Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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quæ 3° inſtanti, & 4° plùs agat
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abbr
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quã
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primo, & ſecundo; </
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<
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id
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N17C40
">igitur eſt peculiaris
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cauſa huius inæqualitatis rationum; </
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<
s
id
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">quòd ſcilicet æqualibus temporibus
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æqualia acquirantur velocitatis momenta; vt ſuprà demonſtrauimus; </
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quippe id præſtari debet in explicandis inæqualitatibus motuum recto
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rum naturalium, quod præſtant Aſtronomi in explicanda inæqualitate
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motuum cæleſtium; qui ſemper æqualitatem aliquam ſupponunt, nec eſt
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quòd hanc ſententiam nonnullis experimentis ictuum quiſquam con
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firmet, in quibus multa fraus ſubeſſe poteſt. </
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</
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<
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<
s
id
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">Tertiò reiicitur illa quoque ſententia, quæ proportionem lineæ ſectæ
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in mediam, & extremam rationem huic lineæ tribuit, quam ferè in his
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numeris vides 1.2.3.5.8, 13. 21. 34. 55. quæ ſub finem etiam longiſſimè
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aberrat, vt videre eſt, quare iiſdem rationibus impugnatur, quibus iam
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aliam impugnauimus. </
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</
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<
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<
s
id
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">Scio eſſe alias multas rationes, quibus aliqui recentiores motus natu
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ralis accelerationem explicare nituntur, ſed iam ſuprà ſatis ſuperque re
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iectæ fuerunt, vel profectò eæ ſunt, quæ ne quidem inter fabuloſa poë
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tarum commenta locum aliquem habere poſſint: </
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>
<
s
id
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">Et verò niſi me ani
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mus fallit in re clariſſima, rationem huius effectus ex communibus
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principiis deductam cum ipſis etiam experimentis conſentire hactenus
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ita demonſtrauimus, vt iam vix vllus dubitationi locus relinquatur; ſed
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interruptam Theorematum ſeriem tandem repetimus. </
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Theorema
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62.
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Si accipiantur ſpatia æqualia primo ſpatio, quod vno inſtanti percurritur,
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inſtantia ſunt inæqualia in motu natur aliter accelerato
<
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type
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; </
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<
s
id
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N17C99
">probatur, quia ſe
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cundum ſpatium æquale primo percurritur motu velociore, quàm pri
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mo, & tertium quam ſecundo: </
s
>
<
s
id
="
N17CA1
">ergo minori tempore per Def.2.l.1. ſed
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primum ſpatium conficitur vno inſtanti; </
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>
<
s
id
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N17CA7
">igitur ſecundum vno inſtanti,
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ſed minore; idem dico de tertio. </
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Theorema
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63.
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In ea proportione decreſcunt hæc instantia,
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vt primum ſit maius ſecundo,
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ſecundum tertio, tertium quarto, quartum quinto, quintum ſexto,
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atque ita deinceps; ita vt ſecundum & tertium ſimul ſumpta, item quar
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tum, quintum, ſextum, ſeptimum, item octauum, nonum, decimum, ſimul
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ſumpta adæquent primum, hoc eſt vt vnum, duo, tria, quatuor, quinque,
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ſex, &c. </
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<
s
id
="
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">faciant ſemper tempora æqualia, quia temporibus æqualibus æ
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qualia acquiruntur velocitatis momenta? </
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>
<
s
id
="
N17CD5
">igitur ſi primo inſtanti per
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curritur vnum ſpatium; </
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<
s
id
="
N17CDB
">ſecundo tempore æquali percurruntur duo ſpa
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tia æqualia primo, & tertio, tria; atque deinceps; </
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>
<
s
id
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">ſed vt ſuprà dictum eſt
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in reſponſ. ad obiect. primam, vno, &
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inſtanti non poteſt idem cor
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pus percurrere duo ſpatia, ne ſimul eſſet in duobus locis; </
s
>
<
s
id
="
N17CED
">igitur ſingula
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ſpatia reſpondent ſingulis inſtantibus licèt minoribus; </
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>
<
s
id
="
N17CF3
">ſed ſecundo tem
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pore æquali primo inſtanti percurruntur duo ſpatia æqualia primo ſpa
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tio; </
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<
s
id
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">igitur ſecundum, & tertium inſtans debent ſimul ſumpta adæquare </
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