem, & ſine reluctatione agnoſcam; quippe qui <lb></lb>eum faciam, quantum eſt ex ſe, æquabilem, perpetuum, <lb></lb>ac talem, qui ſit imprimendus etiam lapidi exſiſtenti <lb></lb>in vacuo, vbi mobile nullam habet ad motum repu<lb></lb>gnantiam, quocumque verſum tandem agatur: verum <lb></lb>quòd eiuſmodi motus cenſeri naturalis poſſit, non id<lb></lb>circò cenſeo caſum lapidis habendum eſſe naturalem. <lb></lb></s> <s id="s.001814">Quoniam tametſi talis motus in hoc caſu interueniat, <lb></lb>euaneſcit tamen, ſiue nullus eſt, reſpectu accelerationis, <pb pagenum="241" xlink:href="028/01/281.jpg"></pb>quæ ipſi ſuperuenit, quæque vtramque paginam facit; <lb></lb>& quam ipſe quoque fateris violentam. </s> <s id="s.001815">Atque vt perſ<lb></lb>picuè appareat cuius momenti ſit ille motus, ſiue, vt <lb></lb>tu vocas, deſcenſus, ab acceleratione ſecretus, & cum <lb></lb>ipſa tamen comparatus; age Experiamur, &, exempli <lb></lb>gratiâ, altitudin m accipiamus non immanem <expan abbr="aliquã">aliquam</expan>, <lb></lb>ſed qualem ſolùm vulgò vſurpant inter tabulatum, & <lb></lb>laquear, duarum videlicet orgyiarum. </s> <s id="s.001816">Huiuſmodi eſt <lb></lb>altitudo, quam lapis decidens peruadit vno minuto <lb></lb>horæ ſecundo. </s> <s id="s.001817">Cùm acceleratio verò ſit intra hoc <lb></lb>tempus, & à primo vſque momento continua, intelli<lb></lb>gamus id tempus diuidi in tertia, quarta, quinta, & <lb></lb>porrò ad vſque horæ decima; vt licet vnum decimum <lb></lb>ſubdiuidi vlteriùs poſſit in vndecima, duodecima, &, vt <lb></lb>volunt, in infinitum, in decimo tamen vno conſiſta<lb></lb>mus, tanquam minimo temporis, ſeu primo momen<lb></lb>to, quo lapis ita decidit, decidereve incipit, vt à ſtatim <lb></lb>ſuperuentura acceleratione ſit liber. </s> <s id="s.001818">Erunt proin<lb></lb>de in vno minuto horæ ſecundo minuta decima <lb></lb>167961600000000. Quoniam autem lapistotis iſtis <lb></lb>decimis ſucceſſiue fluentibus percurrit ſucceſſiuè ſpa<lb></lb>tium duarum orgyiarum, illiuſve particulas; ideò cùm <lb></lb>iuxta memoratam, obſeruatamque proportionem, ſpa<lb></lb>tia ſint interſe vt quadrata temporum, intelligi opor<lb></lb>tebit diſtingui ſpatij particulas 3821109907456 <lb></lb>0000000000000000. Exinde verò ſict, vt cùm pri<lb></lb>mo momento lapis non percurrat niſi vnam huiuſmo<lb></lb>di particularum, neceſſe ſit, vt acceleratione ſecluſa, & <lb></lb>non percurrendo quolibet conſe quentium momento<lb></lb>rum, pluſquam vnam particulam, totidem aſſignentur <pb pagenum="242" xlink:href="028/01/282.jpg"></pb>decima minuta, ſeu momenta primo æqualia, quot <lb></lb>ſunt particulæ ſpatij memoratæ. </s> <s id="s.001819">Reducamus itaque <lb></lb>huiuſcemodi decima minuta in prima, in horas, in dies, <lb></lb>in annos; procreabuntur certè anni Iuliani, ſeu quales <lb></lb>nobis vſui ſunt 5322381, cum vno ferè anno prætereà. <lb></lb></s> <s id="s.001820">Igitur hic erit numerus annorum, quo demùm exacto <lb></lb>lapis ex laqueari ad tabulatum petueniet. </s> <s id="s.001821">Heinc, ſi <lb></lb>inter varianteis Chronologorum opiniones, ſuppona<lb></lb>mus Mundum fuiſſe conditumà ſex mille annis; vides, <lb></lb>vt ſi lapis ab initio Mundi occœpiſſet cadere, non<lb></lb>dum cecidiſſet temporibus noſtris vna ſeptima parte <lb></lb>digiti; vtque oporteret ad <expan abbr="perficiendũ">perficiendum</expan> <expan abbr="motũ">motum</expan> durare ad<lb></lb>hûc <expan abbr="Mundũ">Mundum</expan> <expan abbr="pluſquã">pluſquam</expan> octingenteis, octogies, & ſepties, <lb></lb>quàm durauerit hactenus. </s> <s id="s.001822">Quęſo te ergo cuius ſit pretij <lb></lb>huiuſmodi motus, quo intra ſex <expan abbr="annorũ">annorum</expan> millia percurri <lb></lb>non poſſit pars ſeptima digiti, reſpectu accelerationis, <lb></lb>qua vno horæ ſecundo percurruntur digiti centum <lb></lb>quadraginta quatuor? </s> <s id="s.001823">Quid verò, ſi acciperemus <lb></lb>pro momento primo non momentum horæ <expan abbr="decimũ">decimum</expan>, <lb></lb>ſed centeſimum, ſed milleſimum; quàm multæ myria<lb></lb>des durationum Mundi neceſſariæ forent, ptinſquàm <lb></lb>illo motu digitus vnus peruaderetur? </s> <s id="s.001824">Sed ne eò vſque <lb></lb>rem deducam, quæſo teſolùm, tametſi is motus con<lb></lb>cedatur & naturalis, & à principio intrinſeco; cùm in<lb></lb>ſenſibilis tamen ſit non modò intra vnum minutum <lb></lb>ſecundum, ſed etiam intra centum annos, quibus totis <lb></lb>apparere non poſſit centeſima parte digiti promotior: <lb></lb>quæſo te, inquam, an-non caſus lapidis valeat potiùs <lb></lb>denominari ab acceleratione violentus, quàm ab illo <lb></lb>naturalis; cùm quicquid ſenſibile habet, ab acceleratio. <lb></lb></s> <s id="s.001825">ne obtineat. </s> </p> <pb pagenum="243" xlink:href="028/01/283.jpg"></pb> <p type="main"> <s id="s.001826">IX. </s> <s id="s.001827">Heinc igitur, quando ais, <emph type="italics"></emph>fore, vt mibi eruditiomnes <lb></lb>accelerationem violentam concedant, non verò deſcenſum, niſi <lb></lb>hunc ab eius acceleratione mente, vt dictum eſt, ſeiunctum à <lb></lb>principio externo, & contra naturæ inclinationem procedere <lb></lb>euidentiùs oſtendam:<emph.end type="italics"></emph.end> Vides primò non eſſe opus, vt oſten <lb></lb>dam deſcenſum fieri contra naturæ inclinationem, qui <lb></lb>exiſtimo illum fieri ſine naturæ reluctatione. </s> <s id="s.001828">Deinde <lb></lb>ſatis mihi tribui, cùm acceleratio eſſe violenta conce<lb></lb>ditur; quippe motus ſolus, qui eſt ab acceleratione, ſiue <lb></lb>à cauſſa accelerante, ſenſibilis eſt, atque adeò ſolus, de <lb></lb>quo conſentaneum ſit requirere, naturaliſ-ne ſit, an <lb></lb>violentus; cùm alioquin motum, ſeu deſcenſum illum <lb></lb>reſiduum, qui perſæcula integra fieri non poſſit ſenſi<lb></lb>bilis, nemo perinde ſit curaturus. </s> <s id="s.001829">Tertio requiſiiſſe <lb></lb>me illum, vt eſſet principium, à quo acceleratio incipe<lb></lb>ret, fieretque radix proportionis, qua acceleratio in<lb></lb>creſcit. </s> <s id="s.001830">Quòd autem illum eſſe putârim ab externo <lb></lb>principio, cauſſa fuit imprimis, quia animaduert, ſi <lb></lb>Deus vacuum fecerit locum intra regionem aëris, in <lb></lb>quem nihil prorsùs neque ex aëre, neque ex Terra, ne<lb></lb>que aliunde penetret, ac lapis in eius medio collocetui; <lb></lb>futurum non eſſe, curlapis verſus vllam partem mouea<lb></lb>tur, magis quàm motus fuiſſet, ſi illum Deus in eodem <lb></lb>loco ante conditum Mundum conſtituiſſet, aut mo<lb></lb>uendus eſſet, ſi deinceps totus circa eum Mundus de<lb></lb>ſtrueretur. </s> <s id="s.001831">Nempe, quia nihil penitùs cum toto Mun<lb></lb>do communicaret, perinde illi penitùs foret, ſeu eſſet, <lb></lb>ſeu non eſſet Mundus. </s> <s id="s.001832">Et quia aliunde animaduerti <lb></lb>futurum, vt ſi Deus circum creârit, reſtitueritve aërem, <lb></lb>lapis tum moueatur, feraturque verſus Terram, potius <pb pagenum="244" xlink:href="028/01/284.jpg"></pb>quàm verſus aliam regionem; ideò ratiocinatus ſum <lb></lb>huiuſmodi motus principium eſſe debere vel in aëre, à <lb></lb>quo quam-ptimùm lapis fuerit contactus, cœperit mo<lb></lb>ueri; vel in Terra, verſus quam, non aliò inſtitutus mo<lb></lb>tus fuerit; non verò in lapide ipſo, qui quandiù ſolus <lb></lb>fuerit, nihilque externum ad ipſum appulerit, ipſumve <lb></lb>contigerit, eo motu caruerit. </s> <s id="s.001833">Rurſus autem, quia ani<lb></lb>maduerti, ſi nihil vſquàm rerum eſſet, præter aërem, ac <lb></lb>in aëre lapidem, non fore cur lapis in hanc potiùs par<lb></lb>tem, quàm in aliam quamlibet ferretur; idcircò con<lb></lb>cluſi, cùm lapis cœperit verſus <expan abbr="Terrã">Terram</expan> ferri, debere ſaltem <lb></lb>primam motus cauſſam ab ipſa Terra procedere; vnde <lb></lb>& attracticem vim in ipſa Terra eſſe conceſſi. </s> <s id="s.001834">Et quòd <lb></lb>talis vis eſſe non poſſit procùl actuoſa, propè otioſa; <lb></lb>ideò ex illius actione continente in lapidem, collegi <lb></lb>eſſe neceſſarium inualeſcere impetum, ſeu accelerari in <lb></lb>lapide motum. </s> <s id="s.001835">Quoniam verò peruidere ſum viſus ex <lb></lb>ſola hac attractione non poſſe explicari proportionem <lb></lb>eiuſce accelerationis; & aliunde reputaui aërem, tamet<lb></lb>ſi non poſſit fieri cauſſa initij motus, poſſe nihilomi<lb></lb>nus motum ſemel cœptum iuuare, ac veluti prouchere; <lb></lb>idcircò illum quoque adhibui, & ex eius vi impulſiua, <lb></lb>cum attractrice terræ coniuncta compoſui cauſſam <lb></lb>proportionis integram, quo legiſti modo. </s> <s id="s.001836">Hæc re<lb></lb>peto autem, vt tibi inſinuem, quamobrem non modò <lb></lb>accelerationem, ſed ipſum quoque motum, ſiue pri<lb></lb>mum initium motus, qui à te dicitur deſcenſus, eſſe à <lb></lb>principio externo cenſuerim. </s> </p> <p type="main"> <s id="s.001837">X. </s> <s id="s.001838">Ratio aliunde mihi fuit, quòd nihil videretur <lb></lb>magis conſentaneum, quàm motum foueri, incremen-<pb pagenum="245" xlink:href="028/01/285.jpg"></pb>túmque accipere à cauſſa, à qua fuerit eius <expan abbr="initiũ">initium</expan>; & vice <lb></lb>verſa habere initium ab eadem cauſſa, à qua fomentum, <lb></lb>incrementumque acceperit. </s> <s id="s.001839">Quippe obſeruaui natu<lb></lb>ram ſic in cæteris comparatam, vt qua ratione progreſ<lb></lb>ſum parat, eadem exordium faciat; ac habui planè in<lb></lb>congruum tam imbecillum facere internum rei princi<lb></lb>pium, vt motum incipiat, qui per totannorum myria<lb></lb>das ſit inſenſibilis futurus, indigeatque ſemper externo <lb></lb>motore, qui acceleret, ac perficiat, & vno quidem pro<lb></lb>pè momento. </s> <s id="s.001840">Heinc verò eſt, cur, vt dum aqua igni <lb></lb>admota incaleſcit, non quærimus cauſſam intenſionis, <lb></lb>ſeu <expan abbr="graduũ">graduum</expan> caloris ſuperad ditorum, in igne, & cauſſam <lb></lb>primi gradus in aqua; ſed tam primum gradum, quàm <lb></lb>cæteros ad ſolum ignem referimus: ita dum lapis inua<lb></lb>leſcit, acceleraturve in motu, non videatur accelera<lb></lb>tionis, ſiue partium motus requirenda cauſſa externa; & <lb></lb>initij, ſeu primæ illius particulæ motus, interna, hoc eſt <lb></lb>in ipſo lapide: ſed tam pars prima, quàm cæteræ refe<lb></lb>rendæ videantur ad externam cauſſam. </s> <s id="s.001841">Vſurpo autem <lb></lb>aquam in exemplum; quoniam vt illa ex ſe calore deſti<lb></lb>tuitur, ſic lapis exſe caret motu, quemadmodum in<lb></lb>telligitur ex poſito caſu, quòd in vacuo, ac non exſiſten<lb></lb>te præſertim Mundo, conſtitutus ſit; ſecus profectò, ac <lb></lb>animal, quod habet in ſe ſui motus principium. </s> <s id="s.001842">Quo <lb></lb>ſanè loco non parùm ſuſpexi Ariſtotelem, cùm cenſuit <lb></lb>corpus graue moueri deorsùm <emph type="italics"></emph>non à ſe,<emph.end type="italics"></emph.end> ſed <emph type="italics"></emph>ab alio,<emph.end type="italics"></emph.end><lb></lb>ac inter cæteras rationes, ob quas <emph type="italics"></emph>impoßibile<emph.end type="italics"></emph.end> duxit, <lb></lb><foreign lang="grc">ἀσωύχτον <gap></gap></foreign>, fieri talem motum à principio intrin<lb></lb>ſeco, illam attulit, quod graue alioquin foret anima<lb></lb>tum; <emph type="italics"></emph>cùm à ſe moueri animatorum proprium ſit,<emph.end type="italics"></emph.end><pb pagenum="246" xlink:href="028/01/286.jpg"></pb><foreign lang="grc">ζωτιχό<gap></gap> τε <gap></gap> το̄τ<gap></gap>, <gap></gap> <gap></gap> ἐμγ́ύχων ἴδιον. </foreign></s> <s id="s.001843">Ne<lb></lb>que verò aut non habebis Ariſtotelem inter erudi<lb></lb>tos; aut dices illum fuiſſe de ſola acceleratione loquu<lb></lb>tum; aut probabis ſic diſtinxiſſe, vt omninò cenſuerit <lb></lb>non eſſe deſcenſum à principio externo. </s> <s id="s.001844">An ille ſatis <lb></lb>commodè cauſſam externam aſſignârit, non eſt cur <lb></lb>hoc loco diſcutiam; abundè eſt, ſi ipſe quoque, dum <lb></lb>cauſſam externam conſtituo, illum non modò non <lb></lb>refragantem, ſed ſuffragantem etiam habeam. </s> <s id="s.001845">Nam <lb></lb>quando cæteri quidem eruditi declarauerint, quæ-nam <lb></lb>alia ſit accelerationis, proportioniſque illius cauſſa; & <lb></lb>eandem cauſſam, quæ motum acceleret, non facere illi <lb></lb>initium, exigique omninò aliam, eſſeque illam intrin<lb></lb>ſecam; tunc erit ſanè cur diffidam non meis modò nu<lb></lb>gamentis, ſed placitis etiam tanti Coryphæi. </s> </p> <p type="main"> <s id="s.001846"><emph type="center"></emph><emph type="italics"></emph>Terram grauia attrahere; & Quid illi contingeret, ſi ver<lb></lb>ſus Lunam dimoueretur; Quid lapidi, ſi intra fornicem, <lb></lb>ad centrum Terræ, conſtitueretur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001847">XI. </s> <s id="s.001848">Cauſſaris deinde, <emph type="italics"></emph>me multa mouere, vt grauia non à <lb></lb>propria natura, ſed à Terra diffuſis circumquáque corpuſculis <lb></lb>illecta, atque etiam illigata deorſum trahi perſuadeam.<emph.end type="italics"></emph.end><lb></lb>Sed facio nimirùm, Vir doctiſſime, ac religioſiſſime, <lb></lb>quòd dum in perueſtigatione cauſſarum naturalium <lb></lb>verſor, nuſquam non caligo mihi offundatur; atque <lb></lb>idcircò tanquam incedens in denſiſſimis tenebris, nihil <lb></lb>non palpitem, nihil non moueam, nullam non tentem <lb></lb>ſemitam, ſi fortè in aliquam ſpeciem vel tenuiſſimæ <lb></lb>luculæ emergam. </s> <s id="s.001849">Dicis <emph type="italics"></emph>te non intelligere quomodò ea<emph.end type="italics"></emph.end><pb pagenum="247" xlink:href="028/01/287.jpg"></pb><emph type="italics"></emph>ſint à me ſeriò ſcripta:<emph.end type="italics"></emph.end> ſed potui non ſeria ſeriò ſcribere; <lb></lb>hoc eſt non ioco, ſed vt eruditi, quæ magis ſeria habue<lb></lb>rint, doceant. </s> <s id="s.001850">Neque enim eſt, cur exiſtimes iſtis me <lb></lb>nugis ita hærere, vt ipſas quaſi veritatem ipſiſſimam <lb></lb>habeam, aut colam, ſed cùm totus Mundus ſit nuga<lb></lb>rum plenus, & videre videar nugas quoque eſſe, quæ <lb></lb>vulgò habentur ſeria maximè; ſupereſſe exiſtimo, vt <lb></lb>eas nugas deligam, quæ eſſe minùs nugæ videantur. <lb></lb></s> <s id="s.001851">Quæris, <emph type="italics"></emph>Ecquid nam proferam, cur non poßint grauia deor<lb></lb>ſum moueri naturâ?<emph.end type="italics"></emph.end> Sed protuli primùm illud argumen<lb></lb>tum, quod mox antè repetij. </s> <s id="s.001852">Deinde, vnde colligis <lb></lb>inficiari me moueri lapidem naturâ? </s> <s id="s.001853">Quippe & mo<lb></lb>ueri illum cenſeo non reluctante interna natura; & <lb></lb>quam externam adh<gap></gap>beo, tum natura eſt, tum ex inſtitu<lb></lb>to naturæ. </s> <s id="s.001854">Ad-hæc, non ignoras, quàm nihil ſit ne<lb></lb>ceſſe Philoſophiam excolere, ſiad grauiores difficulta<lb></lb>tes dicere ſufficiat aliquid moueri, aut fieri naturâ. </s> <s id="s.001855">Non <lb></lb>quòd eò tandem, quæ humana eſt imbecillitas, perue<lb></lb>niendum non ſit; ſed quòd dum nobis non datur vltrà, <lb></lb>aliquò tenus prodire ſit. </s> <s id="s.001856">Rursùs, dum natura interna <lb></lb>mouet, agitve aliquid, id niſi certis organis, agendique <lb></lb>modo ſpeciali non præſtat: an verò quis modus is ſit, <lb></lb>quæ hæc organa, docent nos ipſi Eruditi? </s> <s id="s.001857">In deſcenſu <lb></lb>quidem rerum grauium dicunt grauitatem eſſe orga<lb></lb>num, & modum agendi expreſſionem grauitatis: ſed <lb></lb>amabo te, quid hæc grauitas? </s> <s id="s.001858">Et quid nam præſtat <lb></lb>lapidi conſtituto in vacuo? </s> <s id="s.001859">Et, quorsum concipitur <lb></lb>tanta in ingenti lapide; cum ſecluſa tamen cauſſa exter<lb></lb>na accelerante, & violenta, incapax ſit, quæ per cen<lb></lb>tum annos moueat deorsùm lapidem per vnius digiti <pb pagenum="248" xlink:href="028/01/288.jpg"></pb>centeſimam partem? </s> <s id="s.001860">Et, cur grauitas eò maior fit quò <lb></lb>lapis fit acceleratior? </s> <s id="s.001861">Et, qui fieri poteſt, vt grauitas <lb></lb>dicatur eſſe organum internæ naturæ, ac effectiuum <lb></lb>motus deorsùm cùm grauitas tota, & motus totu ob<lb></lb>ſeruabilis procedat à cauſſa externa? </s> <s id="s.001862">Heinc dum re<lb></lb>quiris, <emph type="italics"></emph>quid abſurdum, impoßibileve ea in re ag<gap></gap>o<gap></gap>cam?<emph.end type="italics"></emph.end><lb></lb>Sanè vel hoc vnum di<gap></gap>iſſe, inculcaſſe ve potiùs, eſt la<lb></lb>tis. <emph type="italics"></emph>Tellus ipſa,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>ſi loco tantisper dimoueatur, vt in <lb></lb>vehementioribus eius commotionibus, à qua alia Tellure in <lb></lb>priſtinum locum retrahitur?<emph.end type="italics"></emph.end> Sed ego quidem nondum <lb></lb>accepi Terram vſquam ſic contremuiſſe, ſeu vehemen<lb></lb>tem adeò illius commotionem fuiſſe, vt mota loco tota <lb></lb>fuerit (niſi fortè tremorem illum, qui contigit Chriſto <lb></lb>patiente, ſed pręter naturæ tamen ordinem, intellexeris) <lb></lb>tuque ipſe ſtatim pòſt dicis <emph type="italics"></emph>illam ſic affectare ſuum <expan abbr="locũ">locum</expan>, vt <lb></lb>nullis <expan abbr="cõcuſſa">concuſſa</expan> motibus ab eo dimoueri valeat.<emph.end type="italics"></emph.end></s> <s id="s.001863"> Quare <expan abbr="cũ">cum</expan> omnes <lb></lb>Terræ tremores particulares eſſe videantur; quæ Terræ <lb></lb>vis retrahit glebas, retrahet etiam maiores parteis, quæ <lb></lb>aliqua vehementiore ſucceſſione fuerint commotæ. </s> </p> <p type="main"> <s id="s.001864">XII. </s> <s id="s.001865">Quæris conſequenter, <emph type="italics"></emph>ſi Tellus diuina, aut An<lb></lb>gelica vi à propria ſede dimota verſus Lunam aliquot <lb></lb>milliaribus attolleretur; illeic-ne sponte naturæ conſi<lb></lb>steret, an ad priſtinum potiùs locum reuerteretur?<emph.end type="italics"></emph.end> Non <lb></lb>vis tu heic ſanè fieri controuerſiam de loco Telluris in <lb></lb>Mundo, quod ad motum, quietemve ſpectat: quare <lb></lb>& Reſponſionem prætereo, quæ fieri poſſet iuxta illos, <lb></lb>qui moueri Terram contendunt, quique ſpeciatim <lb></lb>d<gap></gap>c rentmotus illos <emph type="italics"></emph>Terræ trementis, maris æſtuantis, aëris, <lb></lb>ventive reſlantis,<emph.end type="italics"></emph.end> de quibus loqueris, abſorberi pto<gap></gap>s <lb></lb>à rapida illa circumuolutione; eſſeque penitùs ad illam <pb pagenum="249" xlink:href="028/01/289.jpg"></pb>à ſua ſemita exturbandam inefficaceis. </s> <s id="s.001866">Dico ergo po<lb></lb>tiùs probabile eſſe, fore, vt eo caſu Tellus quieſcat, vbi<lb></lb>cum que Deus, Angeluſve conſtituerit ipſam. </s> <s id="s.001867">Scilicet <lb></lb>concipio quicquid eſt ſpatiorum non modò intra cir<lb></lb>cuitum Lunæ, ſed etiam intra ambitum, concamera<lb></lb>tionemve ſiue Firmamenti, ſiue etiam Mundi, eſſe li<lb></lb>berum, ac ſaltem quod ſpectatad totam regionem Pla<lb></lb>netariam, nullam dari ſoliditatem earum, quæ tredun<lb></lb>tur, Sphærarum cæleſtium. </s> <s id="s.001868">Sunt certè tum rationes <lb></lb>aliæ, tum maximè Phaſes illę Veneris, quæ ipſam nunc <lb></lb>vltra, nunc citra Solem eſſe conuincunt. </s> <s id="s.001869">Et poſſet <lb></lb>quidem totum hoc ſpatium intra Mundi ambitum <lb></lb>concipi inane, niſi quà globi Siderum, ac Telluris ſunt, <lb></lb>& quatenus radij ſiderum variè <expan abbr="tranſmitiũtur">tranſmitiuntur</expan>: ſed lar<lb></lb>giri placet quam vulgò Atheream auram nuncupant; <lb></lb>ſubſtantiam nempe tenuiſſimam, & aëre hoc noſtro <lb></lb>incomparabiliter ſubtiliorem, quæ pari modo diffuſa <lb></lb>ſit, totumque ſpatium occupet, niſi qui ijdem globi <lb></lb>ſunt; etiam Telluris, cuius aër, & aqua ſunt tenuiores, <lb></lb>fluidiores, ac exteriores <expan abbr="ſolũ">ſolum</expan> partes. </s> <s id="s.001870">Concipio aliunde, <lb></lb>quod legiſti fuſiùs deductum in Epiſtolis, non Tellu<lb></lb>rem magis, quàm Siderum vllum, eſſe ex ſe grauem, <lb></lb>aut leuem: ſed grauitatem, ac leuitatem eſſe affectio<lb></lb>nes partium proprias, quatenus partes ſunt, & à ſuo <lb></lb>toto diſtrahi quadam tenùs poſſunt: quo eodem mo<lb></lb>do partes Lunæ, & cuiuſvis Mundani globi eſſe poſ<lb></lb>ſunt graues, aut leues abſque grauitate, aut leuitate to<lb></lb>tius. </s> <s id="s.001871">Quare & poſſe quidem dici eſſe aliquid ſupe<lb></lb>riùs, & inferiùs, ſursùm, & deorsùm, reſpectu partium <lb></lb>cuiuſque globi, & comparatè ad animal, cuius illæ, & <pb pagenum="250" xlink:href="028/01/290.jpg"></pb>a<gap></gap>æſint poſitionum diuerſitates; at verò reſpectu to<lb></lb>torum ipſorum globorum, & ſecluſo animalis ſitu, à <lb></lb>quo nihil præter relationem, denominationemve ex<lb></lb>trinſecam habent, nihil eſſe reuerâ ſuperius, aut in<lb></lb>ferius, ſursum, aut deorsùm. </s> <s id="s.001872">Et ſecus quidem Ariſtote<lb></lb>les; ſed non ſecus Plato, qui cùm agnoſcat eſſe in <lb></lb>Mundo extremum, & medium; contendit tamen non <lb></lb>ideò debere aut extremum ſupremum, aut medium <lb></lb>inſimum cenſeri. </s> <s id="s.001873">Heinc proinde dico, & vnumquem<lb></lb>que Siderum globum in ea parte Mundani ſpatij, <lb></lb>quam Deus ab initio ipſi præſcripſit, circumgyrari, & <lb></lb>globum Telluris inea parte Mundani ſpatii quieſcere, <lb></lb>in qua Deus ipſum initio conſtituit. </s> <s id="s.001874">Rem ita eſſe in<lb></lb>telligo, vtſi quis plureis apparet globos ex ea materia, <lb></lb>quæ ſub pari mole, fiue ambitu tantum ponderet, quan<lb></lb>tum aqua, & ipſos in aqua quieſcente conſtituat. </s> <s id="s.001875">Qui<lb></lb>libet enim eorum globorum, vbicumque fuerit conſti<lb></lb>tutus, ibi conquieſcet; & neque ex ſummo imum <lb></lb>petet, neque ex imo ſummum; neque ex vtrouis ex<lb></lb>tremo medium; neque ex medio vtrumvis extre<lb></lb>mum; neque ex medio, extremove locum interce<lb></lb>ptum; neque exloco intercepto medium, aut extre<lb></lb>mum. </s> <s id="s.001876">Et ſi ſingas Dædalum, Architam, aut al um <lb></lb>artiſicem adeò ingenioſum, vt vno eorum alicubi in<lb></lb>tra aquam conſtituto efficere poſſit alios <foreign lang="grc">αὐτεμάτο<gap></gap>ς</foreign>, <lb></lb>ſeu varios illis circa ipſum obeundos motus indere; <lb></lb>ij globi peragent ſuos motus quamcumque ad partem <lb></lb>inſtituti fuerint: nempe ſeu prope ſuperficiem, ſeu <lb></lb>prope fundum; ſeu ſub medium, ſeu prope medium, <lb></lb>ſeu procùl à medio: ſcilicet tam ille, quàm iſti, ob ipſam <pb pagenum="251" xlink:href="028/01/291.jpg"></pb>cum aqua <foreign lang="grc">ι<gap></gap>̓<gap></gap>̔οπίαι</foreign>, ſeu, vt cum Cicerone dicam, <lb></lb><emph type="italics"></emph>æquilil ritatem,<emph.end type="italics"></emph.end> neque graues erunt, vt ſubſidant, neque <lb></lb>leues, vt auolent. </s> </p> <p type="main"> <s id="s.001877">XIII. </s> <s id="s.001878">Subinde ergo comparo cum immoto globo <lb></lb>Tellurem, cum circum-ductis Sidera; & dico, ſicut glo<lb></lb>bus ille emoueri poteſt à loco, in quo eſt, & promoue<lb></lb>ri verſus alium; ſic poſſe ipſam quoque Tellurem emo<lb></lb>ueri à loco, in quo eſt, & promoueri verſus Lunam; <lb></lb>addoque, vt globus ille in quocumque alio aquæ loco <lb></lb>reponatur, in eo pari modo quieſcet, neque priorem <lb></lb>repetet: ſic & Tellurem, in quocumque loco conſtitu<lb></lb>ta fuerit, in eo manſuram, nec priſtinum repetituram. <lb></lb></s> <s id="s.001879">Et dicis tu quidem <emph type="italics"></emph>attolli,<emph.end type="italics"></emph.end> quod ego heic ſimpliciter <lb></lb>dico <emph type="italics"></emph>emoueri:<emph.end type="italics"></emph.end> ſed nimirùm, quia concipis infimum eſſe <lb></lb>in Mundo locum, & Terram ipſum occupare: cùm ſu<lb></lb>perum tamen, & inferum comparatè ſolùm ad nos, & <lb></lb>reſpectu globi, quem inhabitamus, videatur eſſe acci<lb></lb>piendum. </s> <s id="s.001880">Ex hoc certè intelligo, tranſlatà Terrâ verſus <lb></lb>Lunam ad Antipodas exſiſtentem, nos non propterea <lb></lb>auolaturos in derelictum à Terra locum; vt neque <lb></lb>etiam Antipodas, tranſlatâ Terra verſus Lunam factam <lb></lb>nobis ad verticem: ſed & illos, & nos perinde in ea<lb></lb>dem antiqua ſede verſaturos, tanquam ſimùl tranſlato <lb></lb>Terræ centro, reſpectu cuius, & comparatè ad ſitum <lb></lb>capitis, pedumque noſtrorum, cenſebimur ſemper aſ<lb></lb>cendere, & deſcendere, ſiue locum ſurſum, deorſum<lb></lb>que habere; non autem ſimpliciter reſpectu loci, in <lb></lb>quo Terra aut erit, aut fuerit, & qui ſeu centrum Mun<lb></lb>di ſit, ſeu non ſit, nihil ad aſcenſum, aut deſcenſum <lb></lb>ſacit. </s> <s id="s.001881">Prætereo autem nullum eſſe argumentum <pb pagenum="252" xlink:href="028/01/292.jpg"></pb>idoneum, quo Terra eſſe in centro Mundi, potiuſquàm <lb></lb>extra comprobetur; & vel ipſum motum Planetarum <lb></lb>excentricum videri planè conuincere non eſſe Terram <lb></lb>conſtitutam in centro ſpatiorum, motuúmque cæle<lb></lb>ſtium. </s> <s id="s.001882">Nam probare quidem Firmamenti, ſuperio<lb></lb>riſve cæli motum concentricum eſſe, potiuſquàm ex<lb></lb>centricum, ingenij humani viribus eſt maius. </s> <s id="s.001883">Acnoui <lb></lb>quidem quas rationes Ariſtoteles, Ptolomæus, & alij <lb></lb>proferunt: ſed nihil eſt neceſſe heic oſtendere, quàm <lb></lb>illæ ſint inefficaces. </s> <s id="s.001884">Dum igitur quæris, <emph type="italics"></emph>An Terra illeic <lb></lb>conſiſteret?<emph.end type="italics"></emph.end> Conſtituram reſpondeo. </s> <s id="s.001885">Et, dum præoc<lb></lb>cupas, <emph type="italics"></emph>Qua ratione inductus?<emph.end type="italics"></emph.end> Ecce eam iam habes. </s> <s id="s.001886">Præ<lb></lb>occupas quoque, cur ita nunc ſuum locum affectet, vt <lb></lb>nullis concuſſa motibus ab eo dimoueri valeat? </s> <s id="s.001887">Sed <lb></lb>affectat, quia nutui Conditoris obſequitur; & in ſta<lb></lb>tione collocata, eam non deſerit, ſed tuetur. </s> <s id="s.001888">Non va<lb></lb>let autem dimoueri vllis concuſſa motibus; quia om<lb></lb>nes, quos ſupponis, motus partium ipſius propriarum, <lb></lb>cohærentiumque ſunt, neque illam ſecundum ſe totam <lb></lb>mouere loco magis poſſunt, quàm animal totum Pul<lb></lb>ſatio vnius arteriæ. </s> <s id="s.001889">Et ſunto alicubi magni Terræ<lb></lb>motus; ij tamen ad Terræ molem comparati, tale <lb></lb>quid vix ſunt, qualis eſt in nobis pulſatio arteriæ vege<lb></lb>tior, ſi quà in nobis puſtula cum apoſtemate intumeſ<lb></lb>cit. </s> <s id="s.001890">Addendum eſt porrò, cùm Mundi ſapientiſſi<lb></lb>mas Artifex omneis eius parteis ita conſtituerit, vt nullo <lb></lb>eſſe loco, aut ſitu inter ſe commodiore poſſint: idcir<lb></lb>cò ſi contendas Terram ſuum locum repetituram, vt <lb></lb>in quo magis congruè Vniuerſi reſpectu ſit; fore, vt il<lb></lb>lum repetat, non tum propria vi, ſeu grauitate inſita, <pb pagenum="253" xlink:href="028/01/293.jpg"></pb>quàm à cæteris partibus, quarum proprium locum oc<lb></lb>cupârit, compulſa; eo modo, quo trabs, ſi deprimatur <lb></lb>in fundum maris, ſuperficiem repetet, non ſanè vi <lb></lb>propria, ſeu leuitate ingenita: ſed compulſa ab aqua, <lb></lb>cuius occupauerit locum. </s> </p> <p type="main"> <s id="s.001891">XIV. </s> <s id="s.001892">Quod ſpectat ad aliam fictionem, ſecundum <lb></lb>quam me interrogas, <emph type="italics"></emph>Quid euenturum putem, ſi in ipſo <lb></lb>Terræ meditullio concamerata cauerna fiat, & aqua, aëreve <lb></lb>oppleatur: lapis verò conſtituatur, non in eius, Terræque <lb></lb>centro, ſed loco inter centrum, & fornicem medio?<emph.end type="italics"></emph.end> Dico <lb></lb>breuiter, probabile eſſe, vt ſi Terra ſit quaſi Magnes, <lb></lb>tractorios radios quoquo versùm, ac in illam etiam <lb></lb>cauernam diffundens; fore vt lapis attrahatur verſus <lb></lb>eam fornicis partem, è qua ad ipſum radij plures, vni<lb></lb>tioreſque peruenerint; &, ſi ſupponas peruenire ex <lb></lb>æquo, ac vndelibet, fore, vt illeic inter æquas vndique <lb></lb>vireis contineatur, eo modo, quo fabula eſt Moham<lb></lb>medis ſepulcrum ſuſpendi. </s> <s id="s.001893">Sed, ſi lapidem quidem <lb></lb>attrahi contingat ad proximum: fornicem, <emph type="italics"></emph>Cur igitur,<emph.end type="italics"></emph.end><lb></lb>inquis, <emph type="italics"></emph>per puteum dimiſſus lapis à viciniore item Terra ille<lb></lb>ctus, attractuſque ad putei latera non adhæreſcit?<emph.end type="italics"></emph.end> Cauſſa <lb></lb>eſt, quia plures, vnitioreſque radij è maiore Terræ <lb></lb>mole, quæ eſt verſus centrum, concurrunt in lapidem, <lb></lb>quàm ad eum accurrant ex ipſis putei lateribus. <emph type="italics"></emph>Sed <lb></lb>ipſamet Terra,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>rupto ſornice ad centrum deſcende<lb></lb>ret, leuioraque inde corpora expelleret?<emph.end type="italics"></emph.end> Verùm, niſi fortè <lb></lb>ſupponas qua vi excauatus fornix fuerit, eadem poſteà <lb></lb>ipſum abrumpi; ego quidem non video, qua id ratione <lb></lb>dicere poſſi<gap></gap>; qui ne video quidem tot ſubterraneos <lb></lb>fornices rumpi, vt aqua, aut aër inde abigantur, & quæ <pb pagenum="254" xlink:href="028/01/294.jpg"></pb>Terræ partes remotiores à centro ſunt, propiùs verſus <lb></lb>ipſum ferantur. </s> <s id="s.001894">Subdis, <emph type="italics"></emph>Putas enim diſrupto fornice, totàque <lb></lb>ſi placet, Terrâin arenulas redactà, eam non confluxuram ad <lb></lb>centrum?<emph.end type="italics"></emph.end> Ego quidem non puto, qui putare non poſ<lb></lb>ſunt monteis, aliaque Terræ loca diſrumpi, inque are<lb></lb>nulas redigi, vt compleant ſuppoſitas ſpecus, cryptaſ<lb></lb>que aut aqua, aut aëre plenas: idque, niſi fortè, vt dixi, <lb></lb>ſupponas eandem vim deterere Terram in arenulas, <lb></lb>quæ excauárit fornicem; quo caſu, quæ eſſet in arenu<lb></lb>lis ſuperſtes magnetica vis ſic eas mutuò pelliceret, vt & <lb></lb>in crypten confluerent, & aquam, aëremve inde abi<lb></lb>gerent; ſi modò ſuppoſueris quoque rimas, exitumve <lb></lb>patere. </s> <s id="s.001895">Pergis adhûc, <emph type="italics"></emph>confluerent ſanè, & quidem non <lb></lb>ab alio corpore attracta, ſed ſponte naturæ, & à principio <lb></lb>interno, atque innato.<emph.end type="italics"></emph.end></s> <s id="s.001896"> Verumtamen confluere poſſent <lb></lb>attractæ à ſeinuicem, vt & iam confluunt ferri ramen<lb></lb>ta, quæ magneticam combiberunt vim. </s> <s id="s.001897">Concludis, <lb></lb>C<emph type="italics"></emph>ur de cæteris igitur grauibus idem ſimili ratione non <lb></lb>dicatur?<emph.end type="italics"></emph.end> Dico, quia fiunt in cæteris ſenſibiliora experi<lb></lb>menta, ex quibus liceat aliquid veriſimilius coniectari. </s> </p> <p type="main"> <s id="s.001898"><emph type="center"></emph><emph type="italics"></emph>Et Magnetem ferrum, & Terram grauia trahere per in<lb></lb>ſenſilia organula; &,<emph.end type="italics"></emph.end> C<emph type="italics"></emph>ur attractio prope Terram non <lb></lb>ſit ſenſibilior, quam procùl.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.001899">XV. </s> <s id="s.001900">Inſectaris deinde Magneticam illam, ſeu <lb></lb>attractricem Terræ vim; opinariſque <emph type="italics"></emph>me ridere in ſinu, <lb></lb>dum inuiſibileis vncinos, harpagones, chelas, funeiſque tenſos, <lb></lb>& tractorios fingo.<emph.end type="italics"></emph.end></s> <s id="s.001901"> Sed quod me quidem attinet, non <lb></lb>diuendo ſanè haſce meas commentationes, ſeu vt antè <pb pagenum="255" xlink:href="028/01/295.jpg"></pb>dicebam, nugas, vt quidpiam germanum, ac indu<lb></lb>bium; at ſimpliciùs ago, quàm vt rideam; quippe me <lb></lb>potiùs miſeret natiuæ imbecillitatis, cùm nihil ha<lb></lb>beam præclarius, quo meam, aut alterius ſciendi auidi<lb></lb>tatem paſcam. </s> <s id="s.001902">Obiicis, <emph type="italics"></emph>non eſſe, cur magnetieam ferri <lb></lb>vulgò dictam attractionem in exemplum adducam; quòd <lb></lb>Magnes, & ſerrum non ſictis illis meis hurpagonibus, aut <lb></lb>inuiſibilibus catenis, quaſi vi adducta; ſed vtrumque ſponte <lb></lb>naturæ incitata in mutuos amplexus accurrant.<emph.end type="italics"></emph.end></s> <s id="s.001903"> Id verò <lb></lb>ſanè per-eleganter; ſed quid mihi facias, qui ſim ita <lb></lb>hebes, vt vim vocibus ſubiectam non capiam. </s> <s id="s.001904">Dicis <lb></lb><emph type="italics"></emph>vtrumque accurrere in mutuos amplexus:<emph.end type="italics"></emph.end> ſed hoc totum <lb></lb>effectus eſt, de cuius cauſſa ambigitur. </s> <s id="s.001905">Cauſſam ergo <lb></lb>interiicis, <emph type="italics"></emph>quia ſponte naturæ incitantur.<emph.end type="italics"></emph.end></s> <s id="s.001906"> At cùm hæc vi<lb></lb>deatur eſſe generalis, inartiſicialiſque Reſponſio, qua <lb></lb>ad omnia vtimur, quorum cauſſas ignoramus; non vi<lb></lb>deo profectò, quò tu, Vir acutiſſimus, collincees. </s> <s id="s.001907">Quippe <lb></lb>velle te dicere nihil aliud, quàm quod eſt vulgò in ore <lb></lb>omnium, <emph type="italics"></emph>quia talis est rei natura; quia id ſponte naturæ <lb></lb>fit; quia hoc natura ipſa ſcit,<emph.end type="italics"></emph.end> cæteraque huiuſmodi; mihi <lb></lb>in animum non induco. </s> <s id="s.001908">Hæc certè eſt cauſſa, cur <lb></lb>dixerim antè valere iubendam omnem Philoſophiam, <lb></lb>ac omnem præſertim cauſſarum <expan abbr="naturaliũ">naturalium</expan> inueſtigan<lb></lb>darum deponendam curam; ſi huiuſcemodi Reſponſio <lb></lb>videatur poſſe ſufficere. </s> <s id="s.001909">Ac eſt quidem eò denique, vt <lb></lb>etiam dixi, perueniendum: ſed ſunt interim tamen va<lb></lb>rij gradus cauſſarum inſtrum entariarum, de quibus <lb></lb>cùm dicere non liceat quemadmodum à natura, vt à <lb></lb>princip<gap></gap>i cauſſa vſurpentur; aut cur, quomodove ad<lb></lb>natæ, addictæque ipſi naturæ; licet tamen requirere <pb pagenum="256" xlink:href="028/01/296.jpg"></pb>quænam illæ ſint: ac vel Phyſica vniuerſa inutilis eſt, <lb></lb>vel in ipſis explorandis, ſicubi fortè ſecundum gradus <lb></lb>aliquos occurrant, incumbere debet. </s> <s id="s.001910">Et cùm videa<lb></lb>mus ſanè alios eſſe alijs ſagaciores, ipſaque naturæ ar<lb></lb>cana (arcana profecto) ſtudioſiùs rimanteis; tametſi <lb></lb>detur nemini penetrare in adyta; fatendum eſt tamen, <lb></lb>cùm omnes in veſtibulo hæſerint, fieri in ipſo veſtibu<lb></lb>lo alios aliis promotiores. </s> </p> <p type="main"> <s id="s.001911">XVI. Iam, cùm dicis <emph type="italics"></emph>vtrumque sponte naturæ inci<lb></lb>tari:<emph.end type="italics"></emph.end> quánam ratione concipis fieri huiuſmodi incita<lb></lb>tionem? </s> <s id="s.001912">An non, vt fiat incitatio, eſſe alia pars inci<lb></lb>tans, & alia incitata debet? </s> <s id="s.001913">Idem certè mouere ſeipſum, <lb></lb>niſi parteis habeat mouentem, & motam, cùm iis, quos <lb></lb>tu vocas Eruditos, aduerſatur; tum communi etiam no<lb></lb>tioni repugnat, cui Ariſtoteles inhærens, impoſſibilo <lb></lb>eſſe cenſet, vt id ſeipſum moueat, quod eſt <foreign lang="grc">σ<gap></gap>εχὲ<gap></gap></foreign>, <lb></lb><emph type="italics"></emph>continuum<emph.end type="italics"></emph.end> ſ<gap></gap>u <emph type="italics"></emph>vniuſmodi, rigidum, inarticulatum.<emph.end type="italics"></emph.end></s> <s id="s.001914"> Non<lb></lb>ne verò ſunt huius generis tam Magnes, quàm Ferrum? <lb></lb></s> <s id="s.001915">De altero ergo vt ſolùm loquamur, quænam in Ferro <lb></lb>parsincitans? </s> <s id="s.001916">Et quid illam mouet vt incitet aliam? <lb></lb></s> <s id="s.001917">Et, quonam motus genere illam in citat? </s> <s id="s.001918">Pulſu-ne, an <lb></lb>tractu, an alio? </s> <s id="s.001919">Ac ſi poneres quidem ſpeciem animæ: <lb></lb>poſſet illa fortaſſis vti interno quodam ſpiritu ad cien<lb></lb>dum reliquam maſſam: ſed tu animam nempe impro<lb></lb>bas. </s> <s id="s.001920">Quónam ergo modo poteſt concipi incitare ſe<lb></lb>ipſum Ferrum, vt accurrat, aſcendat, deſcendat, viam <lb></lb>flectat, prout illi magnes appoſitus fuerit? </s> <s id="s.001921">Facit <emph type="italics"></emph>ſponte,<emph.end type="italics"></emph.end><lb></lb>inquis: ego de voce ne conteſtor; ſed ea ſaltem maius, <lb></lb>ampliuſque aliquid deſignat, quàm <emph type="italics"></emph>non repugnantiam;<emph.end type="italics"></emph.end><lb></lb>& cùm excludat principium extrinſecum, intrinſecum <pb pagenum="257" xlink:href="028/01/297.jpg"></pb>connotat, quod agat, quod premat, quod inſtet, <lb></lb>quod pellat, & aliud vtique, quàm ſeipſum: niſi fortè <lb></lb>ex accidenti. </s> <s id="s.001922">Id ergo quæritur, quod-nam ſit: &, cùm <lb></lb>ſit quid à maſſa tota indiſcinctum, neque vt in mem<lb></lb>bris animalium fit, commiſſurâ vllâ dearticulatum, <lb></lb>quomodo moueri ipſummet occipiat (quippe nihil; ſi <lb></lb>ſit immotum, mouere poteſt Phyſice) quomodo mo<lb></lb>ueat aliud? </s> <s id="s.001923">quomodo totam incitet maſſam? </s> <s id="s.001924">Dices <lb></lb>quidem fortè, illud eſſe formam, quæ vt ſeipsâ vnitur <lb></lb>materiæ, ita ſeipsâ, abſque vllo intercedente organo <lb></lb>mouere poſſit materiam; vnde & totius maſſæ, ſeu Fer<lb></lb>ri conſequatur motus: verùm vtcumque heinc explice<lb></lb>tur motus Ferri, quà graue eſt, & deorſum tendit; illi <lb></lb>tamen motus, flexuſque in quamcumque partem fuerit <lb></lb>Magnes appoſitus, non videntur poſſe intelligi ex ſola <lb></lb>applicatione formæ ad materiam, niſi & illa anima ſit, <lb></lb>& tum vireis, tum articulos flexanimcis habeat, vt quæ<lb></lb>dam variorum motuum organa; quæ nulla tamen de<lb></lb>prehenduntur. </s> <s id="s.001925">Sed hæc vt præteream; cùm videamus <lb></lb>Ferrum non ex quacumque diſtantia in amplexum <lb></lb>Magnetis accurrere, ſed accurrere ſolum, v. c. ab vno <lb></lb>palmo; quo modo vis intelligamus incitari ferrum <lb></lb>ſponte naturæ in diſtantia palmi, non in diſtantia cubi<lb></lb>ti? </s> <s id="s.001926">An in diſtantia cubiti ſuæ ſpontis non eſt? </s> <s id="s.001927">An na<lb></lb>tura caret? </s> <s id="s.001928">An luſcioſum eſt, neque poteſt Magnetem <lb></lb>agnoſcere, niſi intra diſtantiam palmi? </s> <s id="s.001929">Rides vncinos, <lb></lb>harpagones, chelas, ſimiliave organula, quæ ego opi<lb></lb>nor ex magnete emitti, quibuſque in palmi diſtantia <lb></lb>confertioribus, atque adeò validioribus, quàm ad di<lb></lb>ſtantiam cubiti exiſtimo illeinc, non heine pertrahi ad <pb pagenum="258" xlink:href="028/01/298.jpg"></pb>Magnetem ferrum; Tu, qui nihil tale tranſmitti vis, <lb></lb>quónam modo fieri hanc incitationem, cum tanto <lb></lb>propinqui, & remoti delectu capis? </s> <s id="s.001930">Et homo quidem <lb></lb>ad hominis amplexum ſeſe incitat, quia eſt animatus, <lb></lb>quia videt illum, quia ſpecie ab illo recepta agnoſcit: <lb></lb>at in Ferro nihil tale habes; cùm videaris tamen in ipſo <lb></lb>præclarius quidpiam agnoſcere, quàm ſimplex quæ<lb></lb>dam cognitio ſit, videlicet Diuinationem. </s> <s id="s.001931">Etenim <lb></lb>neceſſe eſt prorsùs diuinare Ferrum, quandò Magnes <lb></lb>propè, quando procùl ſit, vt vireis metiatur, ac delige<lb></lb>re valeat, è quánam diſtantia in ipſum inſiliat. </s> </p> <p type="main"> <s id="s.001932">XVII. </s> <s id="s.001933">An dices Magnetem emittere ex ſe non cor<lb></lb>puſcula quidem aliqua, quæ ſint quaſi vncinuli, chor<lb></lb>dulæ tractoriæ, &c. </s> <s id="s.001934">ſed vim, ſeu qualitatem quan<lb></lb>dam, quæ ſit merum accidens, quæque vbi ad Ferrum <lb></lb>peruenerit, tum ipſum Ferrum veluti ſentiat, ſeſeque <lb></lb>ipſum excitet ad accurrendum verſus Magnetem? </s> <s id="s.001935">Si <lb></lb>dicas, admittes profectò in Ferro ſenſum aliquem, & <lb></lb>aliud quidpiam exiges, quàm ſpontaneam incitatio<lb></lb>nem; cauſſam nimirùm extrinſecam, à qua principium <lb></lb>internum moueatur, & quæ proinde motus Ferri pri<lb></lb>marium dici principium debeat. </s> <s id="s.001936">Sed & de iſta quali<lb></lb>tate, ſeu virtute accidentaria, quanta diffi ultatum ſe<lb></lb>ges? </s> <s id="s.001937">Seu enim ſolitaria, & abſque ſubiecto moueatur <lb></lb>per ſpatium; ſeu de ſubiecto in ſubiectum per varias <lb></lb>parteis aëris, alteriuſve corporis migret; ſeu propaga<lb></lb>tione, hoc eſt, corruptione vnius, & productione al<lb></lb>terius ſucceſſiuè facta in palmaris ſpatij infinitis pun<lb></lb>ctis (aut particulis mauis) innouetur: agnoſcis quàm <lb></lb>multa abſurda ſequantur: & vtcúmque tandem iſtam <pb pagenum="259" xlink:href="028/01/299.jpg"></pb>qualitatem peruenire ad Ferrum detur; ecquiſ-nam <lb></lb>modum energiæillius exprimere valeat? </s> <s id="s.001938">Et, cùm non <lb></lb>dicas Ferri molem ab ea pertrahi; qua ratione tamen, <lb></lb>corpus cùm non ſit, tangere Ferri corpus poteſt? </s> <s id="s.001939">Nam <lb></lb>tangi quidem Ferrum ab aëre, corporeve alio, in quo <lb></lb>ipſa qualitas ſit, id fiebat iam ante: & corpus huiuſce<lb></lb>modi non fit illius organum, neque ab illa afficitur, <lb></lb>moueturve, vt coagat, nouoque modo Ferrum contin<lb></lb>gat, ac ipſum veluti admoneat. </s> <s id="s.001940">Sed &, cùm contactus <lb></lb>nudus fuerit; quonam modo exinde ſiet ſpontanea illa <lb></lb>incitatio? </s> <s id="s.001941">Certè, vt iam dictis hoc addam, vbi Ferrum <lb></lb>ſuppoſitum ad imminentem Magnetem fertur, non <lb></lb>videtur concipi poſſe qua ratione ſe euehat, & non à <lb></lb>Magnete trahatur. </s> <s id="s.001942">Nam animal quidem excitare ſeſe <lb></lb>ad conten dendum ſursùm poteſt; quoniam ob mem<lb></lb>brorum articulationem poteſt Terram premere, à qua <lb></lb>reſiſtente velut reflectatur, vt fiat reſilitio; at Ferrum <lb></lb>tale nihil facit, imò nec poteſt facere: quare & hoc ip<lb></lb>ſum argumento eſt, quòd non ſui concitatione, ſed <lb></lb>Magnetis tractione abripiatur ſursùm. </s> <s id="s.001943">Et ſuſpendatur <lb></lb>manibus homo, ſuſpendatur Ferrum, ita vt vtrique ſit <lb></lb>ſolus aër ſuppoſitus: non ſaliet ſanè ſurſum homo, ne<lb></lb>que ad amicum ſupere-exſtantem accurret, niſi amicus <lb></lb>eum traxerit. </s> <s id="s.001944">quî poſſit iure potiore Ferrum ad ſuper<lb></lb>exſtantem Magnetem, niſi traxent ipſum Magnes? </s> <s id="s.001945">An <lb></lb>ſuæ ſpontis magis eſt, poteſtque magis agere ſponte? <lb></lb></s> <s id="s.001946">An cùm homo pedibus pulſet, prematque fruſtrà aë<lb></lb>rem, Ferrum id præſtat appoſitè magis? </s> <s id="s.001947">Si non capia<lb></lb>mus igitur quomodò ſeu homo, ſeu Ferrum incitare <lb></lb>poſſit ſeipſum, & Ferrum certè magis, quàm homo, <pb pagenum="260" xlink:href="028/01/300.jpg"></pb>defectu firmitudinis, reſiſtentiæque in aëre, propter in<lb></lb>nixum, ſine quo non videtur fieri poſſe incitatio: quid <lb></lb>eſt, cur, vt homo, dum ſurſum effertur, arguit eſſe à <lb></lb>quo trahatur, non ſic Ferrum arguat, dum ſursùm ef<lb></lb>fertur? </s> <s id="s.001948">Ac dum homo quidem trahitur ab homine, <lb></lb>communis eſt notio, debere id fieri aut manu demiſſa, <lb></lb>aut chorda, aut vncino, aut alio ſimili inſtrumento: <lb></lb>cur & dum Ferrum à Magnete; putemus id fieri abſque <lb></lb>organo vllo intercepto? </s> </p> <p type="main"> <s id="s.001949">XVIII. Sugillas, quòd hæc organa dicuntur à me <lb></lb><emph type="italics"></emph>inſenſilia.<emph.end type="italics"></emph.end></s> <s id="s.001950"> Sed nempe, ſi ſenſilia eſſent, in ijs diſqui<lb></lb>rendis non laboraremus. </s> <s id="s.001951">Quod inſenſilia verò dican<lb></lb>tur, non ideò tamen nulla ſunt; magiſquam nulli non <lb></lb>ſunt vitales, animaleſque ſpiritus, qui licet inſenſiles <lb></lb>ſint, cauſſæ ſunt tamen tot motuum, quos in animali<lb></lb>bus obſeruamus. </s> <s id="s.001952">Sed nihil ſanè neceſſe eſt inductio<lb></lb>nem texam innumerarum rerum inſenſilium, oculiſve <lb></lb>imperceptarum, quas tamen & dari, & vehementibus <lb></lb>motibus præditas eſſe ambigat nemo. </s> <s id="s.001953">Nihil etiam <lb></lb>neceſſe eſt, vt argumenta congeram, quibus huiuſce<lb></lb>modi rescontexi ex corpuſculis inſenſibilibus quidem, <lb></lb>ſed præditis nihilominùs ſpecialibus figuris, probem. <lb></lb></s> <s id="s.001954">Nihil prætereà, vt vrgeam ex attractionis effectu ar<lb></lb>gui, organa illa inſenſilia debere analoga eſſe, aut ſi<lb></lb>mile quidpiam habere cum ijs, quibus attractiones <lb></lb>ſenſibiliùs fiunt; quòd à ſenſibilioribus ad inſenſibilio<lb></lb>ra procedendo ſeruari videamus analogiam: quódque <lb></lb>mens humana non capiat attractionem fieri, & ratione <lb></lb>quadam cum his ſenſibilibus analoga non fieri. </s> <s id="s.001955">Ni<lb></lb>hil, inquam, neceſſe eſt, vt hæc, & ſimilia quædam <pb pagenum="261" xlink:href="028/01/301.jpg"></pb>proſequar, quandò tu ea rides, & iure fortaſſis; ſed <lb></lb>non ea ratione, quæ ſit mihi facta perſpicua. </s> <s id="s.001956">Dicis, <lb></lb><emph type="italics"></emph>ſi vincula inſenſilia ſunt, non eſſe cur timeam Magnetem ſentiri <lb></lb>à Ferro.<emph.end type="italics"></emph.end></s> <s id="s.001957"> At tu ludere, opinor, non vis ab æquiuoco: <lb></lb>quaſi ego heic aliud appellem inſenſibile, quàm quod <lb></lb>præ ſui exilitate eiuſmodi eſt, vt nec videri oculis, nec <lb></lb>palpari manibus poſſit? </s> <s id="s.001958">Hoc certè modo ipſas quo<lb></lb>que, quas vocant ſpecies intentionaleis, inſenſibileis <lb></lb>dicimus; quatenus adeò ſubtiles ſunt, vt videri ipſæ ab <lb></lb>oculo nequeant. </s> <s id="s.001959">Vnde & ſicut iſtæ ſpecies, licet alio<lb></lb>quin inſenſiles, oculum tamen donec eſt animatus, ita <lb></lb>afficiunt, vt per ipſas oculus videat, ſentiat, percipiat <lb></lb>ipſa obiecta: ſic reſpondere poſſet Thales, ſi Ferrum <lb></lb>quidem animatum ſit, quantumvis ea vincula ſint ipſi <lb></lb>ferro inſenſibilia, ita tamen Ferrum ab iis affici, vt per <lb></lb>ipſa ſentiat, percipiatque Magnetem. </s> <s id="s.001960">Verba tua de<lb></lb>inde ſunt; <emph type="italics"></emph>Quo enim ſenſu catenas illas tuas percepisti, qui<lb></lb>bus, ne ſurſum auoles, Terræ alligatum te cenſes?<emph.end type="italics"></emph.end> Nempe <lb></lb>me voce quaſi cenſoria cenſuiſti eſſe admonendum, vt <lb></lb>in memet deſcenderem. </s> <s id="s.001961">Accipio, & hoc ſolùm dico, <lb></lb>non magis ſentire me catenas, quibus trahor tamen; <lb></lb>quàm oculus ſpecies memoratas, dum videt tamen. <lb></lb></s> <s id="s.001962">Rogas conſequenter, <emph type="italics"></emph>Cur verear negraue deorſum, & <lb></lb>Ferrum ad Magnetem, cæteraque corpora ad electrica, ſine <lb></lb>ſenſu concurrere non poßint?<emph.end type="italics"></emph.end> Sed quamobrem verear, ex<lb></lb>poſitum habes. </s> </p> <p type="main"> <s id="s.001963">XIX. Pergis, <emph type="italics"></emph>Ad hos certè effectus abundè ſufficit re<lb></lb>bus omnibus à ſapientißimo earum opifice indita naturalis <lb></lb>inclinatio ad conſeruationem, perfectionemque propriam; ad<lb></lb>de, ſi veles, ad conſeruandum vniuerſi ordinem, vt opus non<emph.end type="italics"></emph.end><pb pagenum="262" xlink:href="028/01/302.jpg"></pb><emph type="italics"></emph>ſit ad figmenta hæc tua confugere.<emph.end type="italics"></emph.end></s> <s id="s.001964"> Sed, Vir religioſiſſime, <lb></lb>inter nos non ambigitur, ſit-ne naturalis inclinatio <lb></lb>hiſce rebus ab Opifice ſapientiſſimo indita; quippe <lb></lb>qualiſcumque ea ſit, tam ego illam eſſe à Deo agnoſ<lb></lb>co, & fateor, quam tu: ſed hoc ſolùm ambigitur, qua<lb></lb>lis nimirùm illa ſit? </s> <s id="s.001965">An non repugnantia? </s> <s id="s.001966">An quid <lb></lb>poſitiuum? </s> <s id="s.001967">An mera diſpoſitio? </s> <s id="s.001968">An quidpiam ſub<lb></lb>ſtantiæ adiunctum? </s> <s id="s.001969">An externa affectio? </s> <s id="s.001970">An interna <lb></lb>propenſio? </s> <s id="s.001971">Et, ſi ſit propenſio, ſiue expreſſio, impul<lb></lb>ſio, actus eiuſdem quaſi ponderis; quæ ſit ponderis <lb></lb>huiuſce conditio? </s> <s id="s.001972">Qua id ratione ſe exſerat, vt fiat <lb></lb>propendentia? </s> <s id="s.001973">Et, ſi ſit ſolùm propendentia, quomo<lb></lb>do ab illa non ſit ſolus caſus? </s> <s id="s.001974">Quomodo etiam actio? <lb></lb></s> <s id="s.001975">Quomodo non ſine delectu? </s> <s id="s.001976">cæteraque id genus alia, <lb></lb>quæ noſſe foret operæ-pretium. </s> <s id="s.001977">Quare non debes <lb></lb>mea figmenta ſic accipere, quaſiego ipſa in locum in<lb></lb>ditæ à Deo inclinationis obtendam. </s> <s id="s.001978">Enimverò illa <lb></lb>vſurpo, quaſi quaſdam hypotheſeis, quibus coner, <lb></lb>quatenus poſſum, intelligere, atque explicare indu<lb></lb>ſtriam admirabilem, qua ſapientiſſimus Opifex voluit <lb></lb>ſua hæc opera proprias exſerere actiones. </s> <s id="s.001979">Atque id <lb></lb>quidem eadem ratione, qua Aſtronomi, dum hypo<lb></lb>theſeis, ſeu mavis fig menta in cælum inducunt. </s> <s id="s.001980">Ne<lb></lb>que enim ad eas confugiunt, quaſi motum cælo, aut ſi<lb></lb>deribus fuiſſe à Deo inditum negent; ſed, vt illo ſuppo<lb></lb>ſito, intelligant, ac explicent quomodo huiuſmodi <lb></lb>motus fieri poſſit tam multiplex, tam conſonans, tam <lb></lb>regularis. </s> <s id="s.001981">Ac fortè tu quidem ſapienter, cùm innuis <lb></lb>debere ſufficere nobis, ſi circa rerum contemplatio<lb></lb>nem, cognoſcamus de illis, quòd ſint: neque fingendas <pb pagenum="263" xlink:href="028/01/303.jpg"></pb>eſſe hypotheſeis, quibus explicetur quid ſint, vt ſe ha<lb></lb>beant, quomodo agant, &c. </s> <s id="s.001982">ſed, vt antè dixi, ratio<lb></lb>nem non video; quando exinde ſequitur, vt vniuerſam <lb></lb>eliminare Philoſophiam oporteat. </s> <s id="s.001983">Et vide, vt me con<lb></lb>ſequenter traducas. <emph type="italics"></emph>Si enim eam tibi vim concedis, vt <lb></lb>proiectilibus inclinationem (voca motum, voca impetum, aut <lb></lb>aliter, vt volueris) imprimere talem poßis, quæ recedentibus à <lb></lb>te ijſdem proiectilibus, diutiùs in illis perſeueret; & in quam<lb></lb>cumque partem deſtinaueris, eadem deferat, atque impellat, <lb></lb>imò quæ obuio etiam, impedimento non ſtatim tota deſtruatur, <lb></lb>ſed aliam in partem proiectilia abducat, vt in reflexione tu <lb></lb>ipſe contendis: eriſ-ne tam parum æquus rerum arbiter, vt à <lb></lb>ſapientißimo, ac præpotente Vniuerſi Conditore rebus quibuſ<lb></lb>libet inclinationem longè perfectiorem imprimi poſſe addu<lb></lb>bites?<emph.end type="italics"></emph.end> Heic nimirùm ſic mecum agis, vt ſi me aliquem <lb></lb>haberem; & comparatus præſertim ad Authorem <lb></lb>meum; coram quo non modò factus ſum tanquam <lb></lb>nihilum, ſed ſum etiam nihilo minus. </s> <s id="s.001984">Ac rursùs, vt ſi <lb></lb>ego negarem quicquid eſt inclinationis, aut virium in <lb></lb>rebus naturæ, id debere Deo Optimo Maximo acce<lb></lb>ptum referri: ac denique, vt ſi quæſtio eſſet, poſſit-ne <lb></lb>Deus imprimere inclinationes aliquas rebus, & non <lb></lb>potius qualeſ-nam ſint inclinationes à Deo impreſſæ; <lb></lb>quemadmodum dictum iam eſt. </s> <s id="s.001985">Pergis, <emph type="italics"></emph>Finge vim à <lb></lb>te impreſſam eſſe eiuſmodi, quæ varijs impedimentis ſiſti qui<lb></lb>dem poßit, ſed non deſtrui, aut etiam minui; an non ſublato <lb></lb>impedimento motum redintegraret?<emph.end type="italics"></emph.end> Sed cùm damnes ipſe <lb></lb>figmenta, quorſum poſtulas, vt illa adaugeam? </s> <s id="s.001986">Ne<lb></lb>que enim vim poſſe ſiſti, quin ſimùl deſtruatur, pro<lb></lb>babile puto. <emph type="italics"></emph>Talis,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>omninò naturalis rerum in-<emph.end type="italics"></emph.end><pb pagenum="264" xlink:href="028/01/304.jpg"></pb><emph type="italics"></emph>clinatio eſt; nec babes vnde impoßibilem, aut ipſis etiam gra<lb></lb>uibus reipsâ inditam non eſſe concludas.<emph.end type="italics"></emph.end></s> <s id="s.001987"> Sed quamobrem <lb></lb>talem non habeam, ac eam præſertim, quæ grauibus <lb></lb>indita eſt; tum in ipſis Epiſtolis, tum in iis, quæ hacte<lb></lb>nus deduxi, inculcatum ſatis. </s> <s id="s.001988">Vnde & cùm ſic rogas, <lb></lb><emph type="italics"></emph>Cur eam ergo agnoſcere detrectas, & ad inania illa tua <lb></lb>figmenta recurris?<emph.end type="italics"></emph.end> Dictum ſatis, ſuperque eſt, cur, & <lb></lb>qualis ſit, quam detrectem; & cur veritatis amore nul<lb></lb>lum non moueam lapidem, vt ſaltem, ſi qua eius vm<lb></lb>bra, aut ſimilitudo occurrat, experiar. </s> <s id="s.001989">Et non latet me <lb></lb>quidem quàm multis difficultatibus omnia inuoluan<lb></lb>tur: ſed hoc ipſum eſt, ob quod mea inania figmenta <lb></lb>non diſſimulo, viſurus an ſint, qui pleniora faciant. </s> <s id="s.001990">Sa<lb></lb>nè vbi ex intellecta tuo modo inclinatione declaratum <lb></lb>fuerit, non ſolùm quî ſaluari valeant præmiſſa illa in<lb></lb>commoda; ſed etiam, qua ratione fiat, vt res grauis de<lb></lb>cidens, nulla ſuperaddita inclinatione, acceleretur, & <lb></lb>grauior, quàm fuerit initio, euadat, inclinatiorque <lb></lb>proinde fiat, ac eâ quidem, qua obſeruatur, propor<lb></lb>tione, non alia: & rursùs, vnde-nam contingat, cur <lb></lb>Saxum pondo <expan abbr="duũm">duumm</expan> millium non cadat velociùs, <lb></lb>quàm lapis duellaris: ſecus ac Ariſtoteles tuo illo <lb></lb>principio inductus opinatus fuit, cæteraque ſimilia; <lb></lb>tum non detrectabo, ſed exoſculabor, complectar, <lb></lb>tuebor, & valere longè iubebo non ſolùm quæ inania <lb></lb>ſunt, ſed quæ plena etiam figm enta. </s> </p> <p type="main"> <s id="s.001991">XX. </s> <s id="s.001992">Rem conſequenter adoriris, &, <emph type="italics"></emph>Si grauia,<emph.end type="italics"></emph.end> in<lb></lb>quis, <emph type="italics"></emph>deorsùm à Tellure magneticè traherentur, neceſſa<lb></lb>rium eſſet, vt quo Terræ viciniora eſſent, eò fortiùs ab ea <lb></lb>traherentur, vt in Ferro, ac Magnete euidenter contingit.<emph.end type="italics"></emph.end><pb pagenum="265" xlink:href="028/01/305.jpg"></pb>Ad hoc, illud imprimis dico, diſtinguendam eſſe <lb></lb>in re graui attractionem ſimplicem à compoſita, ſeu <lb></lb>adiectitia, aëris <expan abbr="etiã">etiam</expan> ſollicitatione coniuncta Ex prio<lb></lb>re nempe eſt grauitas ſimplex, quæ lapidi competit, <lb></lb>vbicumque ſit, & dum accipitur extra morum: ex po<lb></lb>ſteriore compoſita, quæ eidem lapidi, dum mouetur, <lb></lb>competit, & tanto quidem maior, quantò fuerit mo<lb></lb>tus vehementior. </s> <s id="s.001993">Deinde dico, debere quidem attra<lb></lb>ctionem ſimplicem eſſe fortiorem propè, quàm procùl: <lb></lb>verùm diſcrimen inſenſile eſſe, nec poſſe agnoſci, niſi <lb></lb>in diſtantia, intercapedineve multorum milliarium. </s> <s id="s.001994">Vt <lb></lb>enim, cùm ſit vniuersè verum tractionem ferri à Ma<lb></lb>gnete eſſe fortiorem propè, quàm procùl, inobſerua<lb></lb>bile tamen eſt diſcrimen, niſi interualla attractionis <lb></lb>per palmos, aut ſaltem digitos ſumantur; quandò ſi aſ<lb></lb>ſumas per milleſimas, aut centeſimas, imò decimas <lb></lb>parteis digiti, nulla eſt diligentia, qua internoſci quid<lb></lb>quam poſſit: ita cùm verum fuerit trahi à Terra lapi<lb></lb>dem tantò potentiùs, quantò propinquiùs, tantò debi<lb></lb>liùs, quantò remotiùs; obſeruari quidem poterit diſ<lb></lb>crimen, ſi interualla accipias tanta, quanta, exempli <lb></lb>gratiâ, eſt, ipſiuſmet Terræ ſemidiameter: at ſi accipias <lb></lb>interuallum, quod ſemi-diametro minus ſit, non <lb></lb>eſt, cur poſſe fieri diſcrimen ſenſibile ſperes. </s> <s id="s.001995">Nempe, <lb></lb>ſi Terram admiſeris eſſe Magnetem quemdam ingen<lb></lb>tem, vides profectò, ſi vel ad ipſam vſque Lunam, <lb></lb>Terræ virtutem extenderis, virtutem Magnetis longè <lb></lb>ſenſibiliùs per digitos decreſcere, quàm Telluris virtus <lb></lb>per ſemidiametros decreſcat: quippe cùm nullum Ma<lb></lb>gnetem videas, qui attrahat ferrum è tot digitis, quot <pb pagenum="266" xlink:href="028/01/306.jpg"></pb>poſſunt Terram inter, & Lunam ſemidiametri Terræ <lb></lb>interponi. </s> <s id="s.001996">Vnde & cùm infers, <emph type="italics"></emph>Deberet igitur corpus <lb></lb>graue quodcumque iuxta Terram ſuspenſum, aut ipſi etiam <lb></lb>Terræ inſiſtens maius exhibere pondus, quàm longiùs à Terræ <lb></lb>ſuspenſum: itemque per centum pedes Terræ vicinos velociùs <lb></lb>deſcendere, quàm per totidem alios pedes à Terra remotiores:<emph.end type="italics"></emph.end><lb></lb>Dico, ne, ſi turrim quidem habueris tribus, pluribúſve <lb></lb>milliaribus altam, exhiberi poſſe pondus maius ad <lb></lb>pedem turris, quàm ad faſtigium, quoniam decremen<lb></lb>tum attractionis (& conſequenter grauitatis) quod ſe<lb></lb>cundum altitudinem turris fiet, erit longè inſenſibi<lb></lb>lius, quàm ſit decrementum virtutis Magnetis per mil<lb></lb>leſimam partem digiti. </s> <s id="s.001997">Res ſe perinde habet, vt ſi ac<lb></lb>ceſſeris ad <expan abbr="arborẽ">arborem</expan> decimo à te milliari diſtantem. </s> <s id="s.001998">Nam <lb></lb>verum quidem eſt apparentem arboris magnitudinem <lb></lb>continenter increſcere; at non proptereà vbi fueris, <lb></lb>vno, duobus, tribus, imò pluribus paſſibus promotior, <lb></lb>obſeruabile erit aliquod diſcrimen magnitudinis in<lb></lb>creſcentis. </s> <s id="s.001999">Atque eadem quidem erit cauſſa, quare <lb></lb>acceptis pedibus altitudinis aliquot, ſiue ad faſtigium, <lb></lb>ſiue ad medium, ſiue ad pedem turris, lapis eos vbivis <lb></lb>æquè velociter percurrat; quoniam & ſimplex attractio <lb></lb>erit ad ſenſum eadem; & compoſita pari modo ad ac<lb></lb>celerationem conducet. </s> <s id="s.002000">Heinc &, cùm paucis inter<lb></lb>poſitis in eandem ſententiam concludis, <emph type="italics"></emph>euidens eſt igi<lb></lb>tur grauia Magneticè deorsùm à Terra non trahi:<emph.end type="italics"></emph.end> vides, vt <lb></lb>hoc euidens fiat, euidens priùs fieri debere, attractio<lb></lb>nem ferri à Magnete ſenſibiliorem eſſe vna digiti mil<lb></lb>leſima parte prope ipſum Magnetem, quàm duabus. <lb></lb></s> <s id="s.002001">Quippe ſeruanda proportio eſt inter attrahentia, attra<lb></lb>cta, & interualla attractionis. </s> </p> <pb pagenum="267" xlink:href="028/01/307.jpg"></pb> <p type="main"> <s id="s.002002"><emph type="center"></emph><emph type="italics"></emph>Non eſſe Atomorum minùs, quàm Aristoteleæ Materiæ <lb></lb>tolerabilem in Religione Poſitionem.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002003">XXI. </s> <s id="s.002004">Quæ ſelegiſti prætereà, tanquam <emph type="italics"></emph>nimia faci<lb></lb>litate admiſſa à me,<emph.end type="italics"></emph.end> &, quantum tu infers, ad Religio<lb></lb>nem attinentia; ea continentur verbis illis, quibus repe<lb></lb>tis me dixiſſe, O<emph type="italics"></emph>rium, & interitum; incrementum, ac <lb></lb>decrementum, omnemque alterationem, qua calor, frigus, hu<lb></lb>mor, ſiccitas; itemque color, odor, ſapor, & qualitates aliæ <lb></lb>gignuntur, nihil videri eſſe aliud, præter motiones localeis, qui<lb></lb>bus rerum principia, tenuißima licet, atque inſenſibilia, variè <lb></lb>inter ſe concernuntur, excernuntur, accedunt, abſcedunt, <lb></lb>tranſponuntur,<emph.end type="italics"></emph.end> &c. </s> <s id="s.002005">Ego verò, obſtupui ſanè hæc, quæ <lb></lb>ſunt merè Phyſica, & ad ſtatum purè naturalem atti<lb></lb>nent, tranſducta abste fuiſſe in Theologiam, ac ſtatum <lb></lb>ſupernaturalem. </s> <s id="s.002006">Quippe oportet non iſta modò atro <lb></lb>lapillo ſubnotare, ſed etiam quicquid dici poteſt ab <lb></lb>vniuerſis Phyſicis, ſi nihil planè dicendum eſt, quod <lb></lb>pari ratione non poſſit tranſduci, parique modo acci<lb></lb>pi; vt ſi nihil diſtinguendum foret inter id, quod fit <lb></lb>ſolis naturæ viribus, & id, quod fit, fierive poteſt ſuper<lb></lb>naturali virtute. </s> <s id="s.002007">Cauſſaris primùm, <emph type="italics"></emph>quòd Democriti, <lb></lb>& Epicuri Atomos tanto iam tempore à Regno Philoſophico <lb></lb>merito ſuo exſulanteis, & tot iam ſæculorum, ac ſapientum <lb></lb>omnium præiudicio damnatas reuocare ab exſilio, iterumque <lb></lb>in Academiam retrudere moliar.<emph.end type="italics"></emph.end></s> <s id="s.002008"> At ego nihil molior, <lb></lb>méque eum non habeo, qui retrudere, reuocareve ali<lb></lb>quid valeam: ſed quia veritatis deſiderio teneor, & il<lb></lb>lam tamen (ſeu hebetudo, ſeu infœlicitas mea eſt) non <lb></lb>reperio in Philoſophico, quod tu dicis, Regno; idcircò <pb pagenum="268" xlink:href="028/01/308.jpg"></pb>exploro, num illi qui exſulant, ac fortè merito non ſuo, <lb></lb>oſtendere quædam veſtigia propiora, ac tutiora poſ<lb></lb>ſint. </s> <s id="s.002009">Et Epicuro quidem, vt pote iuniori, teſtimonium <lb></lb>dicere Ariſtoteles non potuit; ſed Democrito tamen <lb></lb>dixit, cùm cum non commendauit modò, ſed prætulit <lb></lb>etiam Platoni, quem aliunde Sancti Patres Ariſtoteli <lb></lb>ipſi prætulerunt: quantumcumque ipſe deinde recla<lb></lb>mantibus Patribus, <expan abbr="Philoſophicũ">Philoſophicum</expan> Regnum obtinue<lb></lb>rit, exſulante ſimùl cum aliis Platone. </s> <s id="s.002010">Ac meritó<lb></lb>ne, an immeritò Atomi cum iis exſulent (<expan abbr="etiã">etiam</expan> cum ipſo <lb></lb>Platone dico, cumque aliis, pręter Demoeritum, & Epi<lb></lb>curum, viris ſapientiſſimis, qui ipſi quoque illas ſub <lb></lb>aliis aſſerüere nominibus) non eſt heic diſſerendi lo<lb></lb>cus. </s> <s id="s.002011">Hoc ſolùm dico, videri poſſe aſſertores Atomo<lb></lb>rum nihil magis peccaſſe, quàm ipſe peccârit Ariſtote<lb></lb>les, quòd eſſe dixit Materiam primam. </s> <s id="s.002012">Siquidem ipſis <lb></lb>Atomi nihil aliud ſunt, quàm prima Materies, ex qua <lb></lb>primitùs omnia componuntur, in quam vltimò omnia <lb></lb>reſoluuntur; tametſi in eo à Materia Ariſtotelica diffi<lb></lb>deat, quòd ſit quid (ſcilicet <expan abbr="ſubſtãtia">ſubſtantia</expan>, ipſaque corporea) <lb></lb>quòd quanta, quòd qualis (hoc eſt figurata) quòd <lb></lb>prædita motu. </s> <s id="s.002013">Quòd ſi illi quidem Atomos fecerunt <lb></lb>æternas, ac ingenitas; an-non Ariſtoteles quoque ſuam <lb></lb>illam Materiam æternam, ac ingenitam fecit? </s> <s id="s.002014">Ft, ſi <lb></lb>nihilominùs Materia Ariſtotelis retinetur, quatenus à <lb></lb>Deo producta (ſecus ac illi viſum fuit) initio Mundi <lb></lb>aſſeritur: quid retinere Atomos vetat, quatenus pro<lb></lb>ductæ à Deo (ſecus ac iſtis placuit) initio Mundi aſſe<lb></lb>runtur? </s> <s id="s.002015">Æqua certè conditio eſt; neque, ſi quis <expan abbr="cũ">cum</expan> hac <lb></lb>cautione admittat eſſe Atomos, videtur eſſe illi magis, <pb pagenum="269" xlink:href="028/01/309.jpg"></pb>quàm Ariſtoteli ſuecenſendum. </s> </p> <p type="main"> <s id="s.002016">XXII. </s> <s id="s.002017">Et ſtatim quidem pòſt admones, <emph type="italics"></emph>præter ha<lb></lb>litus calidos, frigidos, humidos, odoratos, ac ſapidos, è <lb></lb>plæriſque corporibus exſpiratos, velle vniuerſim quo dictum eſt <lb></lb>modo, de inſenſibilibus corporibus ratiocinari, non videri eſſe <lb></lb>ſapientiæ, ac eruditionis meæ.<emph.end type="italics"></emph.end></s> <s id="s.002018"> Verùm, cùm id ego acci<lb></lb>piam, vt inſignem quandam tuæ erga me beneuolen<lb></lb>tiæ teſtationem (nimirùm, cùm ego neque ſapiens ſim, <lb></lb>neque audire eruditus merear, voluiſti tamen his voci<lb></lb>bus, pro tua bonitate, lenire cenſuram) quod ſupereſt, <lb></lb>non video ſanè, cur res ſpectata Phyſicè à ſapientiæ <lb></lb>ſtudio aliena cenſeatur. </s> <s id="s.002019">Quantum vis enim tu ſecus <lb></lb>putes, dum contendis ſufficere, ſi quis halitus calidos, <lb></lb>alióſque exſpirari dicat: non ideo tamen improban<lb></lb>dum, ſi quis requirat prætereà è quibus principiis quiſ<lb></lb>que halitus ſit ſingulariter contextus: ſi dicere proinde <lb></lb>poſſit, qualia requirantur principia, vt calidus, non <lb></lb>alius ſit; quomodo actionem eliciat, vt calefacere cen<lb></lb>ſeatur; quid imprimat rei patienti, vt dicatur illam ca<lb></lb>lefacere; aliaque id genus complura. </s> <s id="s.002020">Certè, vt præ<lb></lb>teream quos apud Platonem Socrates habet inter Sa<lb></lb>pienteis, Empedoclem, Heraclitum, Protagoram, <lb></lb>omneiſque, præter Parmenidem, antiquiores (etiam <lb></lb>Homerum, & Epicharmum) quoſque declarat fuiſſe <lb></lb>ratione conſimili philoſophatos, ac præcipuè dum <lb></lb>qualitates, cæteraque, nihil eſſe aliud, quàm motiones <lb></lb>exiſtimârunt: vt illos, inquam, præteream, &, vt de vno <lb></lb>Democrito, de quo iam dixi aliquid, loquar; Ecce, ne <lb></lb>Ariſtoteles quidem, licet in hiſce Elementis, qualitati<lb></lb>buſque vulgaribus conſtiterit, deſipere illum putauit; <pb pagenum="270" xlink:href="028/01/310.jpg"></pb>ſed extulit potiùs, quòd hac ratione philoſophatus, <lb></lb><emph type="italics"></emph>res noſſe ſuperficie tenus<emph.end type="italics"></emph.end> <foreign lang="grc">ω<gap></gap>ὰ τη̄ς ἐπιπολη̄ς</foreign> <emph type="italics"></emph>contentus non <lb></lb>fuerit, nihilque, quantum potuit, intactum præterm ſerit,<emph.end type="italics"></emph.end><lb></lb><foreign lang="grc">ἔοικε <gap></gap> ἀπλύτων φ<gap></gap>ντ<gap></gap>σο<gap></gap>. </foreign></s> <s id="s.002021">Non eſt verò etiam De<lb></lb>mocritus deſipere Plutarcho viſus, cùm ipſum vnà, ac <lb></lb>Platonem Ariſtoteli ex eo prætulit, <emph type="italics"></emph>quòd cauſſas caloris, <lb></lb>& grauitatis inquirentes, non in ipſis terra, & igne ſpecula<lb></lb>tionem finierint, ſed ad ipſa vſque principia ſola mente contem<lb></lb>plabilia, ea, quæ ſenſibilia ſunt, deducentes, fuerint ad vſque <lb></lb>minima, & quaſi ſemina,<emph.end type="italics"></emph.end> <foreign lang="grc">μοχ<gap></gap> ἐλαχί<gap></gap>ων <gap></gap>̔σ<gap></gap> σπε<gap></gap>μά των</foreign><lb></lb><emph type="italics"></emph>progreßi.<emph.end type="italics"></emph.end></s> <s id="s.002022"> Non item M. Tullio, cuius verba ſunt: <emph type="italics"></emph>Quid <lb></lb>loquar de Democrito? </s> <s id="s.002023">Quem cum eo conferre poſſum, non modò <lb></lb>ingenij magnitudine, ſed etiam animi? </s> <s id="s.002024">Qui itaſit auſus ordiri: <lb></lb>Hæc loquor de vniuerſo. </s> <s id="s.002025">Nihil excepit, de quo non profitea<lb></lb>tur. </s> <s id="s.002026">Quid enim eſſe potest extra vniuerſa? </s> <s id="s.002027">Quis hunc Phi<lb></lb>loſophum non anteponat<emph.end type="italics"></emph.end> C<emph type="italics"></emph>leanthi, Chryſippo, reliquiſque <lb></lb>inferioris ætatis, qui mihi cum illo collati, quintæ claßis viden<lb></lb>tur?<emph.end type="italics"></emph.end> Prætereo quæ mira de eius ſapientia, & eruditio<lb></lb>ne Laëitius, & cæteri habent. </s> <s id="s.002028">Nimirùm hæc pauca <lb></lb>ſunt ſatis; cum & tu prætereà ad alia reſpicias. </s> </p> <p type="main"> <s id="s.002029">XXIII. </s> <s id="s.002030">Ecce enim inſtas (& humaniter ſanè) <emph type="italics"></emph>An <lb></lb>meam ſagacitatem fugiat, quò tandem vſque ſemel inducta <lb></lb>hæcperſuaſio proceſſura videatur?<emph.end type="italics"></emph.end> Sed fugit profectò, ſi <lb></lb>putas vlteriùs, quàm quò poteſt procedere Ariſtoteleæ <lb></lb>perſuaſio. <emph type="italics"></emph>Si,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>ortus, atque interitus nihil aliud vi<lb></lb>dentur, præter localeis atomorum, vel<emph.end type="italics"></emph.end> (vt me loqui mitiùs <lb></lb>dicis) <emph type="italics"></emph>tenuißimorum, atque inſenſibilium principiorum mo<lb></lb>tiones, de Formis ſubſtantialibus conclamatum eſt.<emph.end type="italics"></emph.end></s> <s id="s.002031"> Et non <lb></lb>adiicis quidem quid incommodi conſequatur, ſi eò vſ<lb></lb>que proceſſum fuerit: ſed coniector tamen inſinuare <pb pagenum="271" xlink:href="028/01/311.jpg"></pb>te, quod periculum ſubeſſe videtur, ne prætereà ad Ani<lb></lb>mam vſque rationalem procedatur. </s> <s id="s.002032">At vides ſanè <lb></lb>periculum pari ratione deuitatum iri, qua & deuitatur <lb></lb>in Ariſtoteleis ſcholis. </s> <s id="s.002033">Nam, vt generali Effato de <lb></lb>formis educibilibus ex Materia, adhibetur exceptio <lb></lb>Rationalis animæ, ex nihilo à Deo creatæ: ita generali <lb></lb>Effato de formis accidentalibus, eadem eiuſdem Ani<lb></lb>mæ, vt à Deo ſimiliter creatæ adhibebitur; & vel ex eo <lb></lb>ipſa Anima ſubſtantia eſſe comprobabitur, ſecùs ac <lb></lb>formæ cæteræ, quòd ſubſiſtat ipſa per ſe: cæteræ verò <lb></lb>non ſubſiſtant. </s> <s id="s.002034">Quid, quòd cæteræ non modò non <lb></lb>ſubſiſtunt, ſed neque dici quidem poteſt, quid, aut vnde <lb></lb>habeant, vt ſubſtantiæ dicantur, ac ſint, & diſtinctæ <lb></lb>quidem ab ipſa materia; quandò ſuam illam ſubſtan<lb></lb>tialem ſuíque <expan abbr="propriã">propriam</expan> <expan abbr="entitatẽ">entitatem</expan> neque habent à nihilo, <lb></lb>ex quo fieri non admittuntur: neque ab ipſa materia, <lb></lb>ex ſubſtantiali cuius entitate detrahi nihil volunt, quod <lb></lb>in formam abeat: adeò proinde, vt commentum inex<lb></lb>plicabile ſit, quòd interim Formas educi ex materia, il<lb></lb>liuſve potentia dicunt. </s> <s id="s.002035">Nam & quòd eò adiguntur, vt <lb></lb>explicent Formam educi ex materia, nihil eſſe aliud, <lb></lb>quàm fieri in materia, & dependenter ab illa; tum di<lb></lb>cunt prorsùs aliud, quàm quid ſit educi, ſiue extrò tra<lb></lb>his; tum non declarant vnde habeat eſſe, ſuamve enti<lb></lb>tatem hæc formæ ſubſtantia, quæ iam eſt, & antè non <lb></lb>erat; quandò id totum non denotat ex quo facta, ſiue <lb></lb>vnde accepta ſit iſta realis entitas, quæ neque materia <lb></lb>ſit, neque vlla portio ipſius (cùm ob ipſam eductam, <lb></lb>materia non cenſeatur aliquid reale, ſeu entitatem vl<lb></lb>lam realem priùs habitam amiſiſſe) & ipſa proinde <pb pagenum="272" xlink:href="028/01/312.jpg"></pb>dependentiæ vox nihil al ud, quàm caliginem auget, <lb></lb>dum in quo conſiſtat, dici, concipique non poteſt. <lb></lb></s> <s id="s.002036">Quid etiam, quòd ipſe Ariſtoteles ſententiam ſuam ita <lb></lb>expoſuit, Græcique eius Interpretes illam nobis ſic tra<lb></lb>diderunt, vt planè videatur non alias, quàm acciden<lb></lb>taleis formas cognouiſſe? </s> <s id="s.002037">Accidentaleis, inquam, <lb></lb>prout accidens ſubſtantiæ opponitur, non eſſentiæ: <lb></lb>nam alioquin tam materiam, quàm formam, quàm <lb></lb>compoſitum, eo eſſe ſenſu <foreign lang="grc"><gap></gap>σίας</foreign> dixit, quo tam diffe<lb></lb>rentiam, quam genus, quam ſpeciem <foreign lang="grc"><gap></gap>ν <gap></gap> τί<gap></gap>σ<gap></gap></foreign> dixit <lb></lb>prædicati. </s> <s id="s.002038">Sed hæc iam dicenda pluribus non ſunt; ac <lb></lb>videndum potiùs, quod ſpecialiùs inſtas; dum pergis <lb></lb><emph type="italics"></emph>maius quoddam inde imminere periculum,<emph.end type="italics"></emph.end> quam ex Ariſto<lb></lb>telis ſententia. </s> </p> <p type="main"> <s id="s.002039">XXIV. <emph type="italics"></emph>Si enim,<emph.end type="italics"></emph.end> inquis, <emph type="italics"></emph>alterationes quoque omnes, <lb></lb>quibus calor, frigus, humor, ſiccitas, itemque color, odor, ſapor, <lb></lb>& qualitates aliæ gignuntur, nihil eſſe aliud videntur, præter <lb></lb>localeis tenuißimorum corporum motiones: formæ igitur acci<lb></lb>dentariæ nullæ ſunt, mulióque minùs inueniri, & eſſe poſſunt <lb></lb>ab omni ſubſtantia ſeparatæ. </s> <s id="s.002040">Quid ſanctioribus igitur no<lb></lb>ſtræ Religionis myſteriis fiet?<emph.end type="italics"></emph.end> At imprimis vides non eſſe <lb></lb>timendum, <emph type="italics"></emph>ne accidentales formæ nullæ ſint;<emph.end type="italics"></emph.end> quippe quæ <lb></lb>eſſe ſupponantur, & ſpeciali ſolùm explicentur modo. <lb></lb></s> <s id="s.002041">Suusigni ſeruatur calor: ſuum frigus glaciei: ſuus ſapor <lb></lb>melli: ſuus odor roſæ: ſuus tympano ſonus: ſuus can<lb></lb>dor niui; ſua lux Soli, &c. </s> <s id="s.002042">Cùm ex vulgari autem ſen<lb></lb>tentia explicari nequeat, in quónam conſiſtat energia, <lb></lb>& modus agendi illius eiuſdem caloris, frigoris, ſaporis, <lb></lb>cæterarumque qualitatum; tentatur, an id declarari <lb></lb>ex tali hypotheſi valeat. </s> <s id="s.002043">Neque verò ipſe quoque <pb pagenum="273" xlink:href="028/01/313.jpg"></pb>Ariſtoteles eſt ab ea alienus, qui niſi velit alterationem <lb></lb>eſſe motionem quandam localem; ſaltem agnoſeit al<lb></lb>terationem abſque motione locali non eſſe. </s> <s id="s.002044">Quòd <lb></lb>verò proptereà <emph type="italics"></emph>qualitates, ſeu<emph.end type="italics"></emph.end> (vt generaliùs videris lo<lb></lb>quutus) <emph type="italics"></emph>formæ accidentales inueniri & eſſe ab omni ſubſtan<lb></lb>tia ſeparatæ non valeant:<emph.end type="italics"></emph.end> vnde nam, quæſo, colligis, vt <lb></lb>non colligas pari modo ex Ariſtotelea ſententia? </s> <s id="s.002045">Et, ſi <lb></lb>cùm Ariſtoteles manifeſtè faciat, qualitates, ſiue acci<lb></lb>dentaleis formas, inſeparabileis à ſubſtantia, id admit<lb></lb>titur, quatenus ſolis viribus naturæ ſpectatis eſt verum; <lb></lb>reiicitur autem, quatenus ſpectata Authoris naturæ <lb></lb>potentia eſt falſum: quid eſt, cur eædem qualitates, alio <lb></lb>licet modo, quàm Ariſtoteleo expoſitæ, dici non va<lb></lb>leant exſiſtere poſſe ſeparatæ à ſubſtantia, non na<lb></lb>turali quidem, ſed diuina tamen virtute? </s> <s id="s.002046">Neque <lb></lb>enim eſt, cur exiſtimes calorem, v.g quà eſt calor, <lb></lb>formaliterve, vt loquuntur, accipitur, eſſe ipſaſmet ato<lb></lb>mos, atomorumve ſubſtantiam; vt neque idem calor <lb></lb>in ſententia vulgari, ignis eſt, eiuſve ſubſtantia. </s> <s id="s.002047">Quip<lb></lb>pe, vt in communi ſententia calor eſt formaliter quæ<lb></lb>dam qualitas ſubſtantiæ ignis attributa, quatenus eius <lb></lb>eſt naturæ, vt calefacere, ſeu certo modo afficere corpo<lb></lb>ra ſibi admota poſſit: ita etiam erit qualitas atomorum <lb></lb>ſubſtantiæ conueniens, quatenus ſui motu, penetratio<lb></lb>neque in aliquod corpus, ipſum diſgregant, exſoluunt<lb></lb>que; & animatum ſifuerit, non ſine ſenſu aliquo ſpe<lb></lb>ciali ipſius id faciunt. </s> <s id="s.002048">Quare & licet vi naturæ non <lb></lb>poſſit talis qualitas ſine talibus eſſe atomis, ipſarumve <lb></lb>ſubſtantia, eo modo, quo dices eſſe eandem abſque <lb></lb>igne, eiuſve ſubſtantia non poſſe, quatenus in neutra <pb pagenum="274" xlink:href="028/01/314.jpg"></pb>ſententia dati poteſt abſtractè calor; ſed coneretè <lb></lb>ſolùm calidum: diuinitùs tamen <expan abbr="tã">tam</expan> eſſe abſque atomis, <lb></lb>atomorumve ſubſtantia poterit, quam tu eſſe dices abſ<lb></lb>que igne, illiuſve ſubſtantia poſſe. </s> <s id="s.002049">Et ratio eſt, quia <lb></lb>vtrouis modo eadem eſt ſubſtantia, à qua ſeparabilis <lb></lb>calor vi diuina defenditur; diſcrimenque ſolummodò <lb></lb>eſt, quod tu dicas ſolùm ſubſtantiam, illi addant talem <lb></lb>ſubſtantiam, eſſe ex atomis contextam: quæ ſanè poſi<lb></lb>tio ad ſeparabilitatem, inſeparabilitatemve acciden<lb></lb>tium nec iuuat, nec nocet. </s> </p> <p type="main"> <s id="s.002050">XXV. </s> <s id="s.002051">Cùm idem verò proportione de cæteris dici <lb></lb>qualitatibus, ſiue accidentibus valeat; nihilo ſecùs de<lb></lb>fendetur, explicabiturve auguſtiſſimum Tranſubſtan<lb></lb>tiationis myſterium, ſi qualitates corporeas dependere <lb></lb>dixerimus ex ſubſtantia corporis, quæ ex atomis com<lb></lb>ponatur: quàm ſi dependere ſolùm vniuersè dicamus <lb></lb>ex ſubſtantia corporis; quatenus ſubſtantia corporea, <lb></lb>quæcumque ea ſit, componitur ſemper ex partibus, <lb></lb>particuliſque, quas quomodocumque appelles (prout <lb></lb>variè ſubdiuidendo aut infinitè pergere, aut peruenire <lb></lb>tandem ad atomos, ſeu indiuiduas licet) nihil penitùs <lb></lb>ad rem interſit. </s> <s id="s.002052">Videlicet vtrovis modo defendetur <lb></lb>Deum conſeruare qualitates, ſiue accidentia, & Sacra<lb></lb>mentaleis ſpecies, ſepoſitis, deſtructiſve principiis, ſeu <lb></lb>partibus, mavis, ſubſtantialis compoſitionis tam pa<lb></lb>nis, quàm vini; & in ſepoſitæ, deſtructæve ſubſtantiæ <lb></lb>locum, ac ſub ijſdem qualitatibus, accidentibus, aut <lb></lb>ſpeciebus, ſubſtituere, collocareve ſubſtantiam glorio<lb></lb>ſiſſimam Corporis & Sanguinis Chriſti. </s> <s id="s.002053">Heinc proinde <lb></lb>quando requiris, <emph type="italics"></emph>Quid ſanctioribus igitur noſtræ Religio-<emph.end type="italics"></emph.end><pb pagenum="275" xlink:href="028/01/315.jpg"></pb><emph type="italics"></emph>nis myſterijs fiet?<emph.end type="italics"></emph.end> Reſpondeo idipſum, quod fit in vul<lb></lb>gari, & quæ haberi ſolet Ariſtotelea ſententia, Vt toto <lb></lb>nempe corde, atque ore credamus, atque profiteamur <lb></lb>quicquid credendum, profitendumque Sacro ſancta, <lb></lb>Catholica, Apoſtolica, & Romana Eccleſia p<gap></gap>ribit: <lb></lb>Vt non modò Epicurum, & Democritum; ſed Ariſto<lb></lb>telem quoque, & Platonem, & alios omneis flocci<lb></lb>faciamus, quoties proferent aliquid, quod ſit à ſacra <lb></lb>Fide alienum: Vt ipſum naturale lumen nihili duca<lb></lb>mus, præ fidei lumine; & quicquid ab eo monſtratur, <lb></lb>damnemus, ſi iſtud monſtret oppoſitum: Vt defen da<lb></lb>mus non eſſe apud Deum impoſſibile omne verbum; <lb></lb>& quod ſpeciatim attinetad ſeparabilitatem, exiſten<lb></lb>tiamque aut ſubſtantiæ ſine accidentibus, aut acciden<lb></lb>tium ſine ſubſtantia, demus Deum aliquid poſſe, quod <lb></lb>nos fateamur inueſtigare non poſſe, cuiuſque tota ra<lb></lb>tio ſit ipſa potentia facientis. </s> <s id="s.002054">Habes quid putem de<lb></lb>bere fieri, & quod ſanguinis effuſione propugnare pa<lb></lb>ratus ſim. </s> <s id="s.002055">Quod me deinde admones, <emph type="italics"></emph>vt videam, per <lb></lb>Deum immortalem, ne mei nominis authoritate, infirmiori<lb></lb>bus quidem errandi, cæteris verò præconceptam de ingenij mei, <lb></lb>ac iudicij ſagacitate opinionem imminuendi præbeam occaſio<lb></lb>nem:<emph.end type="italics"></emph.end> id ſanè, vt par eſt, accipio. </s> <s id="s.002056">Siquidem, quamvis <lb></lb>longè abſim, vt vllam mei nominis authoritatem eſſe <lb></lb>agnoſcam, & hoc eulogium ſingulari tuæ humanitati <lb></lb>totum debeam: quamvis etiam mihi nihil ſit curan<lb></lb>dum, ne minuatur de me opinio, quæ merito meo eſſe <lb></lb>nulla poteſt: attamen, quod caues, ne infirmioribus er<lb></lb>randi occaſionem præbeam; rem caues mihi planè <lb></lb>cauendam, & pro qua me tibi obſtrictum proſiteor: <pb pagenum="276" xlink:href="028/01/316.jpg"></pb>polliceorque me operam, Numine fauente, daturum, <lb></lb>ne vlla vnquam, vel minima errandi occaſio à me ſug<lb></lb>geratur. </s> </p> <p type="main"> <s id="s.002057"><emph type="center"></emph><emph type="italics"></emph>Actum eſſe de motu Terræ proponendo, non aſſerendo: Et, <lb></lb>Ferant-ne magis Sacræ literæ Tellurem in centro, <lb></lb>quàm extra centrum circumuolui.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002058">XXVI. </s> <s id="s.002059">Venio nunc ad ea, quæ habes in ſecundam <lb></lb>Epiſtolam. </s> <s id="s.002060">Memoras imprimis, quod initio dixi, <lb></lb><emph type="italics"></emph>Exobſeruatis circa Motum à Motore tranſlato impreſſum, <lb></lb>videri infirmum reddi argumentum, quo ſolemus vulgò quie<lb></lb>tem aſſerere globo Telluris.<emph.end type="italics"></emph.end></s> <s id="s.002061"> Et poſtquàm addidiſti, <emph type="italics"></emph>idem <lb></lb><expan abbr="argumentũ">argumentum</expan> etiam inde nullum conuinci,<emph.end type="italics"></emph.end> id notas, quod eſt <lb></lb>à me dictum, <emph type="italics"></emph>Non eò me proptereà adduci, vt inde pronun<lb></lb>ciem moueri haud dubiè Tellurem: ſed ſolùm vt inſinuem <lb></lb>conquirendam eſſe rationem veriſimiliorem:<emph.end type="italics"></emph.end> ac tum ſubdis; <lb></lb><emph type="italics"></emph>Bene habet. </s> <s id="s.002062">Si ſcopus iſte tuus est, collimaſti: pluribus <lb></lb>opus non eſt; adeptoque iam fine fruſtrà, ac inutiliter labo<lb></lb>ras.<emph.end type="italics"></emph.end></s> <s id="s.002063"> Sed ohe! humanitas tua adeóne euadit ſeuera, vt <lb></lb>ſcribenti ad amicum exſpatiari non liceat, nec præoc<lb></lb>cupare, ſi quid ille fortè aut requiſiturus, aut quomo<lb></lb>documque habiturus eſſe iucundum videatur? </s> <s id="s.002064">An-non <lb></lb>ſpecialis, vt Dialogorum, ſic Epiſtolarum eſt mos; & <lb></lb>ille quidem non qualis eſſe anguſta ſolet ſemita, ſed po<lb></lb>tiùs qualis regia via, imò & qualis apertus campus? </s> <s id="s.002065">Alia <lb></lb>ſanè ſunt genera ſcribendi, quæ pro cuiuſque inſtituto <lb></lb>certis legibus, quaſi frænis, atque catenis compeſcun<lb></lb>tur; at genus Epiſtolicum ſolutum, liberumque eſt; & <lb></lb>cùm liceat in cæteris variè per vices digredi; facere in <lb></lb>Epiſtolis etiam <foreign lang="grc">π<gap></gap>ρε<gap></gap> ον ἔρ<gap></gap>ν</foreign> licet <emph type="italics"></emph>Frustrà, ac inutiliter<emph.end type="italics"></emph.end><pb pagenum="277" xlink:href="028/01/317.jpg"></pb><emph type="italics"></emph>laboro?<emph.end type="italics"></emph.end> Bene ſaltem eſt, quòd mihi eſt vni iactura tem<lb></lb>poris ferenda; quanquam & tuum affectum probo, <lb></lb>dum ſollicitus es, ne fruſtrà pretioſam adeò rem de<lb></lb>teram. </s> <s id="s.002066">Rogas conſequenter, S<emph type="italics"></emph>i nihil ampliùs quæro, ec<lb></lb>quid rei ſit, quòd plurimorum ſimilium conglobatione præmiſſa <lb></lb>ſic interrogem:<emph.end type="italics"></emph.end> C<emph type="italics"></emph>ur non ratione eadem ſuadente fiat veroſimi<lb></lb>lius, probabilius, magis conſentaneum, moueri Terram verſus <lb></lb>ortum, ac totam Mundi machinam, ſideraque omnia ſalutare <lb></lb>ex ordine; quàm totam illam machinam, totque, & tanta ſi<lb></lb>dera circum ipſam ire, eamque ſalutare?<emph.end type="italics"></emph.end> Rogas &, <emph type="italics"></emph>Quid ſit, <lb></lb>quod tantopere vrgeo, atque exaggero, maiora ex Solis, fixa<lb></lb>rumque, quàm ex Telluris motu ab ſurda ſequi, atque incom<lb></lb>moda?<emph.end type="italics"></emph.end> Rurſus &, C<emph type="italics"></emph>ur adeò ſtudiosè cætera quoque omnia<emph.end type="italics"></emph.end><lb></lb>C<emph type="italics"></emph>opernicanorum argumenta congeram, ſi hoc ſolùm conten<lb></lb>dam, vulgatum illud aliorum Philoſophorum à proiectilium <lb></lb>motu petitum argumentum infirmum eſſe, atque inualidum?<emph.end type="italics"></emph.end><lb></lb>Tandem &, C<emph type="italics"></emph>ur etiam de Telluris eiuſdem circa Solem mo<lb></lb>tu tam prolixam, nec ad prædictum finem neceſſariam adiun<lb></lb>gam disputationem, in qua non modò Copernicanorum argu<lb></lb>menta omnia, & rationes qua poſſum, & valeo dicendi facul<lb></lb>tate<emph.end type="italics"></emph.end> (& hoc quoque eſt tuæ humanitatis) <emph type="italics"></emph>ſtabilire, & <lb></lb>confirmare, ſed aliorum quoque obiectiones infirmare pari ſtu<lb></lb>dio, & contentione moliar?<emph.end type="italics"></emph.end> Sed vno verbo ipſemet cauſ<lb></lb>ſam iam recitaſti illis verbis, quibus me id ſolùm dixi <lb></lb>facere, <emph type="italics"></emph>vt inſinüarem conquirendam eſſe rationem veriſimi<lb></lb>liorem.<emph.end type="italics"></emph.end></s> <s id="s.002067"> Atqui conuicta illa ratione ex proiectilibus <lb></lb>deſumpta quieſcendum fuit, nec aliæ mouendæ: Ve<lb></lb>rùm aliæ quoque viſæ ſunt mouen dæ; nequeid omninò <lb></lb>abs re, atque incohærenter factum. </s> <s id="s.002068">Quia enim iure <lb></lb>obiici potuit, fruſtrà inſinüari à me conquirendas eſſe <pb pagenum="278" xlink:href="028/01/318.jpg"></pb>alias rationes, cùm illæ iam & conquiſitæ, & adinuen<lb></lb>tæ fuerint; ideò viſus ſum non debere cæteras intactas <lb></lb>prætermittere, vt oſtenderem quatenus eas quoque ar<lb></lb>bitrarer eſſe infirmas. </s> <s id="s.002069">Exiſtimaui autem, ſi licuit eam <lb></lb>ſuffodere, quæ quaſi murus aheneus erat, & quam tu <lb></lb>t<gap></gap>et, ipſum pridem improbaſſe teſtatus es; nihil pro<lb></lb>hibere quò minùs cæteræ ſaltem mediocri ar<gap></gap>atione <lb></lb><expan abbr="impeterẽtur">impeterentur</expan>: neque enim illas aut eſſe ſanctior<gap></gap>s, vt in<lb></lb>uiolatiores manerent: aut magis extra aleam, vt vel <lb></lb>non poſſent, vel non deberent parem experiri <expan abbr="fortunã">fortunam</expan>. <lb></lb></s> <s id="s.002070">Quod autem ſimùl interrogaui, aut exaggeraui <gap></gap>am <lb></lb>aliquid in Copernicanorum gratiam; id egi, vt difficul<lb></lb>tates vberiùs innoteſcerent, patefaceremque quibus <lb></lb>argumentis, cuique rationum oppoſitarum probabili<lb></lb>tati occurrendum ſit, ſi quis aduerſus Copernicanos <lb></lb>præſtare voluerit rationem inuictam. </s> <s id="s.002071">Et quæris, <lb></lb><emph type="italics"></emph>Quid ampliùs eram facturus, ſi eam ſententiam animo deſti<lb></lb>nato aſſerendam, propugnandamque aſſumpſiſſem?<emph.end type="italics"></emph.end> At nihil <lb></lb>ſanè ampliùs facturus fui, qui neid quidem fui aſſum<lb></lb>pturus. </s> <s id="s.002072">Alios, qui aſſumunt, vberiore quadam, atque <lb></lb>concinniore methodo vides agere: ego quidvis com<lb></lb>memoraui breuiter, ac præpoſterè; quippe vt ſe fors <lb></lb>obtulit, mentique, & manui properanti obiecit. </s> </p> <p type="main"> <s id="s.002073">XXVIII. Sequitur, <emph type="italics"></emph>Tolerandum fortaßis, & certè non <lb></lb>ita inconueniens viſum iri, ſi cum Heraclide Pontico, & <lb></lb>Ecphanto Pythagoreo Terram in medio Vniuerſi constitutam <lb></lb>quotidiano tantum motu circa proprium axem moueri conten<lb></lb>derem; ſic enim concitatißimum illum Siderum motum, qui <lb></lb>plæriſque<emph.end type="italics"></emph.end> C<emph type="italics"></emph>opernici ſectatoribus diſplicuiſſe viſus eſt maximè, <lb></lb>tollerem; ac ſatis moderatum, quo Sacris literis faciliùs ſatis-<emph.end type="italics"></emph.end><pb pagenum="279" xlink:href="028/01/319.jpg"></pb><emph type="italics"></emph>facerem, tam errantium, quàm inerrantium Siderum motum, <lb></lb>quem proprium vocant, retinerem; atque in portentoſa, quæ ex <lb></lb>Copernici opinione ſequuntur, incommoda, atque abſurda non <lb></lb>inciderem.<emph.end type="italics"></emph.end></s> <s id="s.002074"> Heic verò tu me ſic alloqueris, quaſi ego <lb></lb>Philolai, aut Ariſtarchi ſententiam amplectar, & rem <lb></lb>proinde faciam minùs tolerabilem, quàm ſi ſequerer <lb></lb>hancà te <expan abbr="præſcriptã">præſcriptam</expan>. </s> <s id="s.002075">Ego verò neque me illam ample<lb></lb>cti profiteor, neque iſtam habeo tolerabiliorem, pro<lb></lb>pter eadem Scripturæ loca, <emph type="italics"></emph>Terra in æternum ſtat; Fun<lb></lb>dasti Terram ſuper ſtabilitatem ſuam; Firmauit orbem Ter<lb></lb>ræ, qui non commouebitur:<emph.end type="italics"></emph.end> Itemque, O<emph type="italics"></emph>ritur Sol, & occidit: <lb></lb>Sol ne moueatur; Regreſſus eſt Sol;<emph.end type="italics"></emph.end> & ſimilia: Quibus ſi <lb></lb>putas ex moderati, ac immoderati motus diſtinctio<lb></lb>ne ab authoribus huius ſatisfieri: complanaſti pe<lb></lb>nitus viam illius defenſoribus, qui ſe tuebuntur, quòd <lb></lb>ſacra Scriptura dum patitur minus, non prohibeat ma<lb></lb>ius. </s> <s id="s.002076">Nec verò ipſis diſplicet modò concitatiſſimus <lb></lb>ille motus, attributus vulgò primo mobili Sidera om<lb></lb>nia circum-rapienti; ſed etiam inconcinnitas, qua ne<lb></lb>ceſſe eſt Planetarum directiones, regreſſiones, ſtatio<lb></lb>nes, & non pauca alia ab Heraclide quoque, & Eephan<lb></lb>to ſaluentur. </s> <s id="s.002077">Quod autem ſpectat ad portentoſa, quæ <lb></lb>dicis abſurda, & incommoda; ipſi nulla eſſe agnoſcunt: <lb></lb>vnde & niſi aduerſam habeant ſacræ Scripturæ autho<lb></lb>ritatem, exiſtimant ſe prorsùs nihil intolerabile tueri. <lb></lb></s> <s id="s.002078">Sequitur adhûc, <emph type="italics"></emph>Meminiſſe ſemper oportet nos non Philoſo<lb></lb>phos tantum eſſe, ſed etiam Chriſtianos, Philoſophiamque <lb></lb>noſtram nec debere, nec verò etiam poſſe à Chriſtiana fide <lb></lb>diſcrepare.<emph.end type="italics"></emph.end></s> <s id="s.002079"> Id verò eſt ſanè tua pietate dignum; ipſeque <lb></lb>non modò aſſentior, verùm etiam palam profiteor, ac <pb pagenum="280" xlink:href="028/01/320.jpg"></pb>iuro. </s> <s id="s.002080">Id vnum ſupereſt, vt noſcatur, quid Philoſophia <lb></lb>proferat à Chriſtiana diſcrepans fide. </s> <s id="s.002081">Cùm enim Phi<lb></lb>loſophia quam plurima doceat, quæ vera habentur, & <lb></lb>ab omnibus viris piis, atque Chriſt anis admittuntur; <lb></lb>tametſi ipſis refragari ſacræ Literæ apertè videan<lb></lb>tur; par eſt profectò Literas ſacras eam pati interpreta<lb></lb>tionem, vt oſtendi poſſit eas, cùm veræ ſint, veritati <lb></lb>non repugnare. </s> <s id="s.002082">Id autem D. </s> <s id="s.002083">Auguſtinus allato exem<lb></lb>plo præclarè inſinüat; cùm difficultate propoſita, <emph type="italics"></emph>Quo<lb></lb>modo non ſit <expan abbr="contrariũ">contrarium</expan> ijs, qui figuram Sphæræ cælo tribuunt, <lb></lb>quod ſcriptum est in libris noſtris, Qui extendit cælum ſicut <lb></lb>Pellem?<emph.end type="italics"></emph.end> Reſpondet; S<emph type="italics"></emph>it ſanè contrarium, ſi falſum eſt, quod <lb></lb>illi dicunt; hoc enim verum eſt, quod diuina dicit authoritas, <lb></lb>potiuſquàm illud, quod humana infirmitas coniicit. </s> <s id="s.002084">Sed ſi <lb></lb>fortè talibus illi documentis probare potuerint, vt dubitari inde <lb></lb>non debeat; demonſtrandum est, hoc, quod apud nos est de Pelle <lb></lb>dictum, veris illis rationibus non eſſe contrarium.<emph.end type="italics"></emph.end></s> <s id="s.002085"> Et rursùs, <lb></lb><emph type="italics"></emph><expan abbr="Tãdiù">Tandiù</expan> non eſt extra fidem, donecveritate certißima refellatur. <lb></lb></s> <s id="s.002086">Quod ſi factum fuerit, non hoc habebat diuina Scriptura; ſed <lb></lb>hoc ſenſerat humana ignorantia.<emph.end type="italics"></emph.end></s> <s id="s.002087"> Haud-dubium proinde, <lb></lb>quin ſanctus Doctor, ſi in noſtra incidiſſet tempora; <lb></lb>aut ſi eius temporibus fuiſſet tota Terra, vt nuper eſt <lb></lb>factum, circum-nauigata: tum agniturus Antipodas <lb></lb>fuiſſet, tum ad humanam potiùs ignorantiam, quàm <lb></lb>ad Scripturæ diuinæ ſenſum, præhabitam ſuam relatu<lb></lb>rus ſententiam, quam vidiſſet certiſſima experientiæ <lb></lb>veritate refelli. </s> <s id="s.002088">Quæ memoro ſolùm, vt intelligamus, <lb></lb>non quicquid Philoſophia docet, quod videatur prima <lb></lb>fronte à Literis ſacris eſſe diſcrepans, proptereà verè <lb></lb>diſcrepare. </s> </p> <pb pagenum="281" xlink:href="028/01/321.jpg"></pb> <p type="main"> <s id="s.002089"><emph type="center"></emph><emph type="italics"></emph>De conſequutionibus ex Terra Planetis interſita ductis: De<lb></lb>que ignorata<emph.end type="italics"></emph.end> C<emph type="italics"></emph>opernicanæ opinionis improbatione.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002090">XXIX. </s> <s id="s.002091">Pergis conſequenter, <emph type="italics"></emph>Cogita igitur, non quid <lb></lb>tu fortè ipſe ſentias, ſed quid æſtimaturi ſint plærique alij, qui <lb></lb>tua vel authoritate, vel rationibus inducti, ſibi perſuaſerint <lb></lb>Telluris globum inter Planetas moueri.<emph.end type="italics"></emph.end> C<emph type="italics"></emph>oncludent primùm <lb></lb>vnum è Planetis ſine dubio eſſe Terram, quæ cùm incolas ha<lb></lb>beat, procliue erit deinde etiam credere, in cæteris quoque Pla<lb></lb>netis, atque adeò in ipſis item inerrantibus<emph.end type="italics"></emph.end> S<emph type="italics"></emph>tellis incolas non <lb></lb>deeſſe; & tantò quidem præstantiores, quantò reliqua Sidera <lb></lb>Terram magnitudine, & perfectione excedunt. </s> <s id="s.002092">Heinc<emph.end type="italics"></emph.end> G<emph type="italics"></emph>e<lb></lb>neſis in ſuſpicionem vocabitur, dum ait Terram ante reliqua<emph.end type="italics"></emph.end><lb></lb>S<emph type="italics"></emph>idera factam, illaque quarto tantum pòſt die condita, vt illu<lb></lb>minarent Terram, temporaque, & annos metirentur. </s> <s id="s.002093">Inde <lb></lb>tota Verbi Incarnati œconomia, atque Euangelica veritas <lb></lb>ſuſpecta reddetur; imò & tota fides<emph.end type="italics"></emph.end> C<emph type="italics"></emph>hriſtiana, quæ & ſup<lb></lb>ponit, & docet<emph.end type="italics"></emph.end> S<emph type="italics"></emph>idera omnia non ad hominum, aut aliarum <lb></lb>creaturarum habitationem, ſed ſolùm, vt Terram ſua luce <lb></lb>collustrent, fœcundentque, eſſe à Deo authore producta.<emph.end type="italics"></emph.end><lb></lb>Verùm, religioſiſſime Vir, iſta imprimis in me non <lb></lb>quadrant, qui Telluris globum eſſe vnum ex Planetis, <lb></lb>aut moueri inter Planetas neque dico, neque defendo; <lb></lb>ſed in eos potiùs, qui rem & ſentiunt, & profitentur ſic <lb></lb>ſe habere. </s> <s id="s.002094">Neque verò aut ego vlla ſum authoritate, <lb></lb>qui ſi eſſem aliqua, abſit à me, vt vellem ipſam placito <lb></lb>falſo patrocinari: aut rationes vllæ meæ ſunt, ſed ſuo<lb></lb>rum dumtaxat authorum; quas quia opponere nobis <lb></lb>ſolent, dum noſtras ipſis obiicimus, ideò diſſimulare <lb></lb>viſum non eſt, propter iam expoſitam cauſſam. </s> <s id="s.002095">Deinde <pb pagenum="282" xlink:href="028/01/322.jpg"></pb>ſubuereor, ne illi reſponſuri ad tuas huiuſcemodi conſe<lb></lb>quutiones fuerint, ablegandam igitur eſſe vniuerſam <lb></lb>Phyſicam, quatenusnullum eſt placitum, ex quo dicere <lb></lb>non poſſimus, deduci poſſe ab aliquibus incommoda <lb></lb>non abſimilia. </s> <s id="s.002096">Ponatur enim, exempli cauſſa, <emph type="italics"></emph>Eſſe <lb></lb>Terram sphæricam:<emph.end type="italics"></emph.end> Concludetur, eſſe eam ergo habita<lb></lb>bilem circumquáque; & procliue fore credere Antipo<lb></lb>das. </s> <s id="s.002097">Inferetur, eos non potuiſſe ab Adamo propagari; <lb></lb>atque idcircò Chriſtum Dominum non eſſe eorum <lb></lb>Redemptorem. </s> <s id="s.002098">Nouum proinde Teſtamentum in ſuſ<lb></lb>picionem vocatum iri, & totam Verbi Incarnati œco<lb></lb>nomiam, ac cætera his conſentanea; vt prætereantur <lb></lb>portentoſa abſurda, & incommoda de hominibus, <lb></lb>ædificiis, arboribuſque penſilibus, quæ noſti obiecta <lb></lb>aliquando fuiſſe. </s> <s id="s.002099">Ponatur &, <emph type="italics"></emph>Lunam eſſe ſphæricam, <lb></lb>quemadmodum Terram; illuminari à Sole, obtenebreſceré<lb></lb>que, non ſecùs, ac Terram; Eclipſin pati propter Terram, vt <lb></lb>Terra patitur propter ipſam; habere ſuperficiem perinde <lb></lb>maculoſam, ac appareret habere<emph.end type="italics"></emph.end> T<emph type="italics"></emph>erra, ſi è Luna conspice<lb></lb>retur; habere monteis, valleis, planities, & alia id genus, eo <lb></lb>modo, quo Terram:<emph.end type="italics"></emph.end> Concludetur ſtatim, eſſe igitur Lunam <lb></lb>alteram Terram; eaſdem in Luna, ac in Terra genera<lb></lb>tiones fieri; eſſe in ea incolas; & procliue fore etiam ho<lb></lb>mines credere, qui ex Adamo propagati non ſint, <expan abbr="neq;">neque</expan> <lb></lb>à Chriſto redempti. </s> <s id="s.002100"><expan abbr="Vocatũ">Vocatum</expan> iri in <expan abbr="ſuſpicionẽ">ſuſpicionem</expan> Geneſin, <lb></lb>quæ docet Lunam factam, vt illuminet Terram, non vt <lb></lb>ipſam obtenebret, aut ab illa obtenebretur; vt incolas <lb></lb>habeat, &c. </s> <s id="s.002101">Ponatur <emph type="italics"></emph>Terram eſſe punctum comparatam ad <lb></lb>Firmamentum; & Stellarum minutulas eſſe decies octies, ma<lb></lb>iuſculas verò centies octies maiores, quàm Terram; & con-<emph.end type="italics"></emph.end><pb pagenum="283" xlink:href="028/01/323.jpg"></pb><emph type="italics"></emph>ſequenter vnamquàmque illarum eſſe ſeptingenties maiorem, <lb></lb>quàm Lunam; quamlibet iſtarum pluſquàm quater millies:<emph.end type="italics"></emph.end><lb></lb>Concludetur igitur <expan abbr="Terrã">Terram</expan> non fore adeò profundam, <lb></lb>& latam, vt poſſit meritò cum cæli altitudine compa<lb></lb>rari: cùm ſacræ tamen Literæ iſta interualla quaſi ex <lb></lb>æquo habeant, <emph type="italics"></emph>ſi aſcendero in cælum, tu illeic es: ſi deſcen<lb></lb>dero in infernum ades: ſi ſumpſero pennas meas, &c.<emph.end type="italics"></emph.end> <expan abbr="Suſ-pectã">Suſ<lb></lb>pectam</expan> fore Geneſin, quæ docet fuiſſe ſolum creata duo <lb></lb>magna Luminaria, & Lunam eſſe alterum duorum, <lb></lb>quòd ipſo quidem Sole ſit minus; at non tot Stellis, ac <lb></lb>præſertim <expan abbr="tã">tam</expan> multis illis vicibus. </s> <s id="s.002102">Procliue proinde fore <lb></lb>credere, eſſe igitur Stellarum orbeis Terra, ac Luna lon<lb></lb>gè præſtantiores; neque eſſe adeò ſepoſitos, vt vaſtita<lb></lb>tes inutiles ſint, ſed debere maiore ratione, & à præ<lb></lb>ſtantioribus inhabitari incolis; ac proinde, cùm tota <lb></lb>eorum lux ne tantum quidem inſeruiat ad illuminan<lb></lb>dum Terram, & dimetiendum tempora, quantum in<lb></lb>ſeruit vna lux Lunæ: eſſe ergo illos à Deo in alium <lb></lb>vſum conditos, &c. </s> <s id="s.002103">Denique ponatur quicquid vo<lb></lb>les aliud; & pari ratione opponetur poſſe his ſimilia <lb></lb>concludi; procliue eſſe ea credere; ſacrarum Literarum <lb></lb>fidem, totiuſque Religionis fundamenta nutare. </s> </p> <p type="main"> <s id="s.002104">XXX. </s> <s id="s.002105">Quòd ſi, cum iſta nobis videantur deduci <lb></lb>poſſe ab aliquibus, non ideò minùs placita, quæ ſunt <lb></lb>memorata de rotunditate Terræ; de comparatione <lb></lb>Lunæ cum Terra; de Terræ, Lunæque exilitate, & am<lb></lb>plitudine Stellarum, à viris, qui reuerâ pij, & Chriſtiani <lb></lb>ſint, defendantur; quatenus illæ conſequutiones, vbi <lb></lb>præſertim longiùs, & aduerſus Fidem procedunt, im<lb></lb>probabiles ſunt, nulláque poſſunt aut ratione, aut ob-<pb pagenum="284" xlink:href="028/01/324.jpg"></pb>ſeruatione oſtendi; & mera nixæ coniectura, qua facili<lb></lb>tate conſtituuntur, corruunt; fumuſque cùm ſint, in <lb></lb>fumum excedunr: eadem de cauſſa dicent iſti, hæc, quæ <lb></lb>videntur poſſe deduci ab aliquibus, non debere obſta<lb></lb>re, quò minùs placitum de motu Telluris inter Plane<lb></lb>tas conſtitutæ, à viris, qui reuerâ pij, & Chriſtiani ſint, <lb></lb>defendatur. </s> <s id="s.002106">Nimirùm contendent, cùm Terra id <lb></lb>iuris habuerit, vt inter Planetas verſata, heinc Vene<lb></lb>rem, Mercurium, Solem, illeinc Martem, Iouem, Satur<lb></lb>num, ac aliunde circum ſe Lunam proximè circumdu<lb></lb>ctam ſortiatur; non idem iuris proptereà aliis Planetis <lb></lb>competere, quos propterillam Deus creârit. </s> <s id="s.002107">Neminem <lb></lb>proinde ſanæ mentis colligere poſſe eſſe aut in Luna, <lb></lb>aut in aliis Planetis, Stelliſque fixis incolas, qui autho<lb></lb>mines ſint, aut ſimilitudinem cum hominibus habeant. <lb></lb></s> <s id="s.002108">quoniam, ſi non omnis tellus omnia fert; & Europa, <lb></lb>Americáque, Scythia, & Libya, quæ eiuſdem globi <lb></lb>partes ſunt, diuerſiſſima proferunt; quantò æquius ſit <lb></lb>reputare, non poſſe eadem naſci, educari, degere in <lb></lb>Luna, atque cæteris, qui ſunt orbes planè diuerſi? </s> <s id="s.002109">Si <lb></lb>quædam proinde oriantur, & intereant aut in Planetis <lb></lb>cæteris, aut in aliis Siderum globis, non poſſe illa eſſe <lb></lb>præſtantiora homine; quatenùs nihil eſſe poteſt aut <lb></lb>ratione præclarius, aut ſupernaturalibus donis, quibus <lb></lb>ille ſolus donatur, diuinius. </s> <s id="s.002110">Cæterùm enim poſſe eſſe <lb></lb>corpora maiora, robuſtiora, durabiliora, aut aliis qui<lb></lb>buſdam adiunctis perfectiora, quàm homines, id ne <lb></lb>negari quidem poſſe; cùm etiam in ipſamet Terra mul<lb></lb>ta corpora id genus naſcantur. </s> <s id="s.002111">Et non proptereà Ge<lb></lb>neſin in ſuſpicionem poſſe vocari; quoniam ea docet, <pb pagenum="285" xlink:href="028/01/325.jpg"></pb>quod non negatur, feciſſe Deum Solem, & Lunam, ac <lb></lb>Stellas, vt Terram illuminent, ſintque inſigna, & tem<lb></lb>pora; & non docet tamen Sidera ad hec ſolùm facta. <lb></lb></s> <s id="s.002112">Alioquin enim inferretur, eſſe quidem factum Solem, <lb></lb>vt illuminet Terram, ſed non vt Lunam, aut Venerem, <lb></lb>quod Geneſis tacet: &, Lunam eſſe quidem factam, vt <lb></lb>Terram illuminet; ſed non vt (quod mox dictum eſt) <lb></lb>tenebras in ipſam inducat; nam & Geneſis id non dicit. <lb></lb></s> <s id="s.002113">Vt prætereatur, ſi, quia Geneſis aliud non declarat, ni<lb></lb>hil agitur aliud à Sideribus; non igitur Solem calefa<lb></lb>cere, vrere, fouere, &c. </s> <s id="s.002114">neque Lunam ſpeciale impe<lb></lb>rium in res humidas exercere, in <expan abbr="cõchylia">conchylia</expan>, animalium <lb></lb>medullas, & id genus ſimilia. </s> <s id="s.002115">Non item ſuſpectam <lb></lb>reddi Verbi Incarnati œconomiam, veritatem Euan<lb></lb>gelicam, totam ipſam fidem Chriſtianam; quoniam ea <lb></lb>perinde illibata conferuatur; quatenus nullæ aliæ na<lb></lb>turæ rationales, & redemptionis, gratiæ, gloriæque ſu<lb></lb>pernaturalis capaces vlla ratione colligi poſſunt exſi<lb></lb>ſtere, præter homines in Terris degenteis; in quibus ſo<lb></lb>lis incarnatus Dei Vnigenitus viſus eſt, & cum homi<lb></lb>nibus conuerſatus. </s> <s id="s.002116">Neque verò cæteros globos, ſi in <lb></lb>ipſis creaturæ quædam generantur, & corrumpuntur, <lb></lb>dici magis poſſe ab ijs habitari, quàm dicantur loca <lb></lb>Terræ deſerta à ſaxis, herbis, culicibus, cæteriſque id <lb></lb>genus rebus; neque proptereà dici poſſe incolas habere, <lb></lb>qui ſint homines, aut cum hominibus comparandi. <lb></lb></s> <s id="s.002117">Nam ſupponere quidem, & docere Fidem ſacram, non <lb></lb>habitari Sidera ab aliis aut hominibus, aut naturis, quæ <lb></lb>pari modo vel ratiocinentur, vel participes ſint dono<lb></lb>rum ſupernaturalium: at non ſupponere, nec docere, <pb pagenum="286" xlink:href="028/01/326.jpg"></pb>nihil in ipſis eſſe ortui, interituique obnoxium; & ne <lb></lb>maculas quidem in Sole naſci, ac perire; non in cælo <lb></lb>reliquo Cometas, atque nouas Stellas. </s> <s id="s.002118">Nec porrò <lb></lb>ſacrum ipſum Textum, cùm dicit Solem, & cætera Si<lb></lb>dera facta, vt Terram illuminent, negare prop tereà, <lb></lb>quin ipſa aliude ſint in ſeipſis, ac præter lucem aliquid; <lb></lb>& id genus alia, quæ tamen non dicit, vt nec cætera, <lb></lb>quæ noſſe nihil intereſt ad ſupernaturalem ſalutem. <lb></lb></s> <s id="s.002119">Scilicet præclarè ſanctus ille Doctor, <emph type="italics"></emph>Breuiter,<emph.end type="italics"></emph.end> inquit, <lb></lb><emph type="italics"></emph>dicendum eſt, hoc ſciſſe Authores noſtros, quod veritas habet: <lb></lb>ſed Spiritum Dei, qui per ipſos loquebatur, noluiſſe iſta docere <lb></lb>bomines, nulli ad ſalutem profutura.<emph.end type="italics"></emph.end></s> <s id="s.002120"> Eiuſmodi ſunt, alia<lb></lb>que affinia, quæ prædixi vereri me, ne illi fuerint reſ<lb></lb>ponſuri. </s> </p> <p type="main"> <s id="s.002121">XXXI. Subiicis, <emph type="italics"></emph>Vides igitur, quàm iſta periculosè in <lb></lb>publicum diuulgentur, & à viris præſertim, qui ſua authori<lb></lb>tate fidem facere videantur; & quàm non immeritò iam inde <lb></lb>à Copernici tempore Eccleſia ſemper huic ſe errori oppoſue<lb></lb>rit: eumque etiam nouißimè non<emph.end type="italics"></emph.end> C<emph type="italics"></emph>ardinales tantum aliqui, vt <lb></lb>ais, ſed ſupremum Eccleſiæ caput Pontificio decreto in Galileo <lb></lb>damnauerit, & vt ne in posterùm verbo, aut ſcripto docere<lb></lb>tur, ſanctißimè prohibuerit.<emph.end type="italics"></emph.end></s> <s id="s.002122"> Heic non repeto, quod illi <lb></lb>tuebuntur, non ſequi ex ea, quam diuulgant, ſententia <lb></lb>id, quod tu times, periculum. </s> <s id="s.002123">Tria potiùs dico. </s> <s id="s.002124">Vnum, <lb></lb>me ab illis non ſtare, vel ex eo ſolo, quòd dicis eorum <lb></lb>opinionem haberi Eccleſiæ ſuſpectam. </s> <s id="s.002125">Videlicet ego <lb></lb>Eccleſiæ alumnus, ita me totum ipſi deuoueo, vt quic<lb></lb>quid illa improbat, ipſe anathema conclamem. </s> <s id="s.002126">Alte<lb></lb>rum, fuiſſe me in ea verſatum ignorantia, vt neſcie<lb></lb>rim hanc opinionem ab vſque Copernici tempore <pb pagenum="287" xlink:href="028/01/327.jpg"></pb>habitam ſuſpectam. </s> <s id="s.002127">Nam viſus ſum potiùs mihi agno<lb></lb>uiſſe aliquos eruditos viros, etiam Eccleſiæ Proceres, <lb></lb>Scripturæ ſacræ Interpretes, & Religioſos Doctores, <lb></lb>harum rerum intelligenteis, qui ab ipſa vſque ætate <lb></lb>Copernici illam probârint: ac fuiſſe aliquid omninò <lb></lb>aut inquiſitum, aut pronunciatum ante Galileum, me <lb></lb>penitùs latuit. </s> <s id="s.002128">Quòd enim ſemper aduerſus ipſam <lb></lb>ſpeciales aliqui Scriptores loca quædam ſacræ Scriptu<lb></lb>ræ oppoſuerint, id non magis viſum eſt facere Eccleſiæ <lb></lb>ſuſpectam, quàm fecit ſuſpectam opinionem de ro<lb></lb>tunditate cæli, quod ex D. vſque Auguſtino retulimus <lb></lb>iam obiici, <emph type="italics"></emph>Extende<gap></gap>s cælum ſicut Pellem;<emph.end type="italics"></emph.end> aut illam de <lb></lb>aëre, igne, æthereve circum Terram, & verſus cælum <lb></lb>fuſo, id, quod ex D. vſque Thoma obiectum eſt, <emph type="italics"></emph>Qui <lb></lb>extendit Aquilonem ſuper vacuum, & appendit Terram ſu<lb></lb>per nihilum:<emph.end type="italics"></emph.end> aut aliam de fluiditate cælorum, ſpatio<lb></lb>rumve cæleſtium, id, quod nemo non obiicit, <emph type="italics"></emph>ſunt cæli <lb></lb>ſolidißimi quaſi ære fuſi,<emph.end type="italics"></emph.end> atque ita de cæteris. </s> <s id="s.002129">Noſti ſi<lb></lb>quidem nullam eſſe ex huiuſmodi opinionibus (imò <lb></lb>neque ex omnibus, quas pij Doctores in Scholis tuen<lb></lb>tur) aduerſus quàm loca Scripturæ aliqua proferri non <lb></lb>poſſint, aut ſoleant; cùm illæ tamen proptereà Eccle<lb></lb>ſiæ ſuſpectæ non ſint. </s> <s id="s.002130">Poſtremùm inaudiiſſe me qui<lb></lb>dem latam fuiſſe ſententiam aduerſus Galileum à Con<lb></lb>gregatione ſacra Cardinalium Inquiſitioni præſiden<lb></lb>tium: at non accepiſſe perinde fuiſſe decretum Ponti<lb></lb>ficium, atque generale conſequenter factum. </s> <s id="s.002131">Et donec <lb></lb>quidem nihil aliud, quàm ſpecialis ſententia fuit, dici <lb></lb>fortaſſe potuit cauſſam ad Galileum ſolùm ſpectare, <lb></lb>aduerſus quem eſſe potuerint ſpeciales cauſſæ aliquæ, <pb pagenum="288" xlink:href="028/01/328.jpg"></pb>aduerſus alios non valituræ. </s> <s id="s.002132">At ex quo Summum <lb></lb>Eccleſiæ caput decretum, vt ais, interpoſuit, non vi<lb></lb>deo quid-nam reſpondere Copernicani Catholici <lb></lb>poſſint; niſi fortè ſibi de eo non conſtare, quovſque <lb></lb>promulgatum fuerit, legitiméque iuſſum haberi tan<lb></lb>quam fidei articulum intemeratum. </s> <s id="s.002133">Quod me atti<lb></lb>net, me vel ſola fama, habitáque fides tuis literis ita <lb></lb>mouet, vt non exſpectem promulgationem, ſed ſtatim <lb></lb>prorſus exoſculer, & planè cæcâ, vt dicitur, obedien<lb></lb>tiâ ipſum excipiam. </s> </p> <p type="main"> <s id="s.002134"><emph type="center"></emph><emph type="italics"></emph>Sit ne abſurdum reputare<emph.end type="italics"></emph.end> O<emph type="italics"></emph>rbem magnum (ſeu cælum<emph.end type="italics"></emph.end> S<emph type="italics"></emph>olis) <lb></lb>eſſe quaſi punctum comparatum ad Firmamentum: Et,<emph.end type="italics"></emph.end><lb></lb>S<emph type="italics"></emph>olem quaſi vnam Fixarum, Fixas quaſi<emph.end type="italics"></emph.end> S<emph type="italics"></emph>oleis <lb></lb>totidem habere.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002135">XXXII. </s> <s id="s.002136">Miraris deinde, <emph type="italics"></emph>Qua fronte erroris huius<emph.end type="italics"></emph.end><lb></lb>S<emph type="italics"></emph>ectatores exprobrent communi, ſaniorique ſententiæ, quòd <lb></lb>abſurda quædam videatur inducere: cùm ipſi infinita pro<lb></lb>pemodum abſurditatum portenta admittant; excolant<gap></gap><lb></lb>culicem, & elephantos deglutientes: ac notas me eorum tan<lb></lb>gere nonnulla, ſed diſplicere, quòd etiam excuſem.<emph.end type="italics"></emph.end></s> <s id="s.002137"> Ego <lb></lb>verò ea non excuſo; aut certè ea mihi mens eſt, vt <lb></lb>non tam excuſem, quàm proponam quod illi reſ<lb></lb>pondent; vt quæ nosipſis obiicimus eſſe abſurda, non <lb></lb>eſſe perſuadeant. </s> <s id="s.002138">Dicis, <emph type="italics"></emph>me ſaltem agnoſcere motum <lb></lb>Terræ circa<emph.end type="italics"></emph.end> S<emph type="italics"></emph>olem ſuſtineri non poſſe, niſi etiam admitta<lb></lb>tur magnum illum<emph.end type="italics"></emph.end> O<emph type="italics"></emph>rbem, per quem Tellus deferri fingitur, <lb></lb>instar puncti respectu cæli obtinere.<emph.end type="italics"></emph.end></s> <s id="s.002139"> Et agnoſco ſanè. <lb></lb><emph type="italics"></emph>At dißimulo,<emph.end type="italics"></emph.end> ais, <emph type="italics"></emph>aut certè eleuo quæ inde ſequuntur<emph.end type="italics"></emph.end><pb pagenum="289" xlink:href="028/01/329.jpg"></pb><emph type="italics"></emph>abſurda, vt quòd inerrantia<emph.end type="italics"></emph.end> S<emph type="italics"></emph>idera propemodùm omnia tam <lb></lb>prodigioſæ molis admittenda ſint, vt earum ſemidiameter in<lb></lb>teriectam à Terræ centro ad<emph.end type="italics"></emph.end> S<emph type="italics"></emph>olis centrum diſtantiam exce<lb></lb>dat.<emph.end type="italics"></emph.end></s> <s id="s.002140"> Ego verò id, vt mihi videtur, non diſſimulo; quòd <lb></lb>ſi eleuare viſus ſum; id alienæ ſententiæ fuit. </s> <s id="s.002141">Quan<lb></lb>quam me dixiſſe non commemini, Sidera inerrantia <lb></lb>Orbem magnum excedere; videlicet, potiuſ quàm <lb></lb>Solem, quem dixi quidem poſſe <emph type="italics"></emph>apparere,<emph.end type="italics"></emph.end> at non <emph type="italics"></emph>eſſe<emph.end type="italics"></emph.end><lb></lb>ipſi æqualem. </s> <s id="s.002142">Sed eſto, vt dicis; quandò Copernicani <lb></lb>ſunt, qui illam magnitudinem tribuere Stellis non <lb></lb>erubeſcunt. </s> <s id="s.002143">Proſequeris, <emph type="italics"></emph>Quod ſi' tibi abſurdum, atque <lb></lb>ab omni ratione abhorrens non videtur, quid, amabò, iudica<lb></lb>bis abſurdum?<emph.end type="italics"></emph.end> Id verò tu mihi potes dicere, neque ego <lb></lb>abnuo, ſed adſtipulor; At quæſo te tamen, quid ſim <lb></lb>reſponſurus, ſi cùm idem obiecero, illi ita exceperint? <lb></lb></s> <s id="s.002144">Tu id abſurdum, & ab omni ratione eſſe abhorrens <lb></lb>iudicas: & quam-nam tandem affers rationem? </s> <s id="s.002145">An-ne <lb></lb>quòd exinde Stellæ inerrantes molis ſint nimis prodi<lb></lb>gioſæ? </s> <s id="s.002146">Ecquis verò tu, qui exiſtimes eſſe aliquid nimium <lb></lb>in operibus immenſi Authoris? </s> <s id="s.002147">Non videtur fuiſſe <lb></lb>Deo cauſſa, cur eas tam vaſtas faceret: at fuiſti-ne tu <lb></lb>eius conſiliarius, vt penetraſſe putes te in omnia diui<lb></lb>næ Sapientiæ arcana? </s> <s id="s.002148">Non capis rationem tantæ va<lb></lb>ſtitatis: an ergo quia tibi mens anguſta eſt; ipſa tanti <lb></lb>Opifices opera debent eſſe anguſta? </s> <s id="s.002149">Abhorrere à ratio<lb></lb>ne putas, vt aliquæ Stellæ ſint Sole maiores, ac tot præ<lb></lb>ſertim vicibus: an-non es proinde illi ſimilis, qui vr<lb></lb>bem Romam ſimilem tuguriolis paucis putabat; tan<lb></lb>quam non capiens eſſe poſſe tot vicibus maiorem illa, <lb></lb>in quam ſolebant paſtores ouium teneros fœtus <pb pagenum="290" xlink:href="028/01/330.jpg"></pb>depellere? </s> <s id="s.002150">Et verò ſi fortè vixiſſes ante illud tempus, <lb></lb>quo Mathematici demonſtrârunt, aut ſaltem dixerunt <lb></lb>eſſe Solem circiter centies ſeptuagies Terra maio<lb></lb>rem: quam igitur illud cenſuiſſes ab omni ratione <lb></lb>abhorrens? </s> <s id="s.002151">Et cùm iam vides vulgò admitti id, quod <lb></lb>memoratum iam eſt, eſſe Stellas fixas, quæ ſint centies <lb></lb>octies maiores, quàm Terra, & quater millies, quàm <lb></lb>ipſa Luna: cur non id abhorrens à ratione putas? </s> <s id="s.002152">An <lb></lb>meliùs capis, ob quam rationem Deus illas fecerit tan<lb></lb>tas? </s> <s id="s.002153">An-non, ſi id, quod dicimus, tuo ſenſu abſurdum <lb></lb>eſt: ſecundum magis, & minus ſolùm erit diſcrimen <lb></lb>abſurditatis? </s> <s id="s.002154">Habes-ne verò interim vllum omninò <lb></lb>argumentum, quo Stellas eſſe tantas ſic probes, vt ſi<lb></lb>mùl probes aut non eſſe, aut non poſſe eſſe maiores? <lb></lb></s> <s id="s.002155">Non certè; ſed penitùs gratis in ea conſiſtis magnitu<lb></lb>dine; neque eſt tibi maior ratio quærendi ex nobis, <lb></lb>cur procedamus vlteriùs: quàm nobis quærendi ex te, <lb></lb>quamobrem conſiſtas citeriùs. </s> <s id="s.002156">Dicere ad ſummum <lb></lb>potes, tibi ſic videri; & quia ſic videtur, nos à ratione <lb></lb>abhorrere: quid-ni & nobis pari iure dicere dete idem <lb></lb>liceat? </s> <s id="s.002157">Quanquam & nobis ratio eſt, tum admiranda <lb></lb>concinnitas, quæ hac ſuppoſita amplitudine obſerua<lb></lb>tur; tum commendatio operum Dei, quæ tu, quantum <lb></lb>potes, extenuas, dum ea non maiora tuo captu facis. <lb></lb></s> <s id="s.002158">Quippe huiuſmodi amplitudo diuinæ potentiæ, ſa<lb></lb>pientiæ, & magniſicentiæ conſentanea eſt: neque eſt, <lb></lb>cur tu abſque vlla aut obſeruatione, aut ratione illam <lb></lb>contrahas, vel abſurdam putes. </s> <s id="s.002159">Quæſo te, inquam, Vir <lb></lb>Religioſiſſime, ecquid-nam illis dicturus ſim, cùm <lb></lb>hæc, & ſimilia reponent? </s> </p> <pb pagenum="291" xlink:href="028/01/331.jpg"></pb> <p type="main"> <s id="s.002160">XXXIII. Subiicitur; <emph type="italics"></emph>Eleuas certè plærdque alia, quæ <lb></lb>ex eadem Telluris circa Solem tranſlatione vlteriùs ſequuntur, <lb></lb>abſurda, à quibus tamen vt te expedias, fingis alia fortaßis <lb></lb>adhûc abſurdiora; vt, quòd illuſtriora illa, quæ in<emph.end type="italics"></emph.end> F<emph type="italics"></emph>irmamento <lb></lb>apparent Sidera credi poßint vt mole maiora, ſic etiam Sole <lb></lb>ipſo longè lucidiora: adeò tibi facile eſt tot, tamque ingenteis <lb></lb>in cælo pro tua voluntate verbo vnico creare Soleis.<emph.end type="italics"></emph.end></s> <s id="s.002161"> Ego ve<lb></lb>ro & heic quoque tibi adſtipulor. </s> <s id="s.002162">Sed dic, amabò, <lb></lb>etiam hoc loco, quid illis reſponſurus ſim, cùm ipſi ſic <lb></lb>inſtiterint. </s> <s id="s.002163">Ludis, ac putas deludi nos? </s> <s id="s.002164">De Solis voce <lb></lb>non agitur, quæ Fixis à vulgo non magis tribuetur, <lb></lb>quàm Lunæ vox tribuitur: tametſi nemo diffitea<lb></lb>tur, quin Fixæ ſint Luna maiores. </s> <s id="s.002165">Nempe quantæcúm<lb></lb>que eæ ſint; apparent tamen, donec è Terra ſpectan<lb></lb>tur, quaſi punctula ad apparentem Solis, ac Lunæ ma<lb></lb>gnitudinem comparatæ Enimverò cùm heic agatur <lb></lb>de ea magnitudine, qua Stellæ ſecundum ſe ſunt, & <lb></lb>qua apparerent, ſi tantumdem nobis admouerentur, <lb></lb>quantum Sol; ac de magnitudine etiam, qua Sol eſt in <lb></lb>ſe, quáque appareret, ſi tantumdem à nobis remoue<lb></lb>retur, quantum Fixæ: putaſ-ne ludendo ſcopum atti<lb></lb>giſti? </s> <s id="s.002166">Non eſto Sol, non ſunto Fixæ in tanta à Terris <lb></lb>diſtantia, quanta à nobis aſſeritur: eſto minima, & qua<lb></lb>lem Tycho poſuit, nulla ſanè obſeruatione (quod ad <lb></lb>Fixas pręſertim ſpectat) verùm coniectatione mera, <lb></lb>meróque arbitrio inductus. </s> <s id="s.002167">Diſſidebit à Terra Sol, <lb></lb>cùm diſſebit mediocriter, terrenis ſemidiametris mille <lb></lb>centum, & quinquaginta, & Fixæ quater-decies nulle. <lb></lb></s> <s id="s.002168">Finge igitur Solem quantuſ-quantus eſt, tranſlatum <lb></lb>eſſe vſque ad Fixas: cùm diameter eius apparens im-<pb pagenum="292" xlink:href="028/01/332.jpg"></pb>minuenda ſit pro ratione diſtantiæ, diuide Fixarum <lb></lb>diſtantiam per diſtantiam Solis à Terra, fiet quotiens <lb></lb>amplius, quàm duodecim. </s> <s id="s.002169">Et quia Solis diameter ap<lb></lb>paret iam nobis dimidij gradus, ſiue minutorum tri<lb></lb>ginta; ſequitur vt Sole inter Fixas exſiſtente, eius dia<lb></lb>meter apparitura non ſit, niſi pars huius duodecima, <lb></lb>ſiue minutorum duorum cùm ſemiſſe. </s> <s id="s.002170">Porrò hac ea<lb></lb>dem diametro apparent vulgò quæ Stellæ ſunt magni<lb></lb>tudinis primæ, aut ſecundæ. </s> <s id="s.002171">Igitur ſi Sol fuerit inter <lb></lb>Fixas conſtitutus, non apparebit maior, quàm vna Stel<lb></lb>larum. </s> <s id="s.002172">Et vice verſa, ſi quęlibet earumdem Stellarum <lb></lb>fixarum conſtituta fuerit vbi iam eſt Sol, ſeu pari, qua <lb></lb>ille à nobis diſtantia: apparebit nobis tanta, quantus <lb></lb>Sol; atque adeò omnes erunt quaſi Soles. </s> <s id="s.002173">Quid ſi di<lb></lb>ſtantiam Fixarum augeas pro opinione Albategnij <lb></lb>Ptolemæo inhærentis, ſtatuentiſque illam nouemde<lb></lb>cim millium ſemidiametrorum: an-non apparitura <lb></lb>fuerit Solis diameter infra duo minuta? </s> <s id="s.002174">Quid ſi adhûc <lb></lb>ampliùs, vt debere fieri probabile eſt, nihilque repu<lb></lb>gnat? </s> <s id="s.002175">Verùm hoc ſufficiat, vt intelligas non nos aut <lb></lb>abſurda tueri, aut ijs <expan abbr="propugnãdis">propugnandis</expan> abſurdiora fingere: <lb></lb>ſed te potiùs rem non aduertere, & fingere magis. </s> <s id="s.002176">Qua<lb></lb>re & cùm ſit Deusipſe, qui tot in cælo ingenteis Soleis <lb></lb>pro ſua voluntate, ac verbo vnico creauit: ne cauſſare <lb></lb>nos pro noſtra voluntate, verbóque vno illos creare: <lb></lb>ſed agnoſce potiùs te eos pro tua voluntate, verbóque <lb></lb>vno deſtruere. </s> <s id="s.002177">Si illi, inquam, aduerſum me hac <lb></lb>ratione inſtiterint; dic mihi, te quæſo, quid ſim reſ<lb></lb>ponſurus? </s> </p> <pb pagenum="293" xlink:href="028/01/333.jpg"></pb> <p type="main"> <s id="s.002178"><emph type="center"></emph><emph type="italics"></emph>Poſſe Solem è<emph.end type="italics"></emph.end> F<emph type="italics"></emph>ixis non minorem, quàm<emph.end type="italics"></emph.end> O<emph type="italics"></emph>rbem magnum <lb></lb>apparere: &, Veros omnium<emph.end type="italics"></emph.end> S<emph type="italics"></emph>tellarum diſcos in vnum <lb></lb>compoſitos, vix apparenti diſco vnius <lb></lb>mediocris Stellæ exæquatum iri.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002179">XXXIV. </s> <s id="s.002180">Subiungis verò; <emph type="italics"></emph>Similiter, quod etiam ais, <lb></lb>fieri poſſe, vt Sol hic noſter, quamvis comparatione ſuperio<lb></lb>rum<emph.end type="italics"></emph.end> S<emph type="italics"></emph>iderum adeò exiguus, ac penè nullus admittatur; ab im<lb></lb>menſa tamen illa<emph.end type="italics"></emph.end> S<emph type="italics"></emph>iderum diſtantia conſpicuus nihilominùs <lb></lb>appareat, ac tantæ etiam magnitudinis, quanta est tota regio <lb></lb>Planetaria<emph.end type="italics"></emph.end> (dixi, aut quantus magnus orbis) <emph type="italics"></emph>idque ob <lb></lb>lucem eius vegetam, diffuſoſque ipſius radios, quibus oculus <lb></lb>afficiendus eſſet; eo modo, quo flamma candelæ noctu spectata <lb></lb>ignis ingens apparet. </s> <s id="s.002181">Id, inquam, ingenij tui admirabile qui<lb></lb>dem, ſed incredibile figmentum eſt, quod exemplo candelæ <lb></lb>comodè non probas.<emph.end type="italics"></emph.end></s> <s id="s.002182"> An porrò, cùm iſtud videatur <emph type="italics"></emph>figmen<lb></lb>tum incredibile;<emph.end type="italics"></emph.end> patietur tua bonitas, vt proferam aliud, <lb></lb>quod cum iſto connexum ſit, quodque, quantum con<lb></lb>iector, ſit incredibilius appariturum? </s> <s id="s.002183">Quantum, pu<lb></lb>tas, ſi omnes diſci mille & viginti duarum Stellarum <lb></lb>vulgò agnitarum ſimùl iungerentur, aggregarenturve <lb></lb>in vnum; quantum putas, inquam, totalem diſcum <lb></lb>conficerent? </s> <s id="s.002184">An-non ingentem? </s> <s id="s.002185">At ego opinor vix <lb></lb>tantum futurum, quantus apparet vel vnicus vnius <lb></lb>Stellæ, quæ ſit magnitudinis quartæ, diſcus. </s> <s id="s.002186">Quale<lb></lb>nam, inquies, iſtud eſt, non figmentum iam, ſed planè <lb></lb>delirium! Qualecumque ſit; accipe id tamen. </s> <s id="s.002187">Cùm <lb></lb>aliquando nocte ſerena iter facerem, ſubiit animum <lb></lb>cogitatio, quî fieri poſſet, vt neque Lunâ, neque ma<lb></lb>iuſculis Planetis collucentibus, ſingula tamen circum-<pb pagenum="294" xlink:href="028/01/334.jpg"></pb>ſtantia adeò clarè diſpicerem, parúmque abeſſet, quin <lb></lb>legere paginam poſſem. </s> <s id="s.002188">Tum verò è veſtigio ſubiit <lb></lb>me ingens admiratio, quî fieret, vt potiùs, ſi Stel<lb></lb>larum diſci tanti eſſent, quanti eſſe perhiberentur, non <lb></lb>longè magis collucerent, nempe longè ampliùs, quàm <lb></lb>Luna: quippe cùm & Stellarum lux ſit lunari longè <lb></lb>viuidior; & diſci earum compoſiti viderentur mihi <lb></lb>confecturi diſcum lunari maiorem. </s> <s id="s.002189">Siquidem quam<lb></lb>vis diſculi earum forent toto cælo diſperſi; videban<lb></lb>tur tamen tantumdem præſtare poſſe luminis reſpectu <lb></lb>partis eiuſdem Terræ ab hemiſphærio toto reſpectæ; <lb></lb>ſicut reſpectu eiuſdem aulæ tantumdem præſtant (aut <lb></lb>etiam ampliùs) candelæ variæ, ex quibus poſteà fax <lb></lb>quædam ingens componitur. </s> <s id="s.002190">Rursùs itaque è veſti<lb></lb>gio ſubiit mentem recordatio obſeruatæ exilitatis tam <lb></lb>Planetarum, quàm Fixarum; ac cenſui ad illam refe<lb></lb>rendum eſſe, quòd Stellarum lux adeò debilis ad nos <lb></lb>perueniret. </s> <s id="s.002191">Quam-primùm diuerti ad hoſpitium, in <lb></lb>quo fortè fortuna cælorum ſehema reperi, continens <lb></lb>inter cætera, quot Stellæ eſſent primæ magnitudinis, <lb></lb>quot ſecundæ, quot tertiæ, & ad vſque ſextam, ad <lb></lb>quam retuli obſcuriores alias, quibus mille viginti <lb></lb>duarum abſoluitur numerus; continere non potui me, <lb></lb>quin ad calculos rem totam vocarem. </s> </p> <p type="main"> <s id="s.002192">XXXV. </s> <s id="s.002193">Ac primùm quidem ſupponendo eſſe Stel<lb></lb>larum diametros, cuiuſmodi vulgò apparent, explorare <lb></lb>lubuit quem diſcum earum omnium diſci coniuncti <lb></lb>crearent. </s> <s id="s.002194">Attribuendo igitur Stellis primæ magnitu<lb></lb>dinis, dum profunda nocte ſpectantur, diametrum <lb></lb>minutorum trium; Stellis ſecundæ diametrum duo-<pb pagenum="295" xlink:href="028/01/335.jpg"></pb>rum cum ſemiſſe: tertiæ duorum: quartæ vnius, ac ſe<lb></lb>miſſis: quintæ vnius: ſextæ ſemiſſis: deduxi exinde ſin<lb></lb>gularum diſculos: eoſque in vnum componendo, com<lb></lb>parandóque ad diſcum Solis, cuius diameter, vt iam <lb></lb>dictum eſt, ſit dimidii gradus, ſiue minutorum triginta, <lb></lb>collegi debere ex iis diſcum fieri, cuius diameter ſit <lb></lb>minutorum quinquaginta, & vnius; quique ſit proinde <lb></lb>ad diſcum Solarem, vt ad nouem, viginti ſex, ſeu pro<lb></lb>ximè triplus. </s> <s id="s.002195">Et quia tamen harum Stellarum, non<lb></lb>niſi dimidium horizonti conſpicuum eſt; facile fuit <lb></lb>agnoſcere diſcum ex iſto dimidio eſſe Solaris ſeſqui<lb></lb>alterum, ſiue exæquari Soli ſemel cum ſemiſſe. </s> <s id="s.002196">Quare <lb></lb>& deprehendi me non abſque ratione admiratum fuiſ<lb></lb>ſe, quamobrem, ſi diſci Stellarum tanti ſint, quanti & <lb></lb>apparent, & eſſe dicuntur; Terra ex iis noctu non ma<lb></lb>gis reſplendeat. </s> <s id="s.002197">Subinde verò, quia tantas non eſſe dia<lb></lb>metros Stellarum perſpectum <expan abbr="habebã">habebam</expan> (quippe minores <lb></lb>etiam ducebam, quàm Galileus cenſuerit, quòd in no<lb></lb>cturnis tenebris pupillæ <expan abbr="dilatationẽ">dilatationem</expan> maiorem <expan abbr="cẽſerem">cenſerem</expan>, <lb></lb>quàm ſuppoſitum ab eo videretur) ideò explorare rem <lb></lb>placuit iuxta veriores diametros, quales videlicet appa<lb></lb>rent reſectâ non tam teleſcopio, quàm funiculo, aut ba<lb></lb>cillo tereti interpoſito, circumradiatione. </s> <s id="s.002198">Et ne videret <lb></lb>tamen mihi potiùs, quàm Galileo fidere: ſupponere <lb></lb>volui, quod is obſeruanit, Stellam magnitudinis pri<lb></lb>mæ eſſe diametri ſecundorum quinque, ſiue tertiorum <lb></lb>trecentorum; & conſequenter habere Stellam ſecundæ <lb></lb>magnitudinis diametrum tertiorum ducentorum quin<lb></lb>quaginta: tertiæ ducentorum: quartæ centum quin<lb></lb>quaginta: quintæ centum: ſextæ quinquaginta. </s> <s id="s.002199">Hoc <pb pagenum="296" xlink:href="028/01/336.jpg"></pb>autem poſito, Stellarum mille viginti duarum diſculos <lb></lb>in diſcum vnum compoſui, ipſumque ad diſcum Solis <lb></lb>comparando, comperi non eſſe, niſi illius particulam <lb></lb><expan abbr="quadringẽteſimam">quadringenteſimam</expan> trigeſimam vnam: ac proinde, dia<lb></lb>metro Solis exſiſtente minutorum triginta, ratiocina<lb></lb>tus ſum diametrum diſci ex omnibus Stellis compoſiti, <lb></lb>non eſſe maiorem vno minuto cum ſemiſſe; quantæ <lb></lb>vulgò eſſe apparet Stella magnitudinis quartæ. </s> <s id="s.002200">Quod <lb></lb>ſi dimidium detrahas, ob Stellas, quæ ſub horizonte: <lb></lb>ſequitur diſcum ex reſiduis, non fore maiorem vna <lb></lb>octingenteſima ſexageſima tertia diſci Solaris particu<lb></lb>la: ac eius diametrum futuram vnius proximè minuti <lb></lb>dumtaxat: hoc eſt, quantæ eſſe apparet Stella magni<lb></lb>tudinis quintæ. </s> <s id="s.002201">Quare & ex hoc deſii admirari, quam<lb></lb>obrem lux omnium Stellarum ſupra horizontem lu<lb></lb>centium tam parum Terræ faciem illuſtrent; tuque ex<lb></lb>inde animaduertis quo progreſſu peruenerim ad in<lb></lb>credibile fig mentum. </s> </p> <p type="main"> <s id="s.002202">XXXVI. </s> <s id="s.002203">At verò, inquies, ecquiſ-nam capiat non <lb></lb>eſſe ingens totum maius tantulâ ſui particulâ: ſeu tan<lb></lb>tam, quæ apparet lucem in omnibus Stellis ſupra hori<lb></lb>zontem coruſcantibus, in exiguum adeò ſpatium con<lb></lb>trahi, vt non ſit eo maius, quod à ſtellula magnitudinis <lb></lb>quintæ occupatur? </s> <s id="s.002204">Sed nimirùm conſidera; ſi foret <lb></lb>Stella, quæ reuerâ eſſet diametro minuti vnius, fore, vt <lb></lb>lux eius ſpectata intra nocturnas tenebras appareret <lb></lb>oculo incompa biliter maior. </s> <s id="s.002205">Si enim quæ Stella eſt <lb></lb>diametro ſolùm vnius ſecundi cum beſſe: apparet ni<lb></lb>hilominùs diametro vnius minuti: ſanè, ſi proportio<lb></lb>nem admittas, ea apparitura erit diametro minutorum <pb pagenum="297" xlink:href="028/01/337.jpg"></pb>triginta ſex; atque adeò diſco penè ſeſqui-altero ad <lb></lb>Solem: quemadmodum, ſi aliunde fuerit vera diame<lb></lb>ter minutorum duorum, apparitura erit diſco ad ſola<lb></lb>rem pluſquàm triplo: ſi trium, penè tredecuplo. </s> <s id="s.002206">At <lb></lb>quorsùm Stella, ſi vel tanta appareret, quantus eſt Sol, <lb></lb>non tantum, quantum Sol luceret? </s> <s id="s.002207">Reſpondeo; quia <lb></lb>illa lucis amplificatio reſpectu oculi ſolùm ficret, & <lb></lb>non reſpectu veri diſci, rerumve ab eo illuminatarum: <lb></lb>eo modo, quo flamma candelæ, dum ſeipſa maior per <lb></lb>noctem videtur, non proptereà tamen aut ſe maior eſt, <lb></lb>aut magis illuſtrat. </s> <s id="s.002208">Ex quo fit proinde, vt quemadmo<lb></lb>dum flamma candelæ quantò apparet maior, tantò <lb></lb>etiam adſpectus eius confuſior, & obſcurior euadit, ne<lb></lb>que eminùs tantum illuminat, quantum ſi apparens <lb></lb>eius amplitudo tam ſplendida foret, quàm flammula <lb></lb>cominùs viſa: ita ſtellaris ille diſcus quantò appare<lb></lb>ret maior, tantò foret etiam confuſior, obſcuriorque <lb></lb>appariturus; atque idcircò Terræ faciem non perinde <lb></lb>illuſtraturus, ac ſi eminùs eo fulgore, quo & cominùs <lb></lb>appareret: ac proinde tantam dumtaxat in Terram <lb></lb>lucem effunderet, quantam iam effun dunt Stellæ ſepa<lb></lb>ratæ. </s> <s id="s.002209">Cæterùm huic diſci amplificationi fidem facit <lb></lb>vel ipſa Venus, quæ viſa interdiù non maior, quàm <lb></lb>Stella quædam per-exigua, apparet tamen deinde in<lb></lb>tra tenebras diametri quintuplò, ac idcircò diſci vige<lb></lb>cuplò quintuplò maioris. </s> <s id="s.002210">Sed & fidem facit vberem <lb></lb>Mercurius, qui viſus eſſe circa maximas elongationes <lb></lb>minutorum trium, deprehenſus tamen eſt à me, cùm <lb></lb>eſſet proximè perigeius, ac in ipſo diſco Solari (vbi <lb></lb>imponere ſua luce non potuit, ſpectata nempe eius <pb pagenum="298" xlink:href="028/01/338.jpg"></pb>vmbra, comparatáque cum circulo ſpeciem Solis citra <lb></lb>teleſcopium in obſcura ſcena referente) deprehenſus, <lb></lb>inquam, eſt triente minuti non maior; adeò vt cùm <lb></lb>eſſe apparet minutorum trium (quo tempore deberet <lb></lb>etiam aliquantò minor videri, quàm dum præcisè in <lb></lb>perigeio verſatur) diſcus eius octogies ſemel, quàm <lb></lb>reuerâ ſit, amplificarior appareat. </s> <s id="s.002211">Fidem quoque <expan abbr="faciũt">faciunt</expan> <lb></lb>Iupiter, & Mars: qui cùm Acronychi illam Veneris <lb></lb><expan abbr="magnitudinẽ">magnitudinem</expan> æmulentur, obſeruati ſunt tamen à me ex <lb></lb>comparatione cum diametro Lunæ vix diametro eſſe <lb></lb>vnius minuti. </s> <s id="s.002212">At inſtabis, hoc <expan abbr="decrementũ">decrementum</expan> <expan abbr="per-exiguũ">per-exiguum</expan> <lb></lb>omninò eſſe reſpectu immanis illius, quod affingitur <lb></lb>ſtellis Fixis. </s> <s id="s.002213">Sed nempeid fieri videtur, quòd lux Pla<lb></lb>netarum mutuatitia ſit, & ab illorum ſuperficiebus de<lb></lb>biliſſima reddita, ob diſtractos Solareis radios (quippe <lb></lb>quatenus ſuperficies inæquabiliſſimæ ſunt, & facies <lb></lb>habent aliò, alióque variè diuergenteis, vt de Luna <lb></lb>quidem manifeſtum eſt, & coniicere de cæteris licet) <lb></lb>at ex oppoſito lux Fixarum videtur natiua, ac propria, <lb></lb>& Solaris inſtar, vt puriſſima, ita viuidiſſima; adeò vt ab <lb></lb>exiguo diſco (longè minore ſcilicet, quàm ſit Planeta<lb></lb>ris) procedens, tum fortiùs moueat oculum, tum cir<lb></lb>cumradiationem vberiorem pariat: tum apparentem <lb></lb>proptereà diſcum amplificatiorem exhibeat. </s> <s id="s.002214">Argu<lb></lb>mento autem eſſe poteſt, primùm continens illa ſcin<lb></lb>tillatio, qua radii Fixarum excurrunt, & quam Ariſto<lb></lb>teles quoque ex motu non Stellæ, ſed oculi eſſe conten<lb></lb>dit: ac deinde experimentum factum teleſcopio, quod <lb></lb>cætera cùm amplificet, Stellas tamen Fixas imminuit, <lb></lb>ob ipſam nempe reſectionem radiorum excurrentium: <pb pagenum="299" xlink:href="028/01/339.jpg"></pb>denique gradus exilitatis, quo propter hanc imminu<lb></lb>tionem Stellæ Fixæ exhibentur incomparabiliter mi<lb></lb>nores Planetis, habita ratione diſcorum apparentium: <lb></lb>ſcilicet, quòd ipſarum radii & excurrant longè vberiùs, <lb></lb>& longè proinde ampliùs circum-radient. </s> </p> <p type="main"> <s id="s.002215">XXXVII. </s> <s id="s.002216">Atque hæc quidem omnia eo ſolùm fine <lb></lb>commemoro, vt innuam, Qua ratione Sol è Fixis ſpe<lb></lb>ctatus, tametſi ſuo diſco exilis, appariturus tamen foret <lb></lb>luce adeò circum-diffuſa, vt, tanquam ſpatia in<lb></lb>gentia complens, apparenter exæquaretur, aut to<lb></lb>ti, aut ſaltem inſigni portioni regionis Planetariæ, <lb></lb>cuiuſmodi eſt Orbis magnus, de quo fuit potiſſimùm <lb></lb>quæſtio. </s> <s id="s.002217">Et fac certè Solem non apparere maiorem, <lb></lb>quàm magnitudinis ſextæ Stellam: quia tunc vera dia<lb></lb>meter eius erit vno ſecundo minor, hoc eſt, ex iam di<lb></lb>ctis, tertiorum quinquaginta; orbis magni diameter <lb></lb>continebit ducenties, aut plus paulò certè, quinqua<lb></lb>ginta tertia (quippe totidem vicibus diametrum Solis <lb></lb>continet) efficietur, ſi ea reducas, vt Orbis magni dia<lb></lb>meter apparitura non ſit maior duobus minutis cum <lb></lb>dodrante, ſeu quàm appareat diameter Stellæ magni<lb></lb>tudinis primæ, aut ſecundæ. </s> <s id="s.002218">Quòd ſi Stellarum dia<lb></lb>metri ſint adhûc minores, quàm Galileus cenſuit, ob <lb></lb>inſinuatam antè cauſſam; & magnitudinis ſextæ Stella <lb></lb>non ſit maior diametro, quàm ſextans ſecundi, ſiue <lb></lb>decem tertia; efficietur eadem ratione, vt Orbis magni <lb></lb>diameter apparitura maior non ſit, quàm appareat dia<lb></lb>meter Stellæ magnitudinis ſextæ. </s> <s id="s.002219">Dices, profectò, <lb></lb>figmentum meum tantò magis increſcere, quantò hac <lb></lb>ratione veræ Stellarum diametri magis imminuuntur. <pb pagenum="300" xlink:href="028/01/340.jpg"></pb>Quî enim fieri poteſt, inquies, vt Stella viſibilis fiat ſub <lb></lb>tantulo angulo, qui maior non ſit ſextante vnius ſe<lb></lb>cundi? </s> <s id="s.002220">Sed vide, quæſo, vt non dicam eſſe eam Stellam <lb></lb>viſibilem ſub huiuſmodi angulo: verùm eam Stellam, <lb></lb>quæ viſibilis eſt ſub angulo ſemiſſis minuti, ſiue trigin<lb></lb>ta <expan abbr="ſecundorũ">ſecundorum</expan>, comprehenſa nempe circumradiatione, <lb></lb>non habere <expan abbr="diametrũ">diametrum</expan> veram, circum-radiationeve ſpo<lb></lb>liatam, ſextante ſecundi maiorem. </s> <s id="s.002221">At hoc ipſum quo<lb></lb>que eſt, inquies, quod omni figmento eſt maius, tam <lb></lb>minutulum punctulum ita poſſe circum-radiare, vt fu<lb></lb>turum aliàs planè inconſpicuum, effici viſibile poſſit. <lb></lb></s> <s id="s.002222">Verùm, quid res ſit, vt percipi poſſit: eſto candelæ flam<lb></lb>mula craſſitudinis ſemidigitalis; ea poterit nocte ob<lb></lb>ſcura ſpectari à tribus paſſuum millibus. </s> <s id="s.002223">Fac verò an<lb></lb>gulum, ſub quo viſibilis efficietur, non eſſe dimidio <lb></lb>minuti maiorem, ita vt flammula appareat, quaſi ma<lb></lb>gnitudinis ſextæ Stella; quæſo te, quantus angulus erit, <lb></lb>qui ab ipſius flammulæ vera diametro ſubtendetur? <lb></lb></s> <s id="s.002224">Profecto vix maior ſemiſſe ſecundi. </s> <s id="s.002225">Cùm in tribus <lb></lb>enim paſſuum millibus ſint trecenta, & ſexaginta ſe<lb></lb>midigitorum millia: ſi, vt hic numerus ſe habet ad <lb></lb>vnum, ita centum millia, ſeu radium feceris ad aliud; <lb></lb>procreabuntur ſolum quinque decima octaua vnius, <lb></lb>ſeu tangens ſeptuncis vnius ſecundi. </s> <s id="s.002226">Et minüe, ſi ve<lb></lb>lis, diſtantiam ad ipſum vſque dimidium, vt ſi putes <lb></lb>eam flammulam videri dumtaxat à ſeſqui milliari; tum <lb></lb>vera eius diameter angulum ſubtendet ſecundo vix <lb></lb>vno maiorem. </s> <s id="s.002227">An credidiſſes punctulum, quale eſt <lb></lb>vnicum ſecundum, aut ſecundi etiam dimidium, ita <lb></lb>poſſe circum radiare, vt videri ſub angulo triginta <pb pagenum="301" xlink:href="028/01/341.jpg"></pb>ſecundorum poſſet? </s> <s id="s.002228">Iam igitur, cùm æquum ſit re<lb></lb>putare lucem Stellarum ſuperare ſua puritate, ſuóque <lb></lb>ſplendore lucem flammulæ, fuligini craſſæ, fumove <lb></lb>commiſtæ, multis vicibus: poſtulo dumtaxat, vt ſuperet <lb></lb>ter, ſi putes flammulam videri, quæ ſit angulo dimidij <lb></lb>ſecundi; aut ſexies, ſi putes eam ſolùm, quæ ſit ſecundi <lb></lb>integri. </s> <s id="s.002229">Nempe exinde efficietur, vt Stella viſibilis ſit, <lb></lb>quæ vera diametro ſubtendet non angulum modò <lb></lb>vnius ſecundi, ſed angulum etiam ſextantis ſecundi. </s> <s id="s.002230">Iſta <lb></lb>vberius non proſequor; ne cauſſeris non poſſe me meis <lb></lb>figmentis facere finem. </s> <s id="s.002231">Adnoto tamen; cùm ex iam <lb></lb>dictis, Stella magnitudinis ſextæ eſſe non debeat Sole <lb></lb>maior; ecquid-nam dicturus de figmento fuiſſes, ſi <lb></lb>propoſuiſſem cum Landſbergio Stellam magnitudinis <lb></lb>ſextæ eſſe vicies quinquies ipſo Orbe magno maiorem? <lb></lb></s> <s id="s.002232">Et ille tamen viſus eſt ſibi ex certis principiis demon<lb></lb>ſtraſſe omnia: quanquam illud ſaltem non cauit, quod <lb></lb>circum-radiatio imponit circa magnitudinem veram: <lb></lb>quodque proinde diameter vna Stellæ magnitudinis <lb></lb>ſextæ eſt longè minor quinque ſecundis, ſecùs quàm <lb></lb>ab illo ſuppoſitmu eſt. </s> </p> <p type="main"> <s id="s.002233"><emph type="center"></emph><emph type="italics"></emph>Hûc accommodari non potuiſſe cauſſam quæ redditur vulgò, <lb></lb>quare flammæ noctu maiores appareant.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002234">XXXVIII. </s> <s id="s.002235">Ad te vt redeam, poſtquàm præmiſiſti, <lb></lb><emph type="italics"></emph>non probare me commodè figmentum exemplo candelæ,<emph.end type="italics"></emph.end> ſic <lb></lb>pergis, <emph type="italics"></emph>Quæcùmque enim cauſſa ſit, cur flamma candelæ, ad <lb></lb>certam præſertim diſtantiam, ſemper auctior appareat: ſatis <lb></lb>certè tibi conſtat Lunam, ac Martem, ipſumque etiam Solem,<emph.end type="italics"></emph.end><pb pagenum="302" xlink:href="028/01/342.jpg"></pb><emph type="italics"></emph>cùm propiùs ad nos accedunt, non minores videri, ſed maiores: <lb></lb>vbi verò longiùs à Terra remouentur, non maiores conspici, <lb></lb>ſed apparere minores. </s> <s id="s.002236">Vnde ergo, quæſo te, colligis<emph.end type="italics"></emph.end> S<emph type="italics"></emph>olem ex <lb></lb>immenſa Siderum diſtantia conspectum non modò maiorem <lb></lb>videndum, quàm nobis vicinioribus appareat, ſed tantæ etiam <lb></lb>magnitudinis, vt regionem quoque Planetariam totam, atque <lb></lb>integram æquare videretur.<emph.end type="italics"></emph.end></s> <s id="s.002237"> Sed nimirùm, optime Vir, <lb></lb>cùm ipſe cauſſam reticeas, cur candelæ flamma appa<lb></lb>reat per noctem adauctior; quòd ſagacitas illa tua, quan<lb></lb>tum coniicere par eſt, difficultatem prouiderit, quæ ex<lb></lb>citari in vulgarem cauſſæ explicationem poteſt; non <lb></lb>ea mihi tamen fuit prætermittenda, quæ eſt probabi<lb></lb>liſſima viſa, vt præoccupando declarare poſſem, quod <lb></lb>iam rogas me, vnde-nam putà colligam, Solem è Fixis <lb></lb>conſpectum poſſe apparere æqualem regioni Planeta<lb></lb>riæ, ſicque maiorem, quàm heinc videri. </s> <s id="s.002238">Siquidem <lb></lb>conatus idem explicare ex cauſſa vulgò reddita, viſus <lb></lb>mihi ipſi ridiculus ſum ob illius inanitatem. </s> <s id="s.002239">Ecce <lb></lb>enim dicere ſolent, <emph type="italics"></emph>aërem proximè circumſtantem eâ vehe<lb></lb>mentiâ illuſtrari ob halituoſas quaſdam parteis è flamma con<lb></lb>tinuò diffugienteis, vt computetur in eandem flammam, parti<lb></lb>bus videlicet illis factis adſpectabilibus exſiſtenti oculo procùl, <lb></lb>& in minore lumine; cùm è vicino, ab eximio flammæ ſplen<lb></lb>dore occultentur.<emph.end type="italics"></emph.end></s> <s id="s.002240"> At quomodo probare valeant eſſe has <lb></lb>halituoſas parteis illuſtrationis eius capaceis, vt totum <lb></lb>aëreum ſpatium, in quo ſunt, efficiant non minùs illu<lb></lb>ſtre, quàm flammam? </s> <s id="s.002241">Nam non negabunt profectò <lb></lb>flammam eſſe centies, aut etiam millies ſplendidiorem <lb></lb>eo ſpatio, quod ipſam circumſtat ad vnum, aut ad plu<lb></lb>reis palmos. </s> <s id="s.002242">Itaque dum procùl ſpectamus candelam, <pb pagenum="303" xlink:href="028/01/343.jpg"></pb>oporteret medium flammæ apparentis, ſiue quod ex <lb></lb>vera eſt flamma ſplendidius eſſe, niſi millecuplò, at cen<lb></lb>tuplò ſaltem (imò, vt ampliùs largiar, ſaltem decuplò) <lb></lb>quàm amplitudinem circumſtantem: & nihilominùs <lb></lb>tota illa flamma apparet eſſe vniuſmodi, ſeu æquè lu<lb></lb>cida tam ſub medium, quàm ad extrema. </s> <s id="s.002243">Quod aiunt <lb></lb>verò <emph type="italics"></emph>illas parteis fieri è longinquo adfpectabileis in minore <lb></lb>lumine:<emph.end type="italics"></emph.end> nonne & ipſa vera flamma in eodem lumine <lb></lb>videtur? </s> <s id="s.002244">Quid ergo eſt cauſæ, cur luce illarum par<lb></lb>tiùm cominùs exili (imò ad ipſum ſenſum nulla) acci<lb></lb>piente <expan abbr="incrementũ">incrementum</expan>, ipſa quoque lux veræ <expan abbr="flãmæ">flammæ</expan> eadem <lb></lb>proportione <expan abbr="nõ">non</expan> accipiat: ſicque <expan abbr="idẽ">idem</expan> ſemper diſcriminis <lb></lb>fit, ſiue ex <expan abbr="lõginquo">longinquo</expan> ſiue ex propinquo videatur? </s> <s id="s.002245">Quod <lb></lb>autem dicunt, <emph type="italics"></emph>illas è vicino ab eximio flammæ splendore oc<lb></lb>cultari:<emph.end type="italics"></emph.end> quî poteſt quæſo intelligi, vt occultentur ab eo <lb></lb>ſplendore, à quo habent, vt ſplendeant, adſpectabileſ<lb></lb>ve, vt contendunt, fiant. </s> <s id="s.002246">Nam quod vulgò quidem <lb></lb>etiam dicunt, <emph type="italics"></emph>lumen maius occultare, obfuſcare, aut obli<lb></lb>terare minus:<emph.end type="italics"></emph.end> id minùs verè dicitur; fit enim potiùs ex <lb></lb>vtróque compoſito lumen intenſius: tametſi, quæ viſus <lb></lb>hebetudo eſt, diſcerni gradus non valeant, qui ab vtró<lb></lb>que conferuntur. </s> <s id="s.002247">Quòd inſuper <emph type="italics"></emph>lucidum minus cum <lb></lb>maiore comparatum viſibile fiat non propè, ſed procùl:<emph.end type="italics"></emph.end> id <lb></lb>probabile fieret, ſi ſpectato procul minore lucido, ma<lb></lb>ius abeſſet, nec iuxtim foret; at ſi vtrumque ſimùl vi<lb></lb>deatur, neceſſe eſt, vt proportione debilitationis ob <lb></lb>ſpatium ſeruata, tam procùl, quàm propè videri non <lb></lb>poſſit. </s> <s id="s.002248">Et quid heic contingat, experiri vis? </s> <s id="s.002249">Iube oc<lb></lb>cultari præcisè flammulam candelæ non circumſtans <lb></lb>ſpatium: deberes adhûc videre ſpatium perinde prorsùs <pb pagenum="304" xlink:href="028/01/344.jpg"></pb>lucidum, intercepto ſolùm quaſi hiatulo, propter flam<lb></lb>mam deficientem: at procùl ſanè erit, vt videas. </s> <s id="s.002250">Iube <lb></lb>aliunde occultari totum circumſtans ſpatium, adeò vt <lb></lb>ſola flammula foramine facto libera videatur; deberet <lb></lb>tum ea flammula non maior videri, ſed minor, pro ra<lb></lb>tione diſtantiæ: & tamen procùl aberit, vt contractio<lb></lb>rem videas, & non maiorem potiùs, ac perinde prorsùs, <lb></lb>vt libero ſpatio. </s> <s id="s.002251">Niſi verò iſtud non arguit aliam fuiſſe <lb></lb><foreign lang="grc">τ<gap></gap> φαινομθυ<gap></gap></foreign>, quàm halituoſas illas parteis in ſpa<lb></lb>tium circumſtans diffugienteis, requirendam cauſ<lb></lb>ſam? </s> </p> <p type="main"> <s id="s.002252">XXXIX. </s> <s id="s.002253">Itaque aliam requiſiui (affectionem <lb></lb>putà in pupilla, acretina) quæ vt effectui in candela ap<lb></lb>parenti congrueret, ita lucidis omnibus, quorum ſpe<lb></lb>cies noctu increſcit, accommodari congruè poſſet. </s> <s id="s.002254">Hu<lb></lb>iuſmodi maximè ſunt tam Luna, quàm Stellæ, ſeu <lb></lb>Errantes, ſeu <expan abbr="Inerrãtes">Inerrantes</expan>: nam Lunæ quidem diametrum <lb></lb>non ſemel obſeruauimus octaua propè ſui parte noctu, <lb></lb>quàm interdiù maiorem: Veneris vero diametrum <lb></lb>multis maiorem vicibus; & Iouis conſimiliter (quippe <lb></lb>qui fuerit etiam nobis ſæpenumerò obſeruatus inter<lb></lb>diù) conſtatque vniuersè Stellas cæteras, cùm interdiù <lb></lb>ſint inconſpicuæ, in gruente tamen crepuſculo æger<lb></lb>rimè primùm ob exilitatem videri, ac deinde magis, <lb></lb>magiſque, dum ſenſim grandeſcunt, viſibileis fieri. <lb></lb></s> <s id="s.002255">Quæſo verò iſta-ne valeant ad halituoſas aliquas par<lb></lb>teis, quæ vt à flamma, ſic à Luna, Stelliſque diffugiant, <lb></lb>referri; & non potiùs ad vberiorem tum pupillæ dila<lb></lb>tationem, tum impreſſionem retinæ factam, donec <lb></lb>oculus in tenebris degit? </s> <s id="s.002256">At hæc tamen cauſſa, in-<pb pagenum="305" xlink:href="028/01/345.jpg"></pb>quies, quid ad Solem? </s> <s id="s.002257">Poteſt-ne oculus in Solem reſ<lb></lb>pectans cenſeri eſſe in tenebris? </s> <s id="s.002258">Poteſt-ne Solem noctu <lb></lb>videre? </s> <s id="s.002259">Reſpondeo poſſe haud-dubiè; neque id ha<lb></lb>bendum eſſe Paradoxum; quatenus id fore intelligi<lb></lb>tur, cùm oculus demùm eâ fuerit diftantiâ, è qua Sol <lb></lb>non maior, quàm vna Stellarum appareat, & è qua pro<lb></lb>inde non tenebras magis, quàm Stellarum vna diſcu<lb></lb>tiat, neque oculum magis proinde perſtringat. </s> <s id="s.002260">Ex quo <lb></lb>fit, vt dum ex me quæris, <emph type="italics"></emph>vnde colligam Solem ex immenſa <lb></lb>illa diſtantia non modò viſum iri maiorem, quàm appareat no<lb></lb>bis vicinioribus, ſed etiam tantæ magnitudinis, vt toti regioni <lb></lb>Planetariæ exæquetur?<emph.end type="italics"></emph.end> Rogem te, attendas, cur ex me <lb></lb>id quæras. </s> <s id="s.002261">Nam cùm ego quidem profitear viſum <lb></lb>iri Solem ex illa diſtantia, quaſi vnam aliquam Stel<lb></lb>lam heinc vbi degimus conſpectam; neque dico ſanè, <lb></lb>neque colligo viſum iri nobis maiorem, quàm vici<lb></lb>nioribus iam videatur. </s> <s id="s.002262">Et tametſi dicam viſum iri tan<lb></lb>tum, quantum Orbem magnum, inſignemve portio<lb></lb>nem regionis Planetariæ; cauſſa eſt, quia ex eadem <lb></lb>diſtantia totus Orbis magnus non maiore appareret <lb></lb>amplitudine, quàm heinc appareat vna Stellarum cum <lb></lb>circumfuſis corpuſculo radiis. </s> <s id="s.002263">Tu verò ſic interrogas, <lb></lb>vt ſi cenſerem ex ea diſtantia tum magnum Orbem <lb></lb>appariturum eiuſdem, qua propè amplitudinis; tum <lb></lb>Solem non modò maiorem, quàm heinc conſpiciatur; <lb></lb>ſed etiam quantus Orbis magnus ex Marte, v. g. aut <lb></lb>Ioue conſpiceretur, appariturum. </s> <s id="s.002264">Quòd verò ſic in<lb></lb>terrogas, eo permotus argumento, <emph type="italics"></emph>quòd conſtet Lu<lb></lb>nam, ac Martem, ipſumque etiam Solem quò propiùs acce<lb></lb>dunt ad nos, eò maiores conſpici; quò longiùs abſcedunt,<emph.end type="italics"></emph.end><pb pagenum="306" xlink:href="028/01/346.jpg"></pb><emph type="italics"></emph>minores:<emph.end type="italics"></emph.end> vides rem eſſe incohærentem. </s> <s id="s.002265">Etenim agitur <lb></lb>hoc loco de incremento in lucidis facto non ratione <lb></lb>diſtantiæ, ſed ratione obſcuritatis. </s> <s id="s.002266">Neque enim re<lb></lb>quiritur, cur Mars v. g. dum eſt perigeius, terriſve pro<lb></lb>pinquior, appareat maior, quàm apogeius, ſeu à terris <lb></lb>remotior, & in eodem quidem tenebrarum gradu: ſed <lb></lb>cur in eadem propinquitate, aut in eadem remotione <lb></lb>maior, & minor appareat, prout in variis gradibus ob<lb></lb>ſcuritatis conſpicitur; vt claro adhûc crepuſculo, & no<lb></lb>cte iam facta profunda. </s> <s id="s.002267">Quare & ad hoc non ad il<lb></lb>lud ſimilitudo candelæ facit; & ad hoc, non verò ad <lb></lb>illud, quam cauſſam eſſe prætermittendam cenſuiſti, <lb></lb>referenda fuit. </s> </p> <p type="main"> <s id="s.002268"><emph type="center"></emph><emph type="italics"></emph>Qua mente, & quatenus ex motu Terræ<emph.end type="italics"></emph.end> Æ<emph type="italics"></emph>ſtus maris dedu<lb></lb>ctus: &, Poſſe exinde explicari varietates, quæ tam per<emph.end type="italics"></emph.end><lb></lb>Æ<emph type="italics"></emph>quinoctia, & Solstitia; quàm per Plenilunia, <lb></lb>& Nouilunia contingunt.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002269">XL. </s> <s id="s.002270">Verba tua deinde ſunt, <emph type="italics"></emph>Dicis, atque audacter <lb></lb>affirmas<emph.end type="italics"></emph.end> G<emph type="italics"></emph>alileum ex aßignatis Telluris motibus ita Maris <lb></lb>æſtum expoſuiſſe, vt videatur denique cauſſam eius germa<lb></lb>nam adinueniſſe.<emph.end type="italics"></emph.end></s> <s id="s.002271"> Quàm bene eſt verò, quod verbo <emph type="italics"></emph>vi<lb></lb>deatur<emph.end type="italics"></emph.end> temperaui ſententiam; ne dicere poſſes me id <lb></lb>non tantum <emph type="italics"></emph>audacter,<emph.end type="italics"></emph.end> verùm <emph type="italics"></emph>impudenter<emph.end type="italics"></emph.end> quoque affir<lb></lb>mare! Certè, religioſiſſime Vir, ſi me bene noſti, lon<lb></lb>giſſimè abſum, vt in hiſce rebus, aut ſimilibus quid<lb></lb>piam aſſeueranter dicam; tantum à me abeſt, vt faciam <lb></lb><emph type="italics"></emph>audacter.<emph.end type="italics"></emph.end></s> <s id="s.002272"> Nam & tametſi conſuetudo loquendi non <lb></lb>ſemper patiatur, vt caueam, ne aſſerere videar aliquid <pb pagenum="307" xlink:href="028/01/347.jpg"></pb>(quod ne Socrates quidem ſe cauere profeſſus eſt, <lb></lb><foreign lang="grc"><gap></gap>ωὸ σ<gap></gap>ηθ<gap></gap>ας, καὶ αἰεπισημσσ<gap></gap>γς γ̓να<gap></gap>κασμένος</foreign>) <lb></lb>id tamen ſemper teſtatum volo, quæcumque mea <lb></lb>phraſis ſit, eam mihi inſidere mentem, vt nihil planè <lb></lb>tanquam verum, & indubitatum affirmem, ſiue pluſ<lb></lb>quàm probabile, veriſimileve profitear. </s> <s id="s.002273">Quantò verò <lb></lb>magis hoc loco id volui; vbi ſententiam non tam pro<lb></lb>priam, quàm alienam expoſui! Heinc & quæ dicere <lb></lb>iam pergo, non vt propugnans ſententiam, quæ mihi <lb></lb>rata fixa ſit: ſed tanquam tentans quid iuxta ipſam ſit <lb></lb>vero ſimile, inſinuo: & dum tu ſubdis, <emph type="italics"></emph>neſcire te, an ex <lb></lb>tarditate ingenij tui, an aliunde accidat, vt longè aliter, quàm <lb></lb>ego, hactenus hac in re ſenſeris:<emph.end type="italics"></emph.end> id ſic accipio, quaſi velis <lb></lb>non me ſentire ſecus, quàm te, quod ad rem ipſam at<lb></lb>tinet; ſed quod ad ea, quæ opinioni de motu Terræ <lb></lb>ſunt conſentanea. </s> <s id="s.002274">Non eſt profectò interim, cur vl<lb></lb>lam in te ſuſpiceris tarditatem ingenij: ego illam in <lb></lb>me recipio, qui agnoſco me non potuiſſe ex tot opi<lb></lb>nionibus aliis, quæ hac de re circumferuntur, aliquam <lb></lb>deprehendere, quæ non videretur, quàm iſta nugacior. <lb></lb></s> <s id="s.002275">Gratum feciſſes, ſi inſinuaſſes ecquæ-nam tibi proba<lb></lb>tior foret: ſpes enim fuiſſet quidpiam tua dignum ſo<lb></lb>lertia cognoſcendi. </s> <s id="s.002276">Nam quod ais quidem G<emph type="italics"></emph>alileum <lb></lb>cogi in ſocietatem cauſſæ Lunam adſciſcere,<emph.end type="italics"></emph.end> non auſim ita <lb></lb>interpretari, quaſi tu proptereà totum hunc effectum, <lb></lb>aut quæ ſunt certè <foreign lang="grc">συμω<gap></gap>ώμα<gap></gap></foreign> illius præcipua, referas <lb></lb>in Lunam. </s> <s id="s.002277">Vtcumque ſit, id me permouit, Tum, <lb></lb>quòd viſum fuerit admirabile, duplicem eſſe ſingulis <lb></lb>diebus a quæ affluxum, & refluxum, vt duplex eſt ſin<lb></lb>gulis diebus in motu Telluris inæqualitas (nempe <pb pagenum="308" xlink:href="028/01/348.jpg"></pb>tranſeunte eadem parte ſemel quidem ex ſtatu æqua<lb></lb>bili in celeritatem, ſemel ex eodem in tarditatem, prout <lb></lb>in ea motus diurnus, & annuus ſemel conſpirant, ſemel <lb></lb>abnuunt). Tum quòd aliunde viſum fuerit non poſſe <lb></lb>aquam ob fluiditatem, & in cauitate Terræ continen<lb></lb>tiam, non ſic fluere, & refluere, ſi contingeret ipſam <lb></lb>Terram tanquam vas moueri, & inæqualiter moueri: <lb></lb>imò & non poſſe iteratò poſteriore dici parte non ef<lb></lb>fluere, ac refluere proprio pondere; ſi ſemel priore ef<lb></lb>fluxerit, & refluxerit vi increſcentis celeritatis. </s> <s id="s.002278">Licet <lb></lb>quippe omnium deinde huius motus circumſtantia<lb></lb>rum non videretur perinde eſſe, aut fieri cauſſa explo<lb></lb>rata: non ideò tamen viſum eſt generalem cauſſam eſſe <lb></lb>reiiciendam; ſed quicquid eſſet difficultatis referen<lb></lb>dum eſſe ad difficultatem perueftigationis; & dum ſpes <lb></lb>eſſet, vt ſingula diſquirerentur ſcrupuloſiùs, ac inueni<lb></lb>rentur fœliciùs; eſſe videri magni ducendum, quòd <lb></lb>ſecta eſſet veluti glacies, quam deterere ſolum ſuper<lb></lb>eſſet. </s> <s id="s.002279">Ac ſi fuiſſet quidem aliqua opinio, quæ cauſ<lb></lb>ſam pari neceſſitate cum effectu ſuo coniunctam mon<lb></lb>ſtraſſet, illi primas potiùs tribuendas cenſuiſſem; at, <lb></lb>quæ mea fuit tarditas, talem eſſe nullam perſpexi. </s> </p> <p type="main"> <s id="s.002280">XLI. </s> <s id="s.002281">Succedunt hæc verba, <emph type="italics"></emph>Imprimis enim ignorare <lb></lb>te non arbitror, etiam ex illis motibus cauſſam ſufficientem <lb></lb>non reddi, cur circa<emph.end type="italics"></emph.end> Æ<emph type="italics"></emph>quinoctia æſtus fiant adeò magni præ <lb></lb>cæteris; cùm illis temporibus vix inæqualitas vlla in Telluris <lb></lb>motu appareat; & quæ minima in punctis<emph.end type="italics"></emph.end> Æ<emph type="italics"></emph>quinoctialibus <lb></lb>notatur, non ſubitò, aut vna tantum die exoritur, ſed paulla<lb></lb>tim, diuturnóque tempore accreſcit: cùm æſtus illi tamen non <lb></lb>ita ſenſim, & ſucceßiuè vſque ad aliquem maximum accreſ-<emph.end type="italics"></emph.end><pb pagenum="309" xlink:href="028/01/349.jpg"></pb><emph type="italics"></emph>cant, parique deinde ſucceßione paullatim decreſcant; nec <lb></lb>maiores item eo tempore æſtus fiant, quo Tellus in punctis<emph.end type="italics"></emph.end><lb></lb>Æ<emph type="italics"></emph>quinoctialibus conſtituta, maiorem illam inæqualitatem <lb></lb>patitur: ſed in plenilunio ſolùm proximè inſequente.<emph.end type="italics"></emph.end></s> <s id="s.002282"> Et <lb></lb>fuiſti tu ſanè arbitratu tuo in meam ignorantiam in<lb></lb>dulgens; qui etiam ignoro, quæ tu heic aſſumis. </s> <s id="s.002283">Nam <lb></lb>primùm quidem, <emph type="italics"></emph>non eſſe quoddam paullatim factum in<lb></lb>crementum; ſed repentè maximos æstus in Plenilunio<emph.end type="italics"></emph.end> Æ<emph type="italics"></emph>qui<lb></lb>noctium conſequente contingere,<emph.end type="italics"></emph.end> hoc eſt, quod neque <lb></lb>obſeruaui, neque ab alio quoquam accepi: cùm potiùs, <lb></lb>vt æſtus ſpectati per quadranteis menſis, minimi circa <lb></lb>quadraturas, maximi circa ſyzygias, ſenſim per inter<lb></lb>ceptos dies, & maximi ex minimis, & minimi ex ma<lb></lb>ximis euadunt; ita ſi ſpectentur per quadranteis anni, <lb></lb>audierim ſemper minimos fieri circa tempora inter <lb></lb>cardines tempeſtatum media; maximos circa cardines <lb></lb>(ac præſertim Æquinoctialeis) per tempora autem in<lb></lb>tercepta maximos ſenſim ex minimis, minimos ex ma<lb></lb>ximis fieri: quantumcumque per aliquos dies abſque <lb></lb>apparente incremento, tam ſub quadraturas, & ſyzy<lb></lb>gias, quàm ſub Æquinoctia, Solſtitiáque eſſe videan<lb></lb>tur. </s> <s id="s.002284">Deinde, <emph type="italics"></emph>eſſe maximos æſtus quaſi alligatos Plenilunio <lb></lb>proximè, primúmve post Æquinoctium contingenti,<emph.end type="italics"></emph.end> hoc eſt <lb></lb>mihi ſeu iuxta propriam, ſeu iuxta alienam <expan abbr="experien-tiã">experien<lb></lb>tiam</expan> nouum; cùm conſtare potiùs videatur idem Noui<lb></lb>lunio, quod & Plenilunio competere iuris; & neque <lb></lb>facto paulò ante Æquinoctium Plenilunio, exſpecte<lb></lb>tur ferè poſt menſem Plenilunium conſequens, vt ma<lb></lb>ximi in eo ſint æſtus: neque non ſint æſtus maiores <lb></lb>Plenilunio, Nouilunióque ante <expan abbr="Æquinoctiũ">Æquinoctium</expan> proximè <pb pagenum="310" xlink:href="028/01/350.jpg"></pb>contingente, quàm contingente procùl poſt ipſum. <lb></lb></s> <s id="s.002285">Quòd <emph type="italics"></emph>tales porrò æstus non contingant exſistente Terra in <lb></lb>ipſis æquinoctialibus punctis,<emph.end type="italics"></emph.end> ideò eſt, quia cauſſa, quæ <lb></lb>varietatem in ipſis creat, neque ſola eſt, neque per dies <lb></lb>aliquot variatur ſenſibiliter: ſed ſuperuenit illa cauſſa <lb></lb>alia, varietatis ſcilicet menſtruæ, quæ, quòd in Plenilu<lb></lb>niis, Nouiluniiſque potentiſſima ſit: ideo illi coniuncta <lb></lb>æſtus maximè ſenſibileis creat. </s> <s id="s.002286">Quòd verò, <emph type="italics"></emph>cauſſa ſuf<lb></lb>ficiens exinde reddatur, cur tunc æstus fiant adeò magni præ <lb></lb>cæteris:<emph.end type="italics"></emph.end> ex eo eſt, quòd vtraque cauſſa tunc temporis <lb></lb>vigeat: cùm aliàs in ipſo Æquinoctio (niſi caſu quo<lb></lb>dam) vigor Plenilunij, Nouiluniive non ſit; aut in Ple<lb></lb>nilunio, Nouiluniove, vigor Æquinoctii. </s> <s id="s.002287">Quòd dicis <lb></lb>cauſſam minimam, quæ ad vſque Æquinoctium paul<lb></lb>latim increſcat, ab illo paullatim decreſcat: ſatis eſt ta<lb></lb>men, vt coniuncta cauſſæ ſolitæ, hoc eſt menſtruæ, <lb></lb>effectum intendat. </s> <s id="s.002288">Congruum certè eſt, vt ſi vniuersè <lb></lb>motus diurnus æſtum creat, ob inæqualitatem ſibi ex <lb></lb>motu annuo ſuperuenientem; <expan abbr="alteratũ">alteratum</expan> creet, ob ſuper<lb></lb>uenientem ſpecialem inæqualitatem ex ductu per Zo<lb></lb>diacum: quatenus vbi ille eſt maximè obliquus, nempe <lb></lb>ad ipſum Æquatorem, motus diurnus, qui eſt ſemper <lb></lb>directè ad ortum, maximè reprimitur, hoc eſt cohibe<lb></lb>tur, ne verſus ortum protendatur. </s> </p> <p type="main"> <s id="s.002289">XLII. Pergis, <emph type="italics"></emph>Ex imaginariis illis motibus cauſſam non <lb></lb>reddi, cur in Pleniluniis Mare vehementiùs æſtuet, quàm tem<lb></lb>poribus reliquis.<emph.end type="italics"></emph.end></s> <s id="s.002290"> Verùm imprimis nihil eſt neceſſe <lb></lb>cauſſam reddere illius effectus, quem verum eſſe mini<lb></lb>mè conſtet: ſanè enim quæcumque ſit aliquorum <lb></lb>opinio, obſeruata tamen non deſunt, quæ probent <pb pagenum="311" xlink:href="028/01/351.jpg"></pb><emph type="italics"></emph>non modò in India,<emph.end type="italics"></emph.end> de qua ſtatim loqueris, <emph type="italics"></emph>ſed in ipſa <expan abbr="quoq;">quoque</expan> <lb></lb>Europa<emph.end type="italics"></emph.end> eſſe Noui-lunareis æſtus Pleni-lunarib<emph type="sup"></emph>9<emph.end type="sup"></emph.end> ęſtuoſio<lb></lb>res. </s> <s id="s.002291">Deinde, vbi fuerit conceſſum, æſtuare vehementiùs <lb></lb>Mare Pleniluniorum temporibus; cauſſa ex illis moti<lb></lb>bus reddi poterit non prorsùs incongrua. </s> <s id="s.002292">Siquidem <lb></lb>vtcúmque huiuſmodi motus imaginarii ſint; ſi veri <lb></lb>tamen ſupponantur, declarari poteſt ex illis, cur in <lb></lb>Pleniluniis inæqualitas ſenſibilior, fiat, quàm in No<lb></lb>uiluniis. </s> <s id="s.002293">Cùm enim Luna ſupponatur, quaſi Terræ pe<lb></lb>diſſequa, & dum circumducitur illi motu menſtruo, <lb></lb>ipſum interim motu annuo indiuiduè concomitans; <lb></lb>efficitur, vt quaſi totale cum ipſa mobile habeatur, <lb></lb>quod vna, atque eadem cauſſa motu annuo circum<lb></lb>ueheat: eo modo, quo Lunulas quatuor ipſius Iouis <lb></lb>pediſſequas habere licet quaſi vnum cumipſo Ioue mo<lb></lb>bile, prout dum illi ſpecialibus circumducuntur perio<lb></lb>dis, cùm illo tamen indiuiduè mouentur per Zodia<lb></lb>cum, & ab eadem cauſſa motu illo duodecennali cir<lb></lb>cumferuntur. </s> <s id="s.002294">Quare & ſupponendo Solem eſſe ge<lb></lb>neralem motorem, qui ſibi ipſi circumductus eo mo<lb></lb>tu, quem Maculæ monſtrant, Planetas omneis radiis <lb></lb>quaſi magneticis circumrapiat, & propiores quidem <lb></lb>velociùs, remotiores ſegniùs abſoluere circuitus cogat: <lb></lb>neceſſe erit, vt Luna exſiſtente oppoſita, ſicque di<lb></lb>ſtantiore à Sole, quàm Terra, mobile ex vtraque factum <lb></lb>abripiatur radio, qui ſit, <expan abbr="quã">quam</expan> Luna exſiſtente coniuncta, <lb></lb>Solique propiore, prolixior. </s> <s id="s.002295">Et quia <expan abbr="tũc">tunc</expan> Luna ſe habet, <lb></lb>quaſi plumbum penſile, quod vibratur ſegniùs, ſi ap<lb></lb>pendatur ipſi plumbulum, propter quod euadat ſenſi<lb></lb>le prolixius: idcircò oportet tunc Terra ſe motu annuo <pb pagenum="312" xlink:href="028/01/352.jpg"></pb>quaſi vibratam, moueri ſimiliter ſegniùs. </s> <s id="s.002296">Ac ſi, cùm <lb></lb>Luna quidem eſt Soli coniuncta, Terra eódem redu<lb></lb>ceretur, & radius vtramque abripiens efficeretur tan<lb></lb>tumdem breuior, neceſſe foretipſam tantumdem cir<lb></lb>citer moueri celeriùs; eo modo quò plumbum, dum fi<lb></lb>lum contrahitur, breuiuſque fit: at quia Terra ſemper <lb></lb>conſiſtente in eadem diſtantia, Luna citrò acta, ipſam <lb></lb>nihilo retrahit, neque radium breuiorem facit: eapro<lb></lb>pter non videtur motus tam accelerari ſenſibiliter, do<lb></lb>nec Luna coniungitur, quàm retardatur, dum opponi<lb></lb>tur Soli. </s> <s id="s.002297">Quia verò intereà Luna ſeſe habet, quaſi <lb></lb>plumbulum illigatum filo, à quo plumbum dependet; <lb></lb>eamobrem, vt tunc plumbulum facit vibrationes ali<lb></lb>quantulùm celeriores, quatenus & ipſum dependens à <lb></lb>filo breuiore appetit vibrari celeriùs, ſicque eò facit, vt <lb></lb>plumbum referatur ocyus; ita poteſt Luna præſtare, vt <lb></lb>Terra non-nihil acceleret curſum: quanquam hære<lb></lb>ſcendum in iſtis non eſt: ſed adnotandum potiùs, <lb></lb>quod ais G<emph type="italics"></emph>alileum cogi adſciſcere in ſocietatem Lunam,<emph.end type="italics"></emph.end><lb></lb>non eò ſpectare debere, quaſi ille adciſcat vllum è cæ<lb></lb>lo inſluxum, ſiue occultam qualitatem, vti vulgò <lb></lb>faciunt, qui ad Lunam confugiunt; ſed quaſi aſſumpta <lb></lb>vniuersè motus Terræ inæqualitate, pro generali æſtus <lb></lb>cauſſa, cohærenter faciat, dum ex motu Terræ, prout <lb></lb>eſt cum motu Lunæ indiuiduus, ſpecialem cauſſam re<lb></lb>petit ſpecialis inæqualitatis. </s> </p> <pb pagenum="313" xlink:href="028/01/353.jpg"></pb> <p type="main"> <s id="s.002298"><emph type="center"></emph><emph type="italics"></emph>Poſſe & varietates alias ad locorum ſitus: & acceſſus re<lb></lb>tardationem, quæ dietim fit, ad motum Lunæ menſtruum, <lb></lb>(quatenus eſt idem cum diurno Telluris) referri.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002299">XLIII. </s> <s id="s.002300">Pergis adhûc; <emph type="italics"></emph>Neque profectò ſtatim acquieſ<lb></lb>cit animus, cùm ad ea, quæ aliter explicari nequeunt, vno <lb></lb>verbo reſpondetur, hæc, & ſimilia ex particularibus locorum <lb></lb>affectionibus oriri.<emph.end type="italics"></emph.end></s> <s id="s.002301"> Porrò iſtud non reſpondetur, quod <lb></lb>ſpectat ad ea generaliora accidentia, quæ ſunt omnium <lb></lb>Marium, ac ſpeciatim Indiæ, Europæque communia: <lb></lb>cuiuſmodi eſt vehementia æſtus, tam in Solſtitiis, & <lb></lb>Æquinoctiis, quàm in Nouiluniis, Pleniluniiſque in<lb></lb>tenſior: ſed quod ſpectat ad accidentia, quæ locorum <lb></lb>Terræ particularium propria cùm ſint; quidni cauſſas <lb></lb>habere proprias ex particularibus locis poſſint? </s> <s id="s.002302">Vt <lb></lb>enim dum nauicula aquæ ſemi-plena ſupra lacum pla<lb></lb>cidum inæquabiliter mouetur, ipſa aqua fluit, ac re<lb></lb>fluit vniformiter, pro vniformitate inæqualitatis, ſi <lb></lb>nauicula quidem in interiore circumductu vniformi<lb></lb>ter deflexa, politaque exſtiterit; Pari modo, ſi totum <lb></lb>Mare vna quadam Terræ cauitate ab occaſu in ortum <lb></lb>producta, æquabiliterque deflexa contineretur, illius <lb></lb>fluxus, atque refluxus vniformiter fieret, quod attinet <lb></lb>quidem ad illa generaliora accidentia. </s> <s id="s.002303">At quia, ſi na<lb></lb>uicula deflexionem lateralem habeat variis protubera<lb></lb>tionibus, depreſſionibuſque difformem; & ex fundo <lb></lb>ad ſuperficiem, ſiue etiam altiùs, aſſurgant varij ſtipi<lb></lb>tes tenuïores, craſſiores, & ambitum quoque variè re<lb></lb>cedentem, extuberantemque habentes; obſeruabis <lb></lb>aquam, dum fluet, ac refluet, admirabileis pati varieta-<pb pagenum="314" xlink:href="028/01/354.jpg"></pb>tes, tam ad ipſa latera, quàm ad ſtipites interceptos; ne<lb></lb>que aliò commodiùs has varietates referes, quàm ad <lb></lb>varietatèm, qua aqua tam ad latera, quàm ad medium <lb></lb>variè allapſa interpedictur: Pari ratione, quoniam <lb></lb>Terra capacitatem illam ſuam variantiſſima varietate, <lb></lb>ob promontoria, ſinus, freta, iſthmos, inſulas, cherſo<lb></lb>neſos, & alia id genus paſſim occurrentia affectam <lb></lb>ſortitur: nihil ſanè dici videtur commodiùs, quàm mi<lb></lb>rabilem illam varietatem, quæ in quotidiano fluxu, & <lb></lb>refluxu ad particulareis oras obſeruatur, referendam <lb></lb>eſſe ad varietatem ipſarum orarum, ſiue littorum, tam <lb></lb>in continentibus, quàm in Inſulis occurrentium. </s> <s id="s.002304">Ni<lb></lb>mirùm prout littora properantem aquam in ortum, <lb></lb>occaſumve, ſiue è regione, ſiue obliquè excipiunt; & <lb></lb>ſiue directò accedentem, ſiue deflexione à littoribus <lb></lb>antecedentibus affectam; & ſui ſitu ſiue directo, ſiue <lb></lb>flexuoſo, ſinubuſque, ac promontoriis magnis, paruis, <lb></lb>raris, crebris, regularibus, irregularibus interrupto; & <lb></lb>tractu ſiue longo, ſiue breui, ſiue ſingulari, ſiue repeti<lb></lb>to; & fundo ſiue plano, ſiue prono, ſiue alueoſo, ſiue <lb></lb>ſcopuloſo, &c. </s> <s id="s.002305">neceſſe eſt aquam diuerſiſſimos acci<lb></lb>pere motus. </s> <s id="s.002306">Quod certè in fluminum ripis obſeruare <lb></lb>in promptu eſt, heic nempe aquam leniter, illeic rapidè <lb></lb>fluere; heic abire rectà, illeic torqueri in vortices; heic <lb></lb>vndulare, illeic ſpumare; & id genus ſimilia; idem pro<lb></lb>portione ſeruata conſentaneum eſt fieri, vti & reuerâ <lb></lb>obſeruatur fieri, in ipſis littoribus Maris. </s> </p> <p type="main"> <s id="s.002307">XLIIII. </s> <s id="s.002308">Pergis denique; <emph type="italics"></emph>Sed vide etiam, ſi placet, <lb></lb>an ipſemet quotidianus maris æſtus duplex, ſatu ex quotidia<lb></lb>na Telluris motione explicetur. </s> <s id="s.002309">Nam cùm Tellus viginti<emph.end type="italics"></emph.end><pb pagenum="315" xlink:href="028/01/355.jpg"></pb><emph type="italics"></emph>quatuor horarum spatio proximè reuolui ſupponatur; neceſſe <lb></lb>eſt, vt quæ partes hoc momento celeriùs, tardiuſve moueri inci<lb></lb>piunt, iterùm poſt horas viginti quatuor ſimili celeritate, aut <lb></lb>tarditate moueantur, vt manifeſtum eſt. </s> <s id="s.002310">Si hæc igitur di<lb></lb>uerſitas motus cauſſa eſſet quotidianorum æſtuum, deberent <lb></lb>præcisè poſt horas viginti quatuor recurrere, cùm vnâ ferè <lb></lb>horâ quotidie tardiùs recurrant. </s> <s id="s.002311">Quò fit, vt ſingulis men<lb></lb>ſibus tunc mare maximè quieſcat, cùm habita ratione motus <lb></lb>Telluris ſummè feruere deberet; & contrà, tum vehementer <lb></lb>ferueat, cùm illud paccatè quieſcere oporteret.<emph.end type="italics"></emph.end></s> <s id="s.002312"> Verùm vno <lb></lb>verbo inſinuatum eſt in Epiſtolis naturam aquæ flui<lb></lb>dam obſtare, ne aqua circumferatur tam facilè, ac reli<lb></lb>qui globi compacta natura. </s> <s id="s.002313">Quippe cùm motus re<lb></lb>liqui globi non exquiſitè obfecundet (ſcilicet, ſi ob<lb></lb>ſecundaret, nullus æſtus exſiſteret) ideò neceſſe eſt <lb></lb>eius motum fieri non-nihil retardatiorem, & menſurâ <lb></lb>quidem tarditatis acceptâ ex portione motus Lunæ <lb></lb>menſtrui addita diurno Telluris, quatenus ab ipſo de<lb></lb>pendet, imò idem reipsâ eſt. </s> <s id="s.002314">Quia enim, vt Sol ſibi ipſi <lb></lb>intra dies proximè viginti ſeptem circumductus Ter<lb></lb>ram vnà circumvehit, ſed ſegniùs tamen inſequentem, <lb></lb>& non-niſiintra annum abſoluentem circuitum, pro<lb></lb>pter diffuſiores, paucioreſque radios, qui cùm in Ve<lb></lb>nere, & Mercurio confertiores ſint, circuitus in ipſis <lb></lb>faciunt celeriores: ſic Terra ſibi circumducta intra ho<lb></lb>ras viginti quatuor, Lunam circum ſe abripit, ſed ſe<lb></lb>gniùs tamen obſequentem, & non-niſi intra menſem, <lb></lb>abſoluentem circuitum, qui abſolueretur haud-dubiè <lb></lb>celeriùs, ſi confertiores radios exceptura, circum ferretur <lb></lb>propiùs: Ideò, vt motus Terræ annuus eſt veluti com-<pb pagenum="316" xlink:href="028/01/356.jpg"></pb>poſitus ex pluribus portionibus plurium reuolutionum <lb></lb>Solis, poteſtque adeò non alius ab ipſo Solis motu <lb></lb>cenſeri: ſic motus Lunæ menſtruus contextus intelli<lb></lb>gitur ex pluribus portionibus reuolutionum diurna<lb></lb>rum Telluris: poteſtque adeò idem eſſe cum diurno <lb></lb>motu intelligi. </s> <s id="s.002315">Heinc autem fit, vt quia Terra, ac Lu<lb></lb>na pro vno totali mobili habentur (quod paulò antè <lb></lb>dictum eſt) idcircò alteratio, quæ motui annuo adue<lb></lb>nit ex intermiſtione diurni, non ſit præcisè accipienda <lb></lb>quatenus diurnus ſolius Terræ eſt proprius, ſed quate<lb></lb>nus eſt ipſi cum Luna communis. </s> <s id="s.002316">Et quia propter <lb></lb>hanc communionem efficitur, vt motus diurnus non <lb></lb>ſit integer accipiendus, niſi poſtquàm non modò Ter<lb></lb>ra ex meridiano quopiam digreſſa ad eundem meridia<lb></lb>num redit, ſed poſtquàm ipſa etiam Luna meridianum <lb></lb>eundem repetit: inde eſt, cur Luna illum dietim repe<lb></lb>tente, vnâ prope hora, ſeu quatuor quintis horæ tar<lb></lb>diùs; cur, inquam, alteratio illa, atque adeò æſtus con<lb></lb>tingat dietim tanto tempore: quatuor ſcilicet horæ <lb></lb>quintis tardiùs. </s> <s id="s.002317">Prætereo autem, cùm Luna ad datum <lb></lb>meridianum eádem diei hora, niſi poſt menſem non <lb></lb>redeat, excurſus tamen, & recurſus maris eadem hora <lb></lb>poſt dies quindecim inſtaurari; quòd ij geminentur <lb></lb>in dies ſingulos, ac eadem hora eueniant, non <lb></lb>modò cùm Luna eſt nobis in mendiano ſupra horizon<lb></lb>tem, ſed etiam cùm infià, in meridiano Antipodum. <lb></lb></s> <s id="s.002318">Adeò proinde, vt dici poſſit, quemadmodum Luna <lb></lb>intra menſem apparet reuolui circa Terram vna vice <lb></lb>minùs, quàm Sol; ita Mare affluere, & refluere duabus <lb></lb>vicibus minùs, quàm afflueret, ac reflueret, abſque illa <pb pagenum="317" xlink:href="028/01/357.jpg"></pb>retar datione. </s> <s id="s.002319">Prætereo quoque hanc retardationem, <lb></lb>quatenus ex aquæ ſluore, lentoréque ſimùl dependet, <lb></lb>confirmari poſſe videri ex conſimili retardatione aëris, <lb></lb>de qua in Epiſtolis dictum; cùm ventus illo continuus, <lb></lb>& æquabilis ab ortu in occaſum, quem experiuntur <lb></lb>nautæ in alto, non videatur poſſe explicari <expan abbr="cõmodiùs">commodiùs</expan> <lb></lb>quàm ex retardatione aëris, ob fluiditatem ſuam inca<lb></lb>pacis, qui conſequatur præciſe motum Telluris conti<lb></lb>nuum, & æquabilem verſus ortum. </s> <s id="s.002320">Quo modo quo<lb></lb>que dici poſſet reciprocatione cariturum Mare, futu<lb></lb>rum que motum eius in occaſum continuum, & æqua<lb></lb>bilem, ſi Terræ quaſi nucleus eſſet exquiſitè rotundus, <lb></lb>maréque eſſet illi circumfuſum, neque incurreret in <lb></lb>littora, verſus quæ elatum, effluere, reflueréque cogere<lb></lb>tur. </s> <s id="s.002321">Prætereò & id genus alia; cùm his denique ſit fa<lb></lb>ciendus modus. </s> </p> <p type="main"> <s id="s.002322">XLV. </s> <s id="s.002323">Itaque Finem iam tandem facio; agnoſcens <lb></lb>me reuerâ eum, quem debui, modum non tenuiſſe. </s> <s id="s.002324">Et <lb></lb>conſtitueram quidem initio non-niſi pauca reſponde<lb></lb>re ad ſingula præclaræ tuæ Diſquiſitionis capita: ſed <lb></lb>neſcio, quo pacto abreptus, ita ſenſim ab inſtituto, in<lb></lb>cœptoque receſſerim, vt euaſerim denique in hanc, <lb></lb>quam vides, prolixitatem. </s> <s id="s.002325">Fortè, me quoque peccaſſe <lb></lb>putes aduerſus leges vrbanitatis, cùm ab vſque literis <lb></lb>datis nihil Reſponſi habueris, niſi poſt exactum iam <lb></lb>menſem: at partim cauſſam initio dixi, partim ecce <lb></lb>propalàm facio, cùm tibi iſtam quaternionum, folio<lb></lb>rumque ſeriem obiicio. </s> <s id="s.002326">Quicquid id ſit rei, Tu ſic ac<lb></lb>cipe, quaſi voluerim ſpontaneam <expan abbr="illã">illam</expan> affectus tui teſta<lb></lb>tionem teſtatione conſimili, & cum fœnore quo-<pb pagenum="318" xlink:href="028/01/358.jpg"></pb>dam, compenſare. </s> <s id="s.002327">Quod dignaris mihi ad calcem ſin<lb></lb>gularium ingenij tui parturitionum copiam offerre, id <lb></lb>nimiæ bonitatis eſt, quam vt experiri non mereor, ſic <lb></lb>ſollicitare non auſim. </s> <s id="s.002328">Operam tamen daturus ſum, <lb></lb>vt itinere iſtâc inſtituto, cùm Deo bene propitio in <lb></lb>Prouinciam breui regrediar, tum coràm agam quas de<lb></lb>beo gratias, tum coràm fiam particeps, quorum eſſe <lb></lb>videbitur communicatio non importuna. </s> <s id="s.002329">Si quid <lb></lb>ſupererit, cùm deinceps in Patria conquieſcere dabitur, <lb></lb>beabis me, quicquid me voles. </s> <s id="s.002330">Tu intereà rogatus <lb></lb>perge, quod vltrò cœpiſti; hoc eſt, ama me, & bene, <lb></lb>imò optimè Vale. </s> <s id="s.002331">Pariſiis, VI. Eid. Decembris. <lb></lb></s> <s id="s.002332">M. DC. XLII. </s> </p> <p type="main"> <s id="s.002333"><emph type="center"></emph>FINIS.<emph.end type="center"></emph.end><lb></lb><figure id="id.028.01.358.1.jpg" xlink:href="028/01/358/1.jpg"></figure><pb pagenum="319" xlink:href="028/01/359.jpg"></pb><gap desc="hr tag"></gap></s> </p> <p type="main"> <s id="s.002334"><emph type="center"></emph>VIRO Nobiliſſimo PHILIBERTO DE LA MARE <lb></lb>Senatori Diuionenſi, <emph type="italics"></emph>P.GASSENDVS S.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002335">SErò Reſpondeo; nam eccemenſis, ex quo tuæ li<lb></lb>teræ datæ: ſed in cauſſa fuit tum inualetudo, tum <lb></lb>prolixa Reſponſio, cui hoc adtextum ſchediolum ha<lb></lb>bes. </s> <s id="s.002336">Eadem vtor excuſatione erga religioſiſſimum, ac <lb></lb>eruditiſſimum Patrem. </s> <s id="s.002337">Tu, tametſi ille, qua eſt boni<lb></lb>tate, admiſſurus ſponte eam eſt; intercede nihilominùs, <lb></lb>vt admittat pleniore ſponte. </s> <s id="s.002338">Operam verò imprimis <lb></lb>da, vt qui te authore amare me cœpit, me porrò, te <lb></lb>quoque promotore, amet. </s> <s id="s.002339">Nimirùm tantus ille eſt <lb></lb>vir, vt maximi ducam eius amicitiam, & tibi, cui ipſam <lb></lb>debeo ſolidam, me ſummoperè obſtrictum agnoſcam. <lb></lb></s> <s id="s.002340">Vale. </s> <s id="s.002341">Pariſiis, VI. Eid. Decemb. M. DC. XLII. <lb></lb><gap desc="hr tag"></gap></s> </p> <p type="main"> <s id="s.002342"><emph type="center"></emph><emph type="italics"></emph>SVMMA PRIVILEGII.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.002343">IVxta Priuilegium à Rege Chriſtianiſſimo conceſ<lb></lb>ſum, cautum eſt, ne quistoto Regnoimprimat, alibi<lb></lb>ve impreſſas diuendat PETRI GASSENDI <emph type="italics"></emph>De <lb></lb>Proportione, qua grauia decidentia accelerantur, Epiſtolas <lb></lb>treis,<emph.end type="italics"></emph.end> præter LVD. DE HEVQVEVILLE, Bibliopolam <lb></lb>Pariſienſem, idque in decennium, ſub ſolitis pœnis. <lb></lb></s> <s id="s.002344">Datum Pariſiis 8. April. </s> <s id="s.002345">1642. Signatum CEBERET. </s> </p> <pb pagenum="[320]" xlink:href="028/01/360.jpg"></pb> <p> <s id="s.002346"> [Errata not typed]</s> </p> </chap> </body> <back></back> </text> </archimedes>