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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 204, page id 1041163592:0238
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204
PHITLOSOPMLLE NATDORALIS
DF MorD SCCanS tam PYM in P ec B. quam M F productam in N; ec primo
Conronom si ateractio vel impulsus ponatur unitormis, erie (ex demonstracis
Galilaei) curra F Parabola, cujus haec est proprictas, ut rectan-
culum lub dato latere recto e linca PM aequale sIt (I M quadrato;
sed ex linca _M bilecabitur in L. Unde si ad MI demittatur
xerpendiculum L.O, ∞-
quales CrunE MO, OR;
additis aequa libusON,
OL, HCnE tOEX aequaleS F
MN, FR. Proinde cum
TR detur, datur etiam
MNV; eAque rectangu-
tum NMT ad rectangu-
Jum sub latere recto ec
TM, HOC CA, ad FI M9.
in data ratione. Sed rect.
angulum NMI aequale
eAt rectangulo F M G, id
est, disferentiae quadrato-
rum M L. 93 dc F L.9 ICu
ratione habec ad sui iphus quarram parrem M L
racio MLg -L Lg ad M L. 93 e aru ratio L. I9 ad ML. 9, de
tUx
erSC
L. T9; eC TIM9 datam
racio dimidiata L. T ad ML. Sed in omni triangulo L. MI, sinuS
angulorum sunt proportionales lateribus oppoltis. Eroo datur
racio simus auz  scidentiae L M A ad sinum assull CMetSCA
TIX L LR. Q. F. D.
Ca5. 2. Transeat jam corpus successive per sparia plura paralle
lis planis terminata AabB, BbCC, ecc. ec asitetur ri quae lIC in
ngulis