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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 121, page id 1041163592:0155
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PRINCTPTA MATETEMATTCA.
I. C. L LC
LL
De Notu Corporum in Orbibus mobilibus, deque motu Apsidum.
PROPOSITIO XLII. PRODLEMA XXX.
Fifficiendum est ut corpus in Trajectoria quacunque circa centrum
Virium revolvente perinde moveri possit, atque corpus aliud in
eadem Trajectoria quiescente.
In OrbC V P K PO.
Sitione dato revolvatur
corpus F pergendo a
versus R. A CenErO
C agatur Temper C p,
quae st ipAC P aequalis,
anoulumque VC p an-
SulO VC F proxortio-
nalem constituat; ec 2-
rea quam linea C p de-
scribit eric ad arcam
VCD quam linca CF
simul describie, ut velo-
cicas lineae describentis
Cp ad velocitatem li-
nea describentis C F:
hoc est, uc angulus VCp ad angulum VC P, adeoque in data ra-
tione, ee propterca tempori proporrionalis. Cu aICd ICMPOTI
proportionalis sic quam linea C p in plano immobili describie, ma-
nifectum est quod corpus, cogente justae quantitaris Vi centripeta,
revolri possic. una cum puncto p in Currâ illa linea quam punctum
idem p ratione jam expolita describit in plano immobili. Finc ansu-
lusV Cvangulo P C P, ec linea C W lincx C V, atque Figura u C p Li
Surae VCZ aequalis, et corpus in p semper exictens morebitur in
Peri-
22
P RIMVS.