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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 246, page id 1041163592:0280
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2.46
PHTLOSOPHLE NATDRALIS
Conronon velocitas, altera ue quadratum relociratis: et iplus decremen-
cum est ue summa quanciratum de
CG
CC
CD g. Quarum prior CA
ipta  de polerior G. D q est ut CD q Proinde .  Ob an.
alosum decrementum, est ut velocitas. PF (i quantitas EFD, ipA=
reciproce proxortionalis, quantitare data C G augeatUE; Tumma C D,
cempore ABE. D unitormirer crelcentes crelcet in progressione
Ecometrica. d. F. D.
Corol. 1. Igitur si datis punctis A, C exPOnatuE tempuS PCF
aream typerbolicam ABF. D, exponi potest velocitas per iplius
ED reciprOCAM 
Corol. 2. Sumendo autem C A ad C D ue relocitatis reciproca Tub
initio, ad relocitatis reciprocam in finc temporis cujulris AB P. D,
invenietur punctum C. Fo autem invento, relocitas ex dato quo.
vis alio tempore inveniri potest.
PROPOSITIO XII. THEOREMA IZ:
isdem positis, dico quod si spatia descripta sumantur in progressio
ne drithmetica, velocitates data quadam quantitate auetae e-
runt in prooressione Ceometrica.
In ASMPEOEO C D detur pUn- F
ctum R, et crecto perpendiculo RS,
quod occurrat IIyperbolae in S, Cx-
Donatur delcriptum spacium per a-
ream IIpperbolicam RS F D; e
velocitas erie ut longitudo GD
qua cum data C C componit longi.
cudinem C D, in progressione Cco-
metrica decrescentem, interea dum
spacium RSF. D augetur in Arith.
metica.
tenim ob datum spacii incrementum P. D de, lincola D a, quae
DE AOTV
eocite