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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PTTILOSOPMLA NATDRALIS
SE CTLC
De Motu Cs Resistentia Corporum Lunependulorum.
PROPOSTTTO ZXIV. TIEOREMA ZIX.
duantitates materiae in corporibus funependulis, quorum centra
oscillationum a centro suspensionis aequaliter distant, sunt in ra-
tione composita ex ratione ponderum e ratione duplicata tem-
porum oscillationum in vacuo.
Nam relocitas, quam data ris in data materia dato tempore ge-
nerare potest, cA uc vis e tempus directe, ec maceria inversc. Quo
major est ris vel majus tempus vel minor materia, eo major gene
rabitur relocicas. Id quod per motus Legem secundam manite-
cum est. Jam rero si Pendula ejusdem sine longicudinis, viresmo-
trices in locis a perpendiculo aequaliter distancibus sunt ut ponde
ra: ideoque A corpora duo oscillando describane arcus aequales, et
arcus illi diridtantur in partes aquales; cum tempora quibus cor-
pora describane sinsulas arcuum partes correspondentes (InE vE
tempora oscillationum tocarum, erune velocitates ad invicem in
correspondentibus olcillationum parcibus, uc vires morrices et tota
Olcillationum cempora directe ec quancitates materix reciproce:
adeoque quantitates macerix uc rires ex olcillationum tempora di-
recte ex velocitates reciproce. Sed relocitates reciproce TUINE uE
tempora, atque adeo tempora directe ee velocirates reciproce sunt
NE QuadEAEA TeMPOTUM, eC PrOpterea Quancitates materiae TUnE UE
vires motrices ex quadrata temporum, id eAt, uc pondera de quadra.
Ea FCMPOTUM. R. L.D.
Corol. T. Ideoque si cempora Cune aequalia, quantitates materix
an lingulis corporibus crune uc pondera.
Corol. 2. Si pondera sunt aequalia, quanCitates matCrIX CrUNE UE
quadrata temporum.
Corol. 3. Si quancitates materix aequantur, pondera crunt reci
DEOCE UE QUAdTATA TeMPOTU.
Corol.
P3E HOZD
PORPORVH