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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRTHCIDTA MATHEMATIOA.
arcus TFI convolutione semicirculi R B circa diametrum AB LIDEY
delcribet, ad superticiem circularem, quam arcus ih conrolutione etuos.
semicirculi ak b circa diametrum ab deseribet. It vires, quibus
hae superficies secundum lineas ad se tendentes attrahune corpuseu.
la P ec p, sunE (per IIy Pochetin) ut iplae superticies applicata
ad quadraca distanciarum fuarum a corporibus, hoc est, uc p FXPS
ad P F X P5. Suneque hae rires ad iplarum partes obliquas
quae (Facta per Leoum Corol. 2. resolutione virium) secundum
lincas FS, p5 ad centra tendunt, ut F L ad F Q e pi 2d pg; id
CA (ob similia criangula D F~ ec P S F, piq e p5F) uE FS ad
PL ec p5 ad pf. Ondes ex aequo, tic accractio corpusculi hujus F
vertus s ad ducractionem corputeuli e vertus s, u P F Xp sXpS 2d
DFXD EXDS
B5 = hoc ost, uc p 5 quad. 2d PS quad. FF simili argu-
mento vires, quibus suxerficies convolurione arcuum RL, Rl de-
Teriptae trahune corpuseula, crunt ue ps quad. ad PS quad; inque
eadem ratione erunt rires superficierum omnium circularium in quas
utraque superticies Sphaerica, capiendo semper sd aequalem S D et
se aequalem SF, distingui porest. Er, per compotitionem, rires
cotarum Cuperticierum Spharicarum in corpulcula exCTCITA CrUINE
in eadem ratione. 8. L. D.
PROPOSITIO LXXII. THEOREMA ZKXII
Si ad Sphaerae cujusvis puncta singula tendant vires aequales cen-
tripetae decrescentes in duplicata ratione distantiarum a punctis,
ac detur tum Sphaerae densitas, tum ratio diametri Sphaerae ad
distantiam corpusculi a centro ejus; dico quod vis qua corpus-
culum attrahitur proportionalis erit semidiametro Sphaerae.
tam concipe corpuscula duo scorsim a Sphaeris duabus acrrahi,
unum ab una ec alterum ab altera, ec dictantias eorum a Sphaera-
rum ceneris proxortionales esse diametris Sphaerarum respective,
Sphaeras autem resolvi in particulas similes de similiter positas ad
corpuscula. RE accractiones corpusculi unius, Factae versus singulas
particulas Sphaerae unius, crunt ad actractiones alterius versus ana-
logas tocidem parriculas Sphaerae alterius, in ratione composita ex
cacione particularum directe ee ratione duplicata distanciarum in-
verlCo.