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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 435, page id 1041163592:0469
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PRINCTPTA MATHIEMATICA.
435
NMXmC: de harum disterentia L. NX Mm-- NNIX MC L mC,
est vis particularum ambarum simul sumpearum ad Perram
rotandam. Pujus differentix pars affirmatira L NVX Mm seu
2L. NVX NX, est ad parcicularum duarum ejusdem magnitudi-
nis in s consistentium vim 2 AAIX EC, UE LX9 ad ACg.
FE pAES nEGAEIVA NMX MC F mC ICU 2XYXCY, ad parti
cularum carundem in A consittencium vim 2 AHIXHIC, ut
Cxg ad ACg. Ac proinde partium disterentia, id cA, par-
ticularum duarum L ec Eimul Cumpearum vis ad Terram FOtan-
dam, est ad vim parcicularum duarum iisdem aequalium ec in loco
A consistentium, ad Terram icidem rorandam, ut L Zg =C X9
ad ACg. Sed E circuli PK circumterentia PR dividatur in DaF-
ticulas innumeras aequales L crune omnes L. Xg ad coridem lX 9
UE F 2d 2, (per Lem. I.) acque ad toridem AC 9, ut IX9 ad
2 ACg; e tocidem C Xg ad cotidem ACg uE 2C X9 2d 2 AC 9.
Ouare vires conjunctae particularum omnium in circuitu circuli
TK, sune ad vires conjunctas particularum coridem in loco A, ut
TX9 = 2CX9 2d 2 ACg: _E pFOPEErCa (per L CMI. I.) ad vires
conjunctas parcicularum toridem in circuitu circuli AF, uE
TX9 = 2C X9 2d AC9.
Jam vero si Sphaera diameter Pp dividatur in partes innume-
ras aequales, quibus insistane circuli cocidem PK; materia in peri-
metro circuli cujusque PK erir ut lPg: ideoque ris materix
illius ad Terram rocandam, crit ut IXg in IXg = 2C Xg. EF
vis materix ejusdem, si in circuli AF. perimetro consisteret, esset
uc IN9 in ACg. EC Propterca vis particularum omnium ma-
cerix totius, exera globum in perimetris circulorum omnium con-
Sictentis, eA ad vim particularum toridem in perimeero circuli
maximi AF. consistentis, uc omnia IXg in IXg = 2C X9 2d
cocidem IXg in ACg, hoc eA, ut omma AC9-C Xg in
AC9 = 3C Xg 2d cocidem AC g -C X9 in ACg, id cA, ut
omnia ACgg = 4 ACgZCXg + 3C X99 ad cocidem AC. g9
ACgX C X9, hoc eAt, uE tota quancitas Auens cujus Auxio
est ACgg - 4 ACGXC X9 + 3C X9q ad totam quantitatem AU-
entem cujus Auxio eA AC gg AC gX C Xg; ac proinde per NC-
thodum Fluxionum, ut ACggZCX- Z ACgZC X cub + = C XgC
ad AC99ZCX = = AC 9X C Lcub, id eAt, A PEO C Z CCrIbAEUE
tota Cp vel AC, uE 5 C96 2d 3 C96, hoc cAt, ut duo 2d
quinque. Q. E. D.
IKK L
L1oL
FCRFIVS.
l LLaL L_