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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 183, page id 1041163592:0217
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PRINCTDTA MATHEMATIOA.
Tam A linca P e sCCCE arCUM P F in g; &t recta 
arcu eranescente P.e coincidit, productâ occurrat rectae PS in Y; PnimOSI
ex 2b S demictatur in P F normalis SCr: OD MMMa MtatGUIa
OTF, a= es DFS; Crit D a ad L L al L L, leu L
1
EIBER
L dd
FS; ex ob criangula F eg, F SG (per LCM. VETF, e COrOL. 3.
Lem. VEI) Similia, crie FC ad eq sCu FF, UE FS ad SG; _ CX
aequo, D d 2d Ff uE D F. ad SE; hoc est (ob similia criangula.
PDE FG5) ut P F ad PS. Q. F. D.
PROPOSITIO LXXIZ. TIIEOREMA ZXXIX.
Si superficies ob latitudinem infinite diminutam jamjam evanescens
FFFe, convolutione sui circa axem PS, describat solidum
Sphaericum concavo. convexum, ad cujus particulas sinsulas aequa-
les tendant aequales vires centripetae: dico quod Vis, qua soli-
dum illud trahit corpusculum situm in P, est in ratione compo-
ta ex ratione solidi D F. q X FF e ratione vis qua particula
data in loco FF traheret idem corpusculum.
Nam A primo consideremus vim Cuxerkcici Sphaericae FF, oux
convolutione arcus FP generatur, de a linea de ubiris secatur in r;
erie superficiei pars annularis, convolutione arcusr f genita, ut
lincola D a manence Sphaerae radio P F, (uti demonstravie Ar-
chimedes in Lib. de Sphaera ec Cylindro.) F.C hujus vis secundum li-
neaS PP vel Pr undique in superticie conica sITaS exCrCIta, UE
haec ipsa superticiei pars annularis; hoc cA, ut lineola D d veh
quod perinde est, uc rectansulum tub dato Sphaerae radio P F. dc
lineola