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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 222, page id 1041163592:0256
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222
PTTILOSOPMLE NATDRALIS
DE MorD  datur punctum B per quod FTyperbola, ASymptotisC HL CD,
Conronon delcribi debet; uc dc spatium BCD, quod corpus incipiendo
morum suum cum velocitare illa B, tempore quoris AD, in MC.
dio simitari resistente describere porest.
PROPOSITIO VI. THEOREMA IV.
Corpora Sphaerica homorenea  aequalia resistentiis in duplicata
ratione velocitatum impedita,  solis viribus insitis incitatas
remporibus quae sunt reciproce ut velocitates sub inilio, descri-
bunt semper aequalia spatia, es amittunt partes velocitatum pro-
portionales totis.
Asmproris rectangulis C D,
CH delcripta Hyperbola qua-
vis BB F e fccance perpendicula
AB, ab, DF, des In B, b, F es
exponantur relocicates initi-
ales per perpendicula AB,
DE Sc tempora per lincas
Aa Dd. FK Cr∞O UE Aa 2d
D dica (per FIypochesin) D F.
ad AB, ec ita (ex natura FIy
perbolae) C  ad CD; e com
Donendo, ita Ca ad C d. Ergo
arex ABba D F. ec hoc eA, spatia descripta aequantur inter les
ee velocitates primae AB, D F Cune ultimis ab, des ee proxterea
diridendo) partibus etiam luis amissis AB = ab, DP=de prO.
Dortionales. g. F. D.
PROPOSITIO VII TTTEOREMA V.
Corpora Sphaerica quibus resistitur in duplicata ratione velocitatum,
temporibus quae sunt ut motus primi directe e resistentiae pri
mae inverse, amittent partes motuum proportionales totis, 
satia describent temporibus istis in velocitates primas ductis
proportionalia.
Namque mocuum parces amissae sunE uE resistenFiX _E FEMPOTA
Con