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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 380, page id 1041163592:0414
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HIIIIII
380
PHITLOSOPMIIA NATDRALIS
D Morvi ad diameerum AB uE 100 ad FOL: graritas in loco  in PClta
dLSTEM A X.
foret ad graritacem in eodem loco  in Sphaeram centro C. radio
FCvel DC descriptam, ut 126 ad 125. Fc eodem argumento
oraritas in loco in Sphaeroidem, convolutione KIllip(eos AP BC
circa axem AB delcripram, est ad gravicatem in eodem loco s MM
Sphaeram centro C radio AC descriptam, uc 125 ad 126. FI au-
tem gravitas in loco A in Terram, media proporrionalis inter
oraricates in dictam Sphaeroidem et Sphaeram: propterca quod
Sphaera, diminuendo diamerrum P O in ratione TO1 2d 100,
vertitur in Aguram Perrx; de haec figura diminuendo in cadem
per
ratione diamerrum certiam, quae diametris duabus AB, F C
pendicularis est, vertitur in dictam Sphaeroidem; ex graritas in
A, in calu utroque, diminuitur in eadem ratione quam proxime.
FA igitur graritas in A in SphXrAM CCNErO
C radio AC delcripeam, ad gravitacem in
A in Terram UE 126 2d 12523 ec gravitas
in loco e in Sphaeram centro C radio C
descrixeam, est ad gravicacem in loco A in
Sphaeram centro C radio AC descriptam
in ratione diaWCtrOrUIM (pEF PEOP. LXZII.
L ib. L.) id CA, uc 100 ad IOr. Conjungan-
cur jam hxe cres rationes, 126 ad 125, 120
2d 1252, ec 100 ad 1OT: dE Het gravitas
in loco  in Terram, ad graricarem in loco A in Terram, ut
F26X 126Z 100 24 125Z +25=X FOT, CCu ut 5OI ad 500.
Jam cum (per Corol. 3. Prop. Xer. Lib. I.) gravicas in canalio
crure vtrovis ACca vel QCcg sc ut distantia locorum a CenErO
Terrae; E crura illa superticiebus trantrersis ex requidistantibus di-
singuantur in parces toris proportionales, erunt pondera partium
Lingularum in crure ACca ad pondera parcium coridem in crure
oItero, ut magnicudines et graritates acceleraerices conjunctim; id
est _F TOT 2d 100 8 500 ad GOT, hoc CA, ut 505 2d 501. AC
proinde s vis centrifusa partis cujulque in crure ACc a ex moru
diurno oriunda, fuisset ad pondus partis ejusdem ut 4 ad 505, eo
uc de pondere parcis cujusque, in partes 505 diriso, partes qua-
cuor detraheret; manerene pondera in utroque crure aequalia, de
oropterca Auidum consittoree in requilibrio. Verum vis cenerifuor
parris cujusque est ad pondus ejuldem uc 1 ad 289, hoc est, vis
contritusa quxe deberet esse ponderis pars, 5, CA TanEuM PATS Ly