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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 220, page id 1041163592:0254
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PHILOSOPHILE NATORALIS
S F. C TTC
A A3
De motu Corporum quibus resistitur in duplicata ra
tione Velocitatum.
PROPOSITIO V. THEOREMA HII.
Si Corpori resistitur in velocitatis ratione duplicata, e idem sola
vi insita per Medium similare movetur; tempora vero suman-
tur in proeressione Greometrica a minoribus terminis ad majores
pergente: dico quod velocitates initio singulorum temporum
sunt in eadem proeressione Geometrica inverse, e quod spatia
sunt aequalia quae sinculis temporibus describuntur.
Nlam quontam quacmalo reibena
eis proportionalis eA resistentia MC.
dii, ex resistentix proportionale est
decrementum relocitatis; (I FemPUS
in particulas innumeras aequales divi-
datur, quadrata velocitatum lingulis
cemporum initiis crunt relocicacum
carundem differentiis proportionalia.
Sunto temporis particulae illa K,
RL, L M, _C. in recta C D CumpEx,
ex erigantur perpendicula AB, K k,
LI MIm, _cC. Flyperbolx BkImC.
centro C Asymptoris rectangulis CD, CF descripex, Occutrencia
in B, k, B m, _C. _ Crit AB ad Rk UE C R ad C A, d CIVIII
AB = RK ad KP VE AR ad C A, _ vicisim AB - Rk ad AR
UE KR ad C A, adeoque ut ABX K h ad ABX C A. Onde, cum
AK _ AB XC A denEUT, CrIt AB = RR UE ABX RR; ex ultimo,
ubi cocunt AB _c Rk, ut AB g. FF AmiliarGUMENEO CrunE RR- L. 
T. I - Mm, _CC. UE K k9, L. Ig, ecc. Lincarum igitur AB, Kk, L. h M m
qua-
DE MOXV
EORPORDM