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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 149, page id 1041163592:0183
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11
PRINCEPTA MATEEMATICA.
describit, erie similis ec aequalis Curris quas corpord S, P deseri-
bunc circum se mutuo: proindeque (per Pheor. XX) similis Curris
ST et F EV, quas eadem corpora describune circum commune
Graritatis centrum C: id adco quia proportiones linearum SC, Cs
_ SF vel sp ad invicem daneuF.
Cas. 1. Commune illud graritaris centrum C, per Legum Co-
rollarium quartum, vel quiescit vel morerur uniformiter in direc-
tum. Ponamus primo quod id quielcie, inques et p lOcentur Cor
pora duo, immobile in s, mobile in p, corporibus Se P similia
et aequalia. Dein EaNGANE reCtie P R _E pr CUEVAS PO et p9 in
D _ p, _C prodUCAntUT CD e 59 ad R ec r. FF, ob simil. cudi-
nem Figurarum C P R Q, sprq Crie R _ ad rg uE C P ad 5p, 24-
eoque in data ratione. Proinde si ris qua COrDUS F verTUS COP
puS S, aeque adeo versus centrum intermedium C actrahieur, cNer
ad vim qua corpus p vertus cenerumsactrahitur in eadem illa ra-
tione data; hae vires aequalibus temporibus actraherent TeMmPer COr-
Pora de tangentibus P R, pr ad arcus P Q pq Per incerralla ipsIs
proportionalia  9, rg; adeoque vis posterior cfcerCE UE COrpuS
erraretur in Curva p g2 quae similis cNet CurrX P QV, in qua
vis prior efficit ut corpus P Srretur, de revolutiones iildem tem-
Poribus complerentur. Ac quoniam vires illae non tunt ad invi-
cem in ratione C F ad sp, Scd (ob similicudinem e aequalicatem
corporum Set s, P ec p, ex sequalicarem distantiarum SP, Sp
sibi muruo aequales; corpora aequalibus temporibus aequaliter era-
hentur de tangentibus: ec propterea, ut corpus posterius perahatur
per intervallum majus rg, requiritur tempus majus, idque in sub-
duplicata ratione incerrallorum; propterca quod (per Lemma de-
cimum) spacia, ipso mocus initio deseripta, (une in duplicata racione
temporum. Ponatur igitur relocitas corporis p esse ad velocita-
tem corporis P in lubduplicata ratione distantix sp ad distanciam
C P, eout temporibus quae sinc in eadem subduplicaca ratione de-
TeribAnEUE aECUS P9, F 9, qui lunc in ratione integrZ: PE COrPOTA
E, p viribus aequalibus semper actracta describenE CIrCUM CCNEra
quiescentia C e s Figuras similes P QV, pgV, quarum polterior
p92 similis eA ec aequalis Figurx quam corpus P circum corpuS
mobile Sdelcribit. 8. F. D.
Cas. 2. Ponamus jam quod commune graviearis cenerum, una
cum spatio in quo corpora moveneur inter Cc, progreditur unifor-
miter in directum; ec, per Legum Corollarium sextum, motus
omnes in hoc spatio peragentur ur prius, adeoque corpora deleri-
beme
L
PArMOS
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