Fabri, Honoré, Tractatus physicus de motu locali, 1646

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1nem duplicatam temporum, cùm creſcat ſecundùm proportionem
temporum, etïam ex mente Galilei:
creſcit autem velocitas, vt im­
petus;
effectus, ſcilicet, vt cauſa: idem dico de motu, ratione velo­
citatis;
quippe motus ipſe eſt ſua velocitas: at verò ipſa ſpatia,
quæ decurruntur illo motu, ſi conſideretur crementum in inſtan­
tibus, creſcunt iuxta progreſſionem arithmeticam ſimplicem,
id eſt, ſi primo inſtanti, acquiritur vnum ſpatium, ſecundo acquiri­
tur vnum ſpatium, ſecundo acquiruntur duo, tertio 3. quarto 4. at­
que ita deinceps.
4. Hoc autem facilè poteſt demonſtrari: quia, cùm velocitas creſ­
cat iuxta proportionem temporum, ſi primo inſtanti ſit vnus gradus
velocitatis, ſecundo erunt duo, tertio tres, at que ita deinceps:
igitur,
ſi mobile cum vno gradu velocitatis acquirit vnum ſpatium, certè
cum duobus acquiret duo ſpatia, cum tribus tria, atque ita dein­
ceps: debet autem vera progreſſio crementorum aſſumi in ſingulis
inſtantibus, quia reuerà ſingulis inſtantibus phyſicis (nam de iis
loquor) noua fit huius crementi acceſſio.
5. Quia tamen inſtantia non ſunt ſenſibilia, vt Phyſicæ conſu­
latur, quæ res ſenſibiles conſiderat, aſſumi debent partes temporis
ſenſibiles, in quibus reuerâ progreſſio ſpatiorum non eſt arithmeti­
ca ſimplex; ſed tam propè accedit ad hanc numerorum imparium,
1. 3. 5. 7. &c.
quam Galileus excogitauit, vt ſine ſcrupulo hæc aſ­
ſumi poſſit:
hinc ſpatia ſunt ferè vt temporum quadrata: dixi, ferè:
nam eſt paulò minor proportio, cùm tantùm finita ſint inſtantia
phyſica, quæ reuerà ſi infinita eſſent in qualibet temporis ſenſibilis
parte, haud dubiè ſpatia eſſent omninò in ratione duplicata tem­
porum: ſed, quia parum pro nihilo computatur, hanc progreſſio­
nem Galilei deinceps vſurpabimus in Phyſica.
6. Hinc ratio euidens maioris ictus inflicti à corpore graui,