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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 44, page id 1041163592:0078
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+4
PHILOSOPMLE NATDRALIS
GORFONON I CA, Ut SP X R P g 2C
SF cub. X PV cub.
PT Cub.
trianoula FSG, T PV) ad SC cub.
sive (ob similia
Corol. 3. Vis, qua corpus P in Orbe quocunque circum virium
centrum Srevolritur, est ad rim qua corpus idem P in eodem
orbe codemque tempore periodico circum aliud quodvis ririum
centrum R revolri porest, ut SP X R P g contentum utique sub di-
stancia corporis a primo virium centro s’ec quadrato distantix ejus
a secundo ririum centro R ad cubum rectae SEF quae 2 primo vi-
rium centro Sad orbis tangentem PC ducitur, e corporis a (c-
cundo ririum centro distantia RF parallela est. Nam vires in
hoc Orbe, ad ejus punctum quodris P, eadem tunt ac in C irculo
ejusdem curratura.
PRODOSTTTO. VIII. PROBLEMA. III.
Moveatur corpus in Circulo P C A: ad hunc effectum requiritur L ex
vis centripetae tendentis ad punctum adeo loncinquum S, ut linea
omnes PS, RS ad id ductae, pro parallelis haberi possint.
A Circuli centrO C agatur semidiameter C A parallelas iltas
verpendiculariter secans in MI e
N. ec jungatur CP. Ob similia
crianoula CF MI, PZT _E RZ 
eAt CF 9 2d F MG UE F R9 2c
Fge ex natura Circuli P R9
equale est rectangulO ORXRN F ON
sive cocuntibus punctis P, O) rect.
angulo 4RX2F M. ErgO CA
CP g2d F MIquad. Ut B R X 2TMI
ad 97 quad. adeoque  quad.
aequale
2FMCub.
C+
QR
DE quad. XSF quad.
QR
2qualc
MCub. XSFqu.
CF quad.
FR erGO (PEF COrOL. Z _E S PrOP. VT.) viS CenTrIPETA ReCIpROCE Ux
PMcub. XSF quad. noc est (neglecta ratione determinata 25P quad.
CF quad.
reCIPEOCC UE P MI Cub. 9. F. I.
C
e
Idem tacile colligitur etiam ex Proposirione prxecedente.
denon
DE MOTO