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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 150, page id 1041163592:0184
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150
PETTLOSOPMTTAE NATDRALIS
DF Moro BeHC circum se mutuo Figuras easdem ac prius, de propterea Fixurx
90 Timiles ec xequalc5. Q. F. D.
Corol. 1. FIinc corpora duo Viribus distantix suxe proxortionali-
bus se muruo crahentia, describunt (per PrOV. X,) de circum com
mune graricatis centrum, ec circum le mutuo, FIliples concentri-
ca5: _ vice verla, E cales Figurxe describuntur, sunc Vires distan-
cix proportionales.
Corol. 2. FFcorpora duo Viribus quadrato distantix sux recipro-
ce proportionalibus describunt (per PFOD. XI XIL, XITL) ee circum
commune gravicatis centrum, ex circum se mucuo, Sectiones conicas
umbilicum habentes in centro circum quod Fisurae describuneur. P.F
vice rersa, si tales Figurae describuncur, Vires centripetxe lune qua-
drato distantix reciproce proxortionales.
Corol. 3. Corpora duo quaeris circum gravitatis centrum com-
mune grrancia, radiis de ad centrum illud ec ad se mutuo ductis,
delcribunt areas temporibus proportionales.
PROPOSITIO LIZ TTEOREMA ZXII.
Corporum duorum S  P circa commune gravitatis centrum C
revolventium Tempus periodicum esse ad Tempus periodicum cor-
poris alterutrius P, circa alterum immotum Serrantis es Fien-
ris quae corpora circum se mutuo describunt Ficuram similemes
aequalem describentis, in subduplicata ratione corporis alterius S,
ad summam corporum S + P.
Namque, ex demonstratione superioris Proposicionis, tempora
quibus arcus quivis similes P a de pa delcribuntur, sunt in sub-
duplicata ratione dictantiarum CP ec S F vel sp, hoc cA, in sub-
duplicata ratione corporis s’ad summam corporum S. L P. FF com
ponendo, summae temporum quibus arcus omnes limiles P ) ec p9
describuncur, hoc eA, tempora tota quibus Fisurx torxe similes de-
scribuncur, sunc in eadem subduplicata rationC. R. Fi. D.
lLO.
PORPORVM