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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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RINOTPTA MATHIEMATICA.
PROPOSITIO LXV. THEOREMA ZXV.
Corpora plura, quorum vires decrescunt in duplicata ratione di-
stantiarum ab eorundem centris, moveri posse inter se in Fl-
lipsibus; e radiis ad umbilicos ductis areas describere tempo
ribus proportionales quam proxime.
In Propositione superiore demonstratus est casus ubi motus plu.
res peraguntur in EIlipsibus accurate. Quo magis recedit L ex vi-
sium a LCsc ibi polica, eo masis corpora pertcurbabunt mutuos
IOcuS; neque heri porest uc corpora, secundum Legem hic Politam
se mucuo crahentia, moreantur in Ellipsibus accurate, nisi servando
certam proportionem dictantiarum ab invicem. In sequentibus au-
tem calibus non mulcum ab tlliplibus crrabitui.
Cas. T. Pone corpora plura minora circa maximum aliquod ad
varias ab eo distancias revolris cendantque ad singula vires abTolu-
ex proportionales iildem corporibus. Ec quoniam omnium com-
mune graritatis centrum (per Legum Corol. quartum) vel quie
Ccit vel moretur unitormiter in directum. Aingamus corpora mi-
nora tam parra ese, ue corpus maximum nunquam distee sensibi-
liter aB ROC CCNETO: e maximum illud vel quieleet vel morebitur
unitormiter in directum, ab (que errore sensibili; minora aurem re-
volventur circa hoc maximum in EIlipsibus, acque radiis ad idem
duetis describent areas temporibus proportionales; nis quatenus
errores inducuntur, vel per errorem maximi a communi illo gravi
caris centro, vel per actiones minorum corporum in se mutuo. Di-
minui autem postune corpora minora ulque donec error ilte ec ac-
tiones mutux Aint daris quibulris minores, atque adeo doncc Orbes
cum Ellipsibus quadrent, ee arexe respondeane cemporibus, ab (que
errore qui non sc minor quoris dato. 9. F. O.
Cas. 2. Finsamus jam Syctema corporum minorum modo jam
descripto circa maximum revolventium, aliudre quodris duorum
circum se mutuo rerolventium corporum Spctema progredi unifor.
micer in directum, ex interea ri corporis alterius lonse maximi et
ad magnam distantiam siti urgeri ad latus. Et quoniam sequales
vires accelerarrices, quibus corpora secundum lincas parallelas ur-
GCNEUE, nOn mutane sicus corporum ad invicem, sed ue Systema
cotum, servaris parcium motibus inter se, Simul ErANSFCTatUE CNCI-
unc: manifestum est quod, ex accractionibus in corpus maximum,
nulla
L. IB
PRL H V S.