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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 833, page id 851387705:0853
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AI
PFOD. XXI. De Calculo Centri Cravitatis.
menei Ongule ABBa (Porrionis Semieycloidis) aciem habentis Aa, respectu FiS. 166.
ejuldem Aa: Adeoque iplum ilLIUS MAMENEUM, 32 C R3 = 3 aVR 2 = = 5V R 2 168.
FZ a R  3 a s R  3 a s= R F 8 S R: (Hujulque Duplum, et Semilolidi circa
Aa conveclione lacti, Momencum respectu iplius adis AS: uc Tupra (xpius osten.
Tum elt.
Tludoue Ongulae Bomencum, per magnicudinem suam, 2 a R = 3 a 5 R - 3 y p =
F BS se (per 5I. PrOP. 20.) divisum; extribet ipsius ABCa Ungula, aciem
hrabencis Aa, diltanciam ceneri graritatis ab A a
87 CR2 = 96a v R = 95~ R + 36 a + 108 a 5 + 60a5 + 245
54a = 108a5 = 48V R F 305
(Semiloli.
dique correspondenris, diltantia centri graritaris ab axe Aa, est ad hanc Onsula;
UE, 2R 2d 3X.)
Soeciacim vero, Ongulae corius Semieyeloidis A r an aciem habenis A a, Momen-
tum respectu Aa, (PTODECK a = ZP, V = 2R, _ 5 = 0,) is R X3 = 33 R3 
Cenerique gravitatis ab A a distancia, cst 2
=35 R27
9P2 - 64 22
Similiter ostendetur, Ongula Segmenti Semiercloidis BBr, aciem habentis N
Aa, Momencum respeetu Aa; ad momencum Onsulae segmemi semicirculi a Ba,
aciem habentis Aa, respectu ejusdem A∞; elle, ut 7 ad 3; acque insIIDer, ut
OMM. Y8 a B = 20 a sh: ad Omn. 3 s B: eo spectancia; lumptis a ariitimerice
proportionalibus. Ouae similicer, mutaris murandis, ad calculum reducentur.
Cumque Ungula Segmenti Semicirculi Momentum illud per 5S. proD. 16. inno-
telcac: Habebitur es correspondens Ingulae Scemenei Semiescloidis Momentum;
et quae hinc dependent.
Vel etiam; ex corIuS A Ta Ongula momento, (modo cradico,) Si auteratur
(modo cradicum) momencum Ongulae ABBa: Reltabit 15  ~ 3 - 23 R3∞ 22CR3
+3a0 R7 + 550R7 = Za R = Z a SR - ZaSR, - 56s R, Momencum OnsulX
BBr aciem habemtis Aci respectu ip(US A a
Acque hoc, per iplius magnicudinem (SF. Cradicam) 13 R ~ 2 =3 R3 = ZV R2
3a R = = aS R = 3sR, diritum; extribet ejuldem, ab Aa diltanciam cen-
eri graricacis;
O∞ = 105  P - 174 c R + 102 avR + 185uR - 72 a - 216 a5 - 120a5 - 28 5
2722 - 102 R = +960 R - 208 N 216 a5- 60s
Si vero ex Ongulae ABBa (portionis semiereloidis) momenco illo, modo
reperto; auteracur pomencum Onsulae bBaV, (aciem habencis Aa,) respectu
Aa: Relinguitur Ongula A B V (aciem habentis A a;) momencum respectu Aa
Componitur aurem Ongula illa BB a V, ex Pyramide Priansulo B a V incum-
bence, et Polido incumbence P’arallelogrammo BBa B.
Prramidis iltius MOenCUM (Per SR. prOP. 16.) CAt, in 53B = 5 53 R
Solidum Parallelogrammo b BaB incumbens; alcicudinem habet, in a nul-
lam; in B, aB = a; I B, BV = s; in b, bV = 5 f a. AdEOqUE COPONIEIE
ex prismate, criangulares bases habente, aB, vel Bb, = Z a; (quarum ilaque
CenEra Gravitatis a B, e an lunc Za; e, propter alcicudinem V a = B, naeni
cudo peismatis : a B; centrique staricacis ab A a distancia 3a F Zs, propter cen
erum prismacis in medio recta centra batium conjungente; adeoque momencum
ejus respectu Aa Za B = Z a sh:) Acque ex cunco, alciudinem habente in a B,
nullam; in bB, xqualem ip( BV = s: Adeoque (propter bB = a, de V ∞ = B,
magnicudinem habebit =a Sh, (semillem Prismacis, ejuldem balis de alcicudinis:)
Cencrique graricaris ab A a diltantiam, Ea F 3s: Ejusque proprerea respectu Aa
momentum, a a sh F a s h. Solidique propterea corius parallelogrammo in-
cumbeneis momencum, respectu Aa, 3a3 b = Z a sB = 3 a s B.
Adeoque Solidi Praperio bBa V incumbentis, momentum respectu Aa 3 a3B
F= a sh + =a sB f, L53 B. Aegne hoc per Ungulae magnicudinem ; fa b + 8s B
(per SK. PrOP. 20.) divisum; exhibet iplius bBa V Ingula, aciem habentis A a,
distanciane cenui pravicais ab, A a, + a + 6 a 5 + 4 a5. + s
6fa + 25
AY n A RN
C