Fabri, Honoré, Tractatus physicus de motu locali, 1646

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1pore cum minore perficitur: ratio eſt: quia, cùm ferè decurrantur
arcus iuxta ſubtenſarum proportionem, certè cùm ſubtenſæ om­
nes æquali tempore decurrantur, idem ferè fit in ipſis arcubus:
dixi
ferè:
nam reuerà minor vibratio citiùs, maior tardiùs perficitur, vt
conſtat experientia: neque deeſt ratio, quam in analyticam remittimus.
4. Non aſcendit funependulum ad eam altitudinem, ex qua priùs
deſcenderat:
clara eſt experientia: neque ratio tantùm petitur ab
aëris reſiſtentia;
tam enim reſiſtit deſcenſui, quàm aſcenſui; ſed ex
eo, quòd ſingulis inſtantibus ſit quædam pugna, inter impetum in­
natum, & alium determinatum ad arcum ſurſum:
quippe impetus
innatus ad totum deſcenſum, ſed nullo modo ad aſcenſum con­
currit:
hinc in maiori vibratione imminuitur motus, & ſpatium in
maiori proportione, quàm in minori;
quia in hac lineæ ſingulæ aſ­
cenſus quaſi totidem inclinatæ ſunt inclinatiores; in illa verò minùs.
5. Hinc diu vibratur funependulum per minores arcus, quippe
facilis eſt aſcenſus per planum proximè ad horizontale accedens:

hinc etiam in funependulo maiori diutiùs durant huiuſmodi vi­
brationes, idque in arcubus paulò maioribus;
quia ſubtenſæ his
arcubus ſunt inclinatiores:
hinc refutabis eos, qui dicunt, vibra­
tiones funependuli in vacuo fore perpetuas:
arcus vibratio­
nis aſcenſus fit motu naturaliter retardato, ſed per imminu­
tiones inæquales; quia pro diuerſa inclinatione plani diuerſimodè
retardatur.
6. Vltimum punctum impetus acquiſitus acquiſitum in deſcenſu,
nullo modo ad deſcenſum concurrit, ſed ad aſcenſum, vnico tan­
tùm inſtanti;
quippe eſt omnium imperfectiſſimum; quod reuerà ſi
eſſet eiuſdem perfectionis cum innato, aſcenſus æqualis eſt deſcen­
ſui:
ſi ſint funependula inæqualia, vibrationes non ſunt æquè diu­
turnæ: ratio eſt:
quia, ſi aſſumantur, v.g. duo quadrantes inæquales,
ſunt ejuſdem inclinationis; igitur minor citiùs percurritur.
7. Porrò tempora vibrationum ſunt in ratione ſubduplicata ar­
cuum ſimilium, vel chordarum ſimilium, vel radiorum;
id eſt, vt
radices ſpatiorum ſimilium:
verbi gratia, ſit quadruplus alterius,
tempus vibrationis maioris eſt duplum temporis vibrationis mino­
ris;
quod ita intelligendum eſt, vt hæc proportio conſideretur in
partibus temporis ſenſibilibus, vt iam dictum eſt de motu natura­
liter accelerato deorſum in perpendiculo, & in planis inclinatis;
nam progreſſio arithmetica; aſſumpta in ſingulis inſtantibus, tran­
ſit in hanc, ſi aſſumantur partes temporis ſenſibiles, quarum ſingu­
læ infinitis ferè conſtent inſtantibus.

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