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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 715, page id 851387705:0735
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ed
PFOD. X. V De Calculo Centri Cravitalis.
lingulis in correspomlentis Ongula luperticie curra respectiris rectis, aequales
atque in eadem d convertionis Axe Diltancia, qua sunc illa a Parallelo Plano per
aciem (uam.) Sd, propter curraturam convertione factam; minuenda elt ea Di-
Etancia, pro Racione quam hahet Convertionis Areus ad Chordam Cuam; uc jan
oltentum est. Puta; in Semiconversione, ut Semiperipheria EP, ad Diametrum
2 R; in conrextione Ouadrantali, ut = P ad se V 2: FI universaliter, ut ArCUS 
vel m, ad Chordam luam c vel n; lic distantia in Onsula (jam oltenta)
=,2d  vel   diltanciam Cenuri gravicaris Zonae impertecta, a conversio.
nis AXC.
Sed _ in AUOTUI PLaNOTUM, PrIUS MCMOTATOTUM, Communi lectIOne reperIrI
Tuvra oltentum elt: Freo, in hujus lectionis eo Puncto quae sic (ue dutum ett)
diltat. Dacur isicde, cum in Ongula, cum in Lona ucur impertecta, iplum Ca.
vicatis Ccnrum. Quoc erat ultimo otlendendum.
L AOP. XV.
Sectoris Circuli (duobus Radiis eC ArC COmPTCHENSI) Centrum BTa- A.
ricatis est in Axis suiillo puncto, cujus a Centro Circuli distantia, Fig
eA ad duos Frientes Radii, ut expolici Arcus Chorda, ad ArcuM 158.
Tuum.
Adeoque, in semicirculo; OE Semiperipheria ad Diametrum, sic 3
Radii ad distantiam Centri gxaritatis semicirculi a Circuli Cenero.
Atque hinc etiam Seementi circularis (recta absciMi) Centrum grari-
catis colligitur: Atque de aliis Porrionibus similiter. Cxteraque
quae hinc dependent.
B.
Nempe; Si ponatUE, in exposito circulo, Radius C A vel CB = R; C.
Peripheria integra, P; ArCUS BA = a, adleoque B AB = 2a; CHOF- F1B. 159,
da BA = c; Sinus rectus BV = 5, adeoque Chorda BB = 25s: Si. 160.
nuS VeRTUS A V = v5 xeliguusque V a = 2 R = V = B; 2 CCHErO DI
Rancia VC = ~ = R = V s V EE supra CenEruM, velV C = ∞ = ~ = R
S intra, vel VC = ~ = 0 li in CeNErO: IECM a - 5 = e; a + 5 = f:
R + V == 2
Fric corius Semicireali A Do, Magnicudo, : X P: Cenerique gravitatis, D.
sive ar an sive a Y A. distantia, R; momencum respectur a, vel T A.
1.
 P. P. Distancia Cencri Cravicaris ab A : momentum respe. O.
Au A a, Z R3
Sectoris BC A maxnicudo La R: Centri cravicatis distancia a DC, D.
A; ara _ +  R; a FA, R - == R; momenum cjus, relpectu
ra, La X2 =s R; momentum ejuldem respectu Y A, La R - 2 5 R2:
Ceneri pravicatis distancia ab A 
JVR2
s
=: momentum respectu Aa, O. W.
Trianguli BC. V, magniendo : Sr: Distancia Ceneri pravitatis a DC, 3 ~; F.
a 7 an R =3 X = Z R = ZV; a TA, R + 3 4 = 3R + ZV; MOmenTIM FCsBC.
Au 2oy 3 5 X R L 1 5~
LSX; resPeCtU FA, 35 XR F5 5X2
R.
x: Diltantia Ceneri Gravitatis ab Aa J S; MOIENEUM R. Y.
respectu A a, 3 52 V
Semitcementi B V a, masnieudo ie P + : SV: Momencum respectu ran F.
X X X d 2
ZCR2