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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)
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De Calculo Centri Cravitatis. Cap. V.
Fio. 169, plus ZV R2 - 4 52 R: HOC est, à A2 R - = S2 R = = ef R. (Nempe Solidi hu-
jus porcio ABK.
Erso, Omnia OZa, SZ a, _c. Scementa; hoc elt cocidem Semicireuli, dem
Dtis ipliS AZO, AZS, _c. Tunc (propter Semicirculum = ZRZ;) EARF.
minus Z A R - = 5=R; IIOC elt, E ARP = = A R + LS R: leu (reltiuris mi-
nulcularum. valoribus,) a RP = = a R F Z S R = = a RP - = e fR: Ouae eltu
Portionis Solidi quadestineo ABBa incumbentis magnicudo.
Adeoque, torum A dr a Tolidum, (PTOPter a = = P, e 5 =O;) clt 5R2=
16RP2 = ERY
Sed e eadem corius Solidi magnitudo, sic Facilius colligitur. Sumpris in A a
diametro, duobus punctis quibulvis equaliter a C Ceniro vrrinque remoris, ut
S Z: manifestum est, cum linus rectos 5Z, Z F, tig. 160. invicem aequales esse;
tum rectas 52, 2 C, Seu Z. 2, F C, Fg. 170. hoc est, areus BA, F A, Scu B A, Ba
Fig. 269. Timul aequales Semiperipheria ABa, seu ra rectae. Adeoque duo limul
rectangula, ZT X L, S, CF X F. Z, aequalia uni xaxSZ. HOC clt, Omnes BV 10.
tius Semicirculi, in respectiras bB; cancundem este acque Omnes BV unius qua-
drantis (hoc elt ipse quadrans A DC. = 3 RP,) in 70 = = P, ducta. HOC cAt,
SRDZ; totius Solidi magnitudo; ut prius.
FIinc etiam; Porrionis Solidi bBr magnicudo colligitur. Nam tocum Solicum
sRPZ; dempio scomento AbB4 = = a R~ - = a R = Ls= R: Relinquie
Scomentum i6 R~ Z = = a RP. + + a 2 R  L52 R; V el (TUmPIO a == = P - a,
a2R = =52 R. Quod iplum in inguilicione prius rOPCrEUM CraL. OuipDC, Sumpto
AK = 7B, (adeoque relticuro a pro e) cric rBB == A K b, cujus magnieudo si-
pra invenia cA + a = R = = s= R; COU L ef R. Fst enim, es, hoc ett a = sin a Y sy
POrrO; Si ex Solido ABB~ = E a RP - + a R F + 52 R: Auseratur Solidum
bBa B; HOC est, bB = a, in Segmenum Semicirculi V B a = Z a R = = 5 R L =SB
lper GF. prOP. F5. quippe quod, in B V A elt an V, idem in BV a olt a h; et s
uirobique idem;) hoc cst (PrOPtEF a = ZP = a, e B = 2 R (v,) in = RP -
Za R = =5 R - 25V; NempC = a RF - = a R ( = a 5 R = = a 5V, Teu l’a R F-
Zea R - = a 5V; Relinguicur Solidi porrio AbB = : a R - 3 a 5 R f : 52 R +
2a5V = =CR + =a5v: Seu summa rectansutorum omnium as Colidum illud
complencium; sumpris v arichmetice proportionalibus.
Auretiam; Si ex Semicylindri portione AK BB; hoc elt, ex Semicirculi Ser-
menio ABV = = C R + 35~ (per B F. prOP. 15. ) in DB = a ducto; hoc Cst, CX
SCaR + 3 a5V = 3 a = R - 3 a5R = = a 5V: auteratur Semicylindri portio ABR
= a2 R -  52 R (per BK, ) reltabic Semieytindri porrio ABB, = : a R=
2a5 R + 3 52 R + Za5V; UE prius.
Similicer de Momenris judicandum erit.
Nempe, Momentum Solidi AbK, respectu T A; idem elt acque Mometira
Omnium A B V Semicirculi Sesmentorum illud complentium respectu iplius (plani
tangentis) Y A: HOc cst, (Dex SL. DTOD. 25.) Omn. Z C R = ZSVR = 353.
seu Omn. Za R - = sR + L SV R 55 553: Sumpris a arichmetice proporciona
libus.
Siine aurem Omn. a Carictmetiee proporcionales ulque ad, a maximum,) 5a:
(DEE PFOB. I. hujus. ) Adeoque Omn. Za R: = a2 R.
Trem, Omnes s(eo spectantes,) Tunc iptum a B0 = v. R, (Per 5O. PrOP. 17.)
Adeoque Omn. = =5 R2. = = = V R3
item, Omnes su, tunc ipsum A bK Solidum ex ductu rectarum, B0 in bR
hoc est (per SI. ) LV= R == V R2 - 352 R. A deoque Omn. L 5V R: = = V R3
TIem, Omm. S3: (PEF S V. prOP. 23.) = Omn: d R. Sun autem Omn. 02
hoc est, quadrata Ordinacim axplicararum, Segmencum ABV complencium, seu
Omn. 52, Tumpris v arictmerice proporeionalibus: Duptum Momenti Segmenit
ABV (Aig. 269.) respectu Aa: HOC est (per 5 V. prOD. 15.) ZV R2  45 2 R - +
352V: Adeoque Omn. 0 R: (= Omn. 53:) L RV R3 3 52 R2 u 3 sEB R: F. D
proprerea Omm. L 1. 5t:  3d  H392 R2-. B3 _ A.
FNBO
2
st