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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 832, page id 851387705:0852
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o Centri Cravitatis. Cap. V.
F1B. 166, uarums omnium Agorepatum (per eandem sprop. Z.. ) est B B A2- = Z B B A
10d. 10. + b56a + 36562+ 5b5B + 1b 5 B, seu 2bB ∞ + 3b56 1+ 3 b 5. B.
ainsia BsA2uf B oloiS B. A pu. 1125.B1A f. 1 1S2 B of. CI se B.
B A2 = 2b A2 = 4 sR A F 8 5b A. F 4 s B L 8 s b
(edteao B 4C. f 30 90 f 65 B 1 F 185b  + 9s R . 1
12 1. 1C
n oriprr
1.833. OcC
tit es B e
sersalsiel eici LIRESC BquO, acta LS ei) saedec icte cen c cces
E vise 13 a B A et SiB  v B  S t SE.R. tarla
IeC  BB L : bY EB SB 1 H 3cB. GBII L2B92 B 2B, SE B. 2 = Y Ct 1M. L1I1
1. Cn 3B B, 1423LCICP 1gCIC cuisp gE  CAEEteSNISIENE C
ICBI L TLHILHISICBBM eETO ∞IC EE ESE n t es adC
Adeoque Solidi Praperid  S ED merinibemtis maghieuido; dd magnicudinem
Hyramidis i FriansuloP a AV Eneumbonto es ui 3B B H  3B S B, 1ad = B B5.
Acque momentum iMiuss ad momenetm hiijiis (Tesfectu ejusdem A a) ut
BB A2 F ZBSB  F 3BS=B, ad Z hS B. Seu, excrito B ubique, (urpote
intinite exisuo, et ubique aequali;) duetisque omnibus in 6 (pro magnicudinibus,)
seu (pro momentis) in 12, (quo ttractiones rollaneur :). Magnieudo ad magni-
cudinem exit, uc 9h+ s hS, ad, 2 A Pc. momentum iljuS, ad Momenium
hujus, uc 28B A2 F 20h 15 F 7h52, ad 3h 52. Seu (relticuris minuscularum
valoribus. ). Magnicuda ad Maemicudinem uE) 0a tsSi sh, ad 2. s h: FF MOmen
cum ad momenum, HETE. A  A ZBIABAit B(SB, a 3 S  C
Cumue, hor ubique obcineac; eric. Solidorum omnium. L raperiis V DEP inSI.
sencium (.sire qua cocam Genereloidem lpectantui spo, sura spectant. ip(uis Por-
cionem,, ABGau BBP, cB. Bi _C. Jtgigudois ad magnicudinem omnium Pri
angulis,  a. P, insistencium a sire squae tocum spoctum. Demicireulum sire iptius
respeetiram, porrionem, ut. Be A, BBe B a C. Y ut Omnia da h =15. S, B: 2d
Omn. 2sh: eo spectancia. (De quo non ulera Coliciti lumus, urpore quo d in ca-
pire praecedente tractarimus.) Forumque omnium Momencum, ad Momentum
horum; UE Omn. 18 a = B f 20. a Shfois B: ad Onder 3. 52h: co srectantia.
(Duod ec supra invencum exat. ) 2 br 911pls 02.
BP. 131IXI
2B: (Teu 7 ad 3:) acque insuper ut
Omn. rBn B = 20 a sR: cad. Omm.. 3, s B.) Sumpris, lpristmetioe, provorriona-
libua
e1
15 si e  EE BB 31 PIB 
Sune hutem Omn. a B: (puta, quae portionem. A Bea Spectants ) hec e Vn.
sula ABBa Fg. 270. aciem habencis Ra momencum respectu Aa, (per SK.
PEOP. 19.) 2 e R = 2 a V R = F 3a R + a2s R, Adeoque Omn. 18 a 2 B:
= 36CR 3 = 36 aV R + 6 a R + +8 a 5 R
tiem, Omn. asB: eo spectantia; hoc est, Solidi ABBa Fg. 170. ex ductu re
ctarum bB in burlaetis momentum respectu A en (per S. HL. prop. 28.)  Z etR.
25C R3 + 20a0 X
555VR3 p 76 2  G) CICLest MosE cii
p18 d 5 R. = Y0 a se R. 1BB 15G) WWNSECS sS O
Similiter; Omn. 3 P B: Dise CR; Solidi A B Ba tig. 270. ex ductu rectarum bB
in B0 facti, momenium respectu plari A ra (per SC. prop. 18.) aC R  + à 52 R
LSS R. Adeoque Omn.
SB = 2C R3 + Z5VR 2 + s R
Momentum ixicur Ongula portionis Semieycloicis AB Ba aciem tatentis A e
respectu ejuldem Aa; elt ad Momencum respectira Onsula porcionis Semicirculi
BaA, aciem habentis Aa respectu ejuldem A_: UI ET C R3 = +6 aV R=
= 5 5VR= + 6 a R F 2B S A  10 s A ad Z C R3 + 35V R = S R; a1.
que insuver (ut modo dictum) ib 7 ad 3; hoc cst, uC 3C R3 + 2 5V R2 = 3 5R,
ad 3C R3 = 3 5V R 2 = s R: Adeoque ornino, ut 23 C R 3  16 a V R 2 - 2 5V R
+ 6a R F 28a S R, + 10a s R + Z53 R, 2d 3 C R. + 35V R 2 f 53R. Cum-
que Hoc polterius siC (per S l prop. 25) duodecuplum Momenei Onoulae B a A,
aciem habentis A respectu iplius Ra: Lric et priis illud, duodecuplum mo-
5t0IC
menei
D