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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 186, page id 1041163592:0220
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50
PHTLOSOPMTSE NATDRALIS
PROPOSITIO LIXKI PROBLEMA XLI.
stantibus jam positis, mensuranda est Area ABN A.
a puncto  ducatur recta A SpeaM CanSCHS I1I, l al
axem P AB demissa normali FYI, BisCCCtUF FY in L; _ CriE
(per PrOD. 12, Lib. 2. Elem.) FFg aequale FS9 + SF9 +
2FSD. EA auTem SF. 9 Ccu SPIg (ob similitudinem trianou-
lorum SP FI, SHT) aequale rectangulo PSI. ErgO F F.g aequale
eA CONTeNEO SUB FS e F5 + ST + 3SD, hoc CA, (UB FS de
2F.5 = 2SD, id est, sUb FS _C 2F. D. POrrO D F quad aequale
CA SFg - SD g. Teu SF g - L S9 + 25L. D = F D 9, id eAt,
2SL. D = Z. Dg - AL B. Nam L.S9 =SF4 (Cu L,5g -5A.q
DE NOTD
EORPORVM
(Der PrOP. 6, Lib. 2. Flem.) aequatur rectangulo AL B. Scriba-
eur ieaque 2SLD =T Dg - AL B PTO D F.g; de quancitas
DF 9
F
X TS
YV quae secundum Corollarium quartum Propostionis
praecedentis est ut longitudo ordinatim applicatae DN, resolvet
sese In EreS Dartes 2SL D XFS LD9XF5 ALBX FS
P L XV
PEXV
ribi s prO V scribatur ratio inversa vis centripCtX, _ pFO F F me
dium proportionale inter P S _ 2L. D; tres illae partes cradene
ordinatim applicatae linearum toridem curvarum, quarum arex PCF
Mechodos rulgatas innoteleunt. d. F.. F.
CiXe