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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 52, page id 1041163592:0086
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21
PFTLOSOPEILLE NATDRALIS
DEMOTD CorOl. 3. EF concursus tangentis cujuris P MI cum recta SN.
Conronvu quae ab umbilico in iplam perpendicularis est, incidit in rectam AN,
quae Parabolam tansi in vertice principali.
PROPOSITTO. ZIII. PROBLEMA VTII.
Moveatur corpus in perimetro Parabola: requiritur L ex vis centri-
petae tendentis ad umbilicum hujus ficurae.
incac constructio Lemmatis, ltque F corpus in perimerro P
rabolae, ex a loco  in quem cOrpuS Proxime OveTUT, asC ipAISF
parallelam R ec perpendicularem I, necnon QV tangenti pa-
rallelam ex occurrentem tum diametro YF G in v, cum dictancia
SF in x. Jam ob similia triangula P ∞ V, SP M et aequalia unius
latera SM, SP, aequalia sune alterius latera P a (eu R ec F V.
Sed, ex Conicis, quadratum ordinata dV aequale cAt rectangulo sub
lacere recto ex seomento diametri PV, id cAt (per L em. Z III.) rectangu.
10 4 F SX P V, Cen 4 F SZ OR; Et punctis P ec O) cocuntibUS, ra-
eio V 2d 8 x per (Per Corol. 2 L Cm. VII.) Sic ratio aequalitatis. Rr-
∞0Daquad. eo
in catu, aequale
eA rectangu.
104 FSXOR.
F. A autem (0b
similia crian-
outa  x 7,
SPN) Q∞g.
ad dY g. uE
P59. ad5N
hoc eA (per Z M
Corol. I. LCM. XEV.) UE PS ad S A, id cAt ut 4 F S X  R
ad 4.S AX QR, de indc (DEF PFOD. LX. Lib. V. F. lem.) GF9. d
 ex
45 AX QR aequantur. Ducantur haec aequalia in 
QR de Aet
S Pg. X Q=4. aequale S P g. X 4. S A: _ Propterea (per C OrOl. L ex 5
R
PrOD. VI.) ris centripeta es reciprOCO UF S F g. X4 S A, id cst, ob da-
tam 4.S A, reciproce in duplicata ratione distantiae 5F. 8. F. l.
Coret.