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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 239, page id 1041163592:0273
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PRINCIPTA MATHEMATICA.
239
AsymPEotOn ejus in V, Fuerit VG reciproce ut ipsIUS Z X vel DN LIVEn
dignitas aliqua D N, cujus indlex cA nUCTUS n: _E GuATATUY SECLNDOS.
Medii densitas, qua Projectile proorediatur in hac Curva.
Pero BN, BD, NX Scribantur A, O, C respectire, sItque V L
ad XZ vel D N ut d ad es e VC aequalis
lis A =O, VG -
=VO aequalis C-
b
d
b
V7
A + -O.
in seriem infnicam
n = 3n n + 2n
A = O, de CD CCU NX = VZ
A
=n. Relolratur terminus ille
nbb
 F O = 2n + n
2 A 2 = 2 b bO2 +
6A2 +3 bbO ecc. ac Het C D aequalis C-
2bB
A F, O.
+nn +n
2 A F 2bbO:-
jus seriei terminus secundus--
cerrius
_ N + n
n + 3nn + 2n
A + 2
A--
+
6A + 3 bbO ecc. TTu-
ebB
n F. O usurpandus est pro10
2 A F 2bbO2 PrO RO2, Quareus
502. Ec inde Medii densitas
= 3nn + 23
6A2 + 3 bbO prO
R sF + 9~ in loco quoris 6, EC
3Va + ad  - 2dnbb nnb, adeo que A in Y Z capiacur VY
eA
aequalis nX V G, densitas illa CI rECIpTOCC UE XY. Sune enim A=
da
 ecA
2dnbb
nnB
eA A F n ipsarum XZ _ ZY quadrata. Ressten
cia autem in eodem locoC Ac ad gravitatem ut 35 in   ad +RR,
id est, XY 24 2 nn + 2n
n +2 VG. Et relocitas ibidem ea ipsa est qua-
cum corpus projectum in Parabola perseret, verticem G, diametrum
SD ex lacus rectum
+O
a
ser
2 XY quad.
nn +n inY C habente. Q. F.. I.
Scholium