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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 125, page id 1041163592:0159
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PDINCIPLA MATTIEMATICA.
F25
qua corpus in Ellipsi mobili u p h iildem temporibus revolvi LIvex
DONIE.
Corol. 3. Ad cundem modum colligetur quod, si Orbis immo-
bilis VL X Fllipsis sic centrum habens in virium CCNErO C; ei
que similis, aequalis e concentrica ponatur Rllipsis mobilis W p R5
sitque 2 R Ellipseos hujus lacus rectum principale, et 2Y latuS
transversum sire axis major, acque angulus V C p semper sit ad
angulum VC P uc G ad F; vires quibus corpora in Lllips im
mobili ec mobili temporibus aequalibus revolvi pONUNE, CrUnE VE
A F A
E Cub.
EE A RGG = R F P
PCub.
Acub. respective.
Corol. 4. EF universaliter, A corporis alcieudo maxima CV no-
minetur V, e radius curraturae quam Orbis V P R habet in V, id
est radius Circuli aequaliter curris nominetur R, ex vis centripera
qua corpus in Trajectoria quacunque immobili V P R revolvi po-
test, in loco V dicatur satque aliis in locis P indetinite dica-
cur Z, altieudinc C P nOminatA A, ex capiatuE C ad F in data
ratione anguli VCp ad angulum VCP: crit vis centripeta qua
corpus idem eoldem motus in eadem Prajcccoria u p e circula-
riter mora remporibus iildem peragere potest, ut summa virium
X L VRC G-V RFF
A CMb.
Corol. 5. Dato igitur motu corporis in Orbe quocunque immo-
bilis augeri vel minui porest ejus mocus angularis circa centrum
virium in ratione data, ex inde inveniri novi Orbes immobiles in
quibus corpora novis viribus cencripetis orrentur.
Corol. 6. Isitur ( ad rectam CV PO.
sitione dacam erisatur perpendiculum
P lonsicudinis indererminata, jun-
Sacurque C P, ex ipA aequalis agaEur
C.P. constituens angulum VC p, qui (IE
ad ansulum VC P in data ratione;
vis qua corpus srrari potest in Curra
illa VPk quam punctum p DerpCEHIO
tansir, erit reciproce ur cubus altitu-
dinis C p. Nam corpus P, per rim inertix, nulla alia vi urgente,
unitormiter progredi porest in recta VP. Addacur vis in cenrrum
cubo alcicudinis C F vel Cp reciproce proporrionalis, _ (PeF
jam demonstraca) decorquebitur mocus ille rectilineus in lincam
PRLMDS.
CVEVAM