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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 43, page id 1041163592:0077
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s
e
PRTNCIPTA MATHTEMALTCA.
+3
ac denique per punctum Q aSaTUE L. R quae ipsi SF parallela LInun
sIE ec OCcurrat cum circulo in L cum tangenti P Z in R. RF PRIMVS.
ob similia triangula Z QR, ZTP, V P A; Crit R F quad. hOc
CA QRL ad Q T quad. uE AV quad. ad FV quad. Ideoque
DRLX FV quad.
e
A
quad.
5 F quad.
equatUE Q F quad. Ducantur haec aequalia in
QR e punctis P ec Q cocuntibus, seribaEUF PV PrO RL.
Sic Het SP quad. X PV cub.
AV quad.  _quale  quad. X Q F quad. F. rBO (DeT
QR
Corol. L _E S PrOD. VT. )vis centripeta est RCCipEOCCNE SPQXPV cub
AV quad
id cAt, (ob datum AV quad.) reciproce ut quadratum distantix seu
alticudinis SP ec cubus chorda PV conjunctim. 9. F. L.
Idem aliter.
Ad tansentem F R productam demittatur perpendiculum SY.
ec ob similia criangula SYP, V P A; CrIE AV ad PV ut SF ad
SY, ideoque SEXF
aequale SP, et
Pquad. X F V cub.
AV quad
aequale
SXquad. X PV. EE PTOPtErCa (per C OrOL. Z _C SPFOD. VI.) visCenErI
Deta estrecIpROCEME SP qXP cub.
hoc cAt, ob datam AV, reci
PFOCC UE SF 9Z F V cub. G. F.. I.
Corol. 2. Flinc si punctum datum S ad quod ris cencripeta sem-
per cendit, locetur in circumterentia hujus circuli, puca ad V; exit
vis centripeta reciproce ut quadrato. cubus alticudinis SF.
Corol. 2. Vis qua corpus P in cir-
culo AP TV circum ririum centrum
Srevolvitur, est ad rim qua corpus
idem F in eodem circulo ex eodom
cempore periodico circum aliud quod
vis virium centrum a revolvi potest.
UE RP quad. XSF ad cubum rectae SC
jua a primo virium centro Sad Or-
Bistansentem F C ducitur, et distan-
cix corporis a secundo virium centro
Parallela cAt. Nam, per constructionem hujus Propositionis, vis
prior est ad rim polteriorem, ut R P qX P F cub. ad S P qX PV cub.