Fabri, Honoré
,
Dialogi physici in quibus de motu terrae disputatur
,
1665
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phyſicorum; hîc non diſcutio cauſæ merita, ne ſaltem extra chorum; id
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vnum dumtaxat dico, illam progreſſionem alteri præferendam eſſe, quæ &
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vtrique quantitatis hypotheſi ſatisfacit, & ipſis experimentis non repu
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gnat: quòd autem progreſſio Galileana in hypotheſi finitorum inſtan
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tium non ſubſiſtat, perſpicuè demonſtro; Sit enim motus quiſpiam natu
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ralis, qui duret per 4. inſtantia, in quorum primo, mobile acquirat ſpa
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tium 1. in ſecundo 3. in tertio 5. in quarto 7. cùm velocitas creſcat, vt
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tempus, in ſecundo inſtanti velocitas erit dupla, quomodo igitur acquiri
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tur triplum ſpatium? </
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Auguſtin.
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"> Nihil facilius triangulo Galileano, in quo res iſta clariſſi
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mè demonſtratur: Sit enim triangulum AEI, ſit
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tempus diviſum in 4.partes æquales, & primo tempo
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re AB, ſpatium acquiſitum ſit triangulum ABF, &
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velocitas acquiſita BF, ſecundo tempore erit veloci
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tas acquiſita CG, creſcit enim, vt tempus, & vt AB
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ad BF, ita AC ad CG ; idem dico de quolibet alio
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temporis puncto accepto inter BC ; igitur ſpatium ac
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quiſitum erit trapezium BCGF, triplum trianguli
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ABF, nempe cum velocitate BF æquabili motu, tem
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pore BC, acquireret rectangulum BM, ſed virtute ve
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locitatis acquiſitæ tempore BC æqualis velocitati BF, acquiritur triangu
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lum FMG æquale ABF; igitur ſecundo tempore triplum ſpatium
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prioris. </
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Antim.
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Hæc omittere poteras, quæ iam trita ſunt, nec à me negantur;
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nempe velocitas BF acquiritur ſucceſtivè tempore AB, quod ſi ſuppona
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tur eſſe inſtans phyſicum, accipienda eſt velocitas. </
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">BF tota ſimul, re
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ſpondeo enim toti inſtanti, ac proinde tota ſimul eſt, non verò ſucceſſi
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vè acquiſita, igitur ſpatium debet accipi in rectangulo, non verò in trian
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gulo; v.g. Sit tempus AE 4. inſtantiam, ſit pri
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mus gradus velocitatis AG, & ſpatium acqui
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ſitum rectangulum AV; ſecundo inſtanti ve
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locitas acquiſita erit BH, dupla ſcilicet AG;
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nempe tota prior remanet, & tantumdem ab ea
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dem cauſa, æquali tempore ponitur; igitur ſpa
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tium eſt duplum prioris, ac proinde erit rectan
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gulum CH duplum prioris. </
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Auguſtin.
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<
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"> Duo abſurda ex his mihi deducere videor; primò enim, pri
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mo tempore AB, duplum ſpatium trianguli Galileani aſſumis; nempe re
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ctangulum AV duplum eſt trianguli ABV, cùm tamen æquale primum
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tempus aſſumi debeat, ad perfectam comparationem; ſecundò longè majus
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ſpatium decurritur ſecundùm tuam progreſſionem, quàm ſecundùm Ga
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lileanam, in qua ſpatium decurſum tempore AE continet 16. triangula
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æqualia triangulo ABV, in tua verò continet 10. rectangula æqualia
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AV; igitur 20. triangula æqualia ABV, igitur ſpatium Galileanum erit
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ad tuum vt 16. ad 20. ſeu vt 4. ad 5. igitur majus vna quarta parte, quod </
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