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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 382, page id 1041163592:0416
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IIII
PTIILOSODHIIA NATVRALIS
PROPOSITIO XZ PROBLEMA IV.
invenire es inter se comparare Pondera corporum in Terrae hujus
regionibus diversis.
Duoniam pondera inaqualium crurum canalis aquexe AC Qgc a
requalia unt; ec pondera parcium, cruribus coris proxortionalum
e similiter in eoris sicarum, sunc ad invicem uE pondera FEOFOTUM,
adeoque etiam aequantur inter sc; crunt pondera aqualium et in
cruribus similiter Cicarum parcium reciproce ut crura, id cAt, reci
procC ut 230 2d 229. Ec par cA ratio homogeneorum ec xequa-
lium quorumris ex in canalis cruribus similiter litorum corporum.
Hlorum pondera sune reciproce ut crura, id cA, reciproce ut di-
BanEIK COrPOrUM a CenErO Terra. Proinde si corpor in sUDre.
mis canalium parcibus, sive in superticie Terra COnSISAnE; erunt
pondera eorum ad invicem reciproce ut distantix COrUM a CCnFTO.
Et eodem areumento pondera, in aliis quibuscunque per Fotam
Ferrae superticiem regionibus, sunt reciproce ux distantiae locorum
A CeNETO; _E PFODECFCAS CX FTYPOTheH quod Terra SphaerOIS SIE
dantur proportione.
Onde cale conhe Theorema, quod incrementum ponderis per-
sendo ab Aiquatore ad PolOS, sic quam proxime ut sinuS verTuS
Laticudinis duplicaca, vel, quod perinde est, ut quadratum sinuS
recti Lacitudinis. Et in eadem circiter ratiOnC AUGENEUE arCUS
oraduum Lacicudinis in Meridiano. Ideoque cum Latitudo L.H-
Tetiae Parisiorum sIC 488. 50, ea locorum (ub SE qUaFOTC 00PF.00
e ea locorum ad PoloS 908. ex duplorum sInUS verH SInE 11334,
00000 e 20000, existente Radio 10000, e graricas ad Polum sIE
ad gravieatem sub LEguaTOrC UE 230 ad 229, _E CXCCNUS GraVI
tatis ad Polum ad graritatem (ub A quatore ut 1 ad 229: CriE CX-
cessus oravitatis in Lacicudine Lutetiae ad graritacem sub F quAEOTC,
_E 2X 25038 2d 229, SCv 5667 2d 229000O. FE prOPECrCA gravitateS
Eocx in his locis erunt ad invicem ut 2295667 2d 2290000. Onare
cum consitudines pendulorum xequalibus temporibus olcillaneium
SInE UE GravitaTeS, X in Lacitudine Lutetia Parisiorum longieudo
penduli singulis minucis sccundis oscillaneis sic pedum erium Pa-
risientium ec linearum 85: lonsitudo penduli sub A. quatore su-
perabitur a longirudine synchroni penduli Parisiensis, excesu li-
ex unius ec 87 parcium millesimarum linca. E.F simili computo
contir Tabula sequens.
Latituao
DE AEVNDI
YETEMAEI