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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 126, page id 1041163592:0160
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126
PHITLOSOPMLAE NATVRALIS
DEMOrVCUENM VPh. FA aurem haec Curra Vp h eadem cum Curra illa
ouroRDA B in Corol. 3. PrOP. ZLF inventa, in qua ibi ciiximus corPOTa
hujusmodi riribus actracta oblique alcendere.
PROPOSITIOXLV. PROBLEMA XXXI.
Orbium qui sunt circulis maxime sinitimi requiruntur motus Ap-
Sidum.
Problema Solritur Arithmetice Faciendo ut Orbis, quem corpus
in FIlipE mobili (uc in Propositionis superioris Corol. 2, vel 3)
revolvens describit in plano immobilis accedat ad Formam Orbis
cujus Apsides reguiruntur, ex quarendo Apsides Orbis quem cor-
pus illud in plano immobili describit. Orbes autem candem ac-
quirene formam, si vires centripetae quibus describuntur, inter (e
collatae, in aequalibus altitudinibus reddantur proxortionales. Sit
punctum V ApsIS Cumma, ex scribantur T pro alcitudine maxima
CV, A Pro alcitudine quaris alia C F vel C p, ec X pro alei-
titudinum difterentia CV = C P; de vis qua corpus in Ellipfi
circa umbilicum Cuum C. (ut in Corollario 2.) revolrente move.
tur, quaeque in Corollario 2. Crac ut
At
i
E F A F R CTC+ -R F I
A cub.
A cub.
A F
AA
RC C -R F F
Acub.. id est
substimendo Y = X PrO A, Crit UE
R GC -RF F L TFF -FFX
Reducenda similiter est vis alia
quaeris centripeta ad Fractionem cujus denominator sIE A cub., 8c
numeratores, Facta homologorum terminorum collatione, statuendi
sunt analogi. Res Exemplis patebit.
ut
Fxempl. 1. Ponamus rim centrivetam unitormem eNse, adeoque
A CuB.
sire (scribendo T = Z PrO A in NUMCrALOTC) ut
TCnb. = ZTTZ + ZTZ X = Z cnb.
A CMb.
: de collatis NVuMCrAtOruM FCF-
minis correspondentibus, nimirum daris cum datis de non datis
cum non daris, ACER CC = R F F L TF F ad T cMb. VE = F F X ad
ZTTXC + 3TXZ - X cnb. sIVO UE = F F ad - 3TT + 3TX
Z X. Jam cum Orbis ponatur Circulo quam maxime finicimus,
cocat Orbis cum Circulo; ec ob tactas R, Paequales, atque X in infi-
nitum