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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 133, page id 1041163592:0167
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PRINCIPTA MATTEMATIC A.
33
bi centripeta TV qua corpus Q in spatio liberO CIFCA CeNTTUM LIBEK
datum C revolvitur, datuT PEr PFOD. ZLLI, tum PrajcctOria P _ R PRTMOS.
quam corpus describit, cum locus D in quo corpus ad datum quod.
vis tempus vertabitur, cum denique relocitas corporis in loco illo
Q ec contra. 8. L.. I.
PROPOSITIO ZEVII. THEOREMA XV.
Posito quod vis centripeta proportionalis sit distantiae corporis a
centro; corpora omnia in planis quibuscunque revolventia de
Scribent Ellipses, S revolutiones Temporibus aequalibus perarent:
quaeque moventur in lineis rectis, ultro citroque discurrendo;
sinsulas eundi es redeundi periodos iisdem Temporibus absol
vent.
NTam, Stantibus quae
in superiore Provolicio-
ne, vis SV qua cOrDuS
Din plano quovis FOR
revolvens trahitur ver-
Tus centrum S est ut di-
Rantia SQ; acque adeo
ob proportionales SV
e Sd, TV et CQ, vis
FV
qua corpus crahi-
tur versus punctum C
in Orbis plano datum,
eAt ut dictantia C. d. Vi-
res igitur, quibus COr-
Pora in plano P  R
verCantia FraHUnEUE Ver-
sus punctum C, Tunt prO
ratione distanciarum aequales viribus quibus corpora undiquaque
crahuntur versus centrum S; ex propterea corpora morebuntur iil-
dem Temporibus, in iisdem Figuris, in plano quoris P O R circa
punctum C, acque in spatiis liberis circa cenerum S; adeoque (Der
LOrOl. 2. PFOD. X, ec C. orol. 2. PFOP, XXXVLTL) Pemporibus (CMPCE
aGua-