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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 276, page id 1041163592:0310
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276
PHILOSOPMLA NATORALIS
DE Moro Mentia in arcu B eNet ad resistentiam in arCU A UE AB ad A A;
tempora in arcubus A ec B Forent aequalia, per Propolitionem su-
periorem. Ideoque relctentia A A in arcu A, vel AB in arcu B,
efticie excessum temporis in arcu a supra tempus in Medio non
relistente; ee relistentia BB efficit excessum temporis in arcu B
supra tempus in Medio non resiltente. Sunt aurem excessus illi
ue vires efficientes AB ec BB quam proxime, id eAt, uE arcuS
A e B. D. F. D.
Corol. I. Flinc ex oscillationum temporibus, in Medio resistente,
in orcubus inaequalibus factarum, cognosci pollunt tempora oscilla-
cionum in ejusdem graricatis specificae Medio non resistente. Nam
differentia temporum erit ad exceltum temporis in arcu minore su-
pra tempus in Medio non resistente, ur differentia arcuum ad ar-
cum minoreim.
Corot. 2. Oseillationes breviores Tunt masis Tochronae, et bre-
rissimae iisdem temporibus peraguntur ac in Medio non resistente,
quam proxime. Earum vero quae in majoribus arcubus AUnE, tem-
ra tunt paulo majora, propterca quod relictentia in descensu cor-
Doris qua tempus producitur, major sc pro ratione longitudinis
in descensu descripeae, quam relistentia in alcensu subsequente qua
tempus contrahitur. Sed ec cempus olcillationum tam brevium
quam longarum nonnihil produci videtur per motum Medii. Nam
corporibus cardescentibus paulo minus resistitur, pro ratione velo-
citatis, ex corporibus acceleratis paulo magis quam iis quae unifor-
miter proorediuntur: id adeo quia Medium, eo quem a corporibus
accepit mocu, in candem plagam persendo, in priore casu magis
asicatur, in posteriore minus; ac proinde magis vel minus cum
corporibus motis conspirat. Pendulis isitur in descensu magis re
liltit, in ascentu minus quam pro ratione relocitatis, de ex utraque
caula tempus producitur.
PROPOSITIO ZZVIII YHEOREMA XXIII.
Si Corpori Funependulo in Cycloide oscillanti resistitur in ratione
momentorum temporis, erit ejus resistentia ad vim gravitatis
ut excessus arcus descensu toto descripti supra arcum ascensu
subsequente descriptum, ad penduli lonsitudinem duplicatam.
Delignet BC arcum descensu descriptum, C’a arcum ascensu de-
scripeum, ec Aa ditterenciam arcuum: ec stantibus quae in PrOPO.
AciOnO
Fouronon