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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 46, page id 1041163592:0080
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DEITLOSOPTTLM NAIDRALIS
PROPOSITIOZ. PROBLEMA. V.
Opretur corpus in Fllipsi: requiritur lex vis centripetae tendentis ad
centrum Fllipseos.
Sunto C A, C B Cemiaxes E. llip (COS; GP, D R diameErL COH
Sata; P F, 9t Derpendicula ad diametros; 42 ordinatim appli-
cata ad diametrum
EF; et Acompleatue
Parallelogrammum
QVPR, erit (exConi-
Cis) PoC 2d Ququad.
uE PC quad. ad C D
quad. et (0b Similia
criangula OVt, PCF
Q quad. est ad Q
quad. UE PC quad. a
D F quad. e Conjun-
etisrationibus, PVC
2d QF quad. UE PC
quad. 2d C D quad.
ec FC quad. ad F P
quad. id CA, V CF 2d
tquad.
FV UEF C quad.
ad CD gZ P Fg. SCribC G R PTO D V,EE (DET L EMMA XIT.) BCXC A
FC
PrOCD X P F, nec non, punctis P et Q cocuntibus, 2F C prO
26, _ ductis extremis ec mediis in se mutuo, sct QF quad. X P C 9
QR
aequale ZBCgXC A4. Es erso (per C or0l. 5 PrOP. YL.) vis cencri
Deta reciprOCC uc E BCgXC A9; id cA (ob datum Z BC qXC A9)
rCCIPEOCC UE = C; hoc eAt, directe ut dictantia P C. d. F. I.
Idem aliter.
In PC ab altera parte puncti s polica intelligatur tu aequalis ipA
+V; deinde cape w V quae sIc ad v C ut CA DC quad. ad P C quad.
FF quoniam ex Conicis est Ququad. ad F VG, ut DC quad. ad
eC quad: erit q quad. aequale P VX u V. Onde quadratum chor-
dae
40
DE MOTV
bORPORVM