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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 852, page id 851387705:0872
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De Calculo Centri Cravitatis. Cap. V.
F13. 177, 4 S R - = R3. Unde Si Subducatur portio ec d s; hoc Cst, Factum CX CB = E, in
1827 163, F Z a (ti8. 269.) hoc C, (per SF. PrOD. 25.) in 3a s - 35 R = q SB (potitm
a = ∞. = a E areui, et B = a = = CE;) hoc cst (DOLIIO a = =  = E, e B = H - v. 1)
in 5E R = ZE R = 35 R F = 5 R - 35 _; HOC elt, In  Z R = = 5 R = 3 5 _; Dem.
Des SE P R = 1 53 R = 2 F s. _: Relinguieur porcio de8 = - E R + 3E 5 X + 1 5. se
Ec porcionis Colidi b= B Seu Cr e, respectu ra, momentum cst, = a R = = -8s R2
=ZB R3 = 3 s B R, Der SO. PrOP. 18. (POsItO ZE = a, _ a Z. =B;) HOC CA,
(potitis a = = ~ = E, e B = R = ∞,) s 2 2 R2 = 3EP R2 + LG2 R = - -8 s R=
3R 2 + 3 a R = 95 R + 3s _ R; SeB  D = R  - dE P R= + + E R -  5. R.
3 Ra- + 3 N R = 3s x R. Adeoque momentum Colidi d FS (DEOPICT E = 0, e
_ = , e 5 = R,) 6 D2 R 2 = a R2 = 3 R4, (CV, s R 2 ∞2 - 18 R 4. FF PTODICI-
ea, Momentum porrionis deEd (respectu cjusdem 70) elt 3EZ R 2 - + 32R
+ R4 = 2s R2 = 3 ∞ R = = sX R. VndC lI ANIFETALUE MOMeNtM PORCIONIS.
ccd 3; hoc est, factum ex c3 =E, in momencum segmenci semicirculi F. Z a
(ti8. 169.) respectu iptius Za; hoc CA (PerS L. PrOV. 25.) in L a R = = = 5P=
FZSBR = Z s (DOFIEO XE = an _ a Z = B;) hoc Cst, (DOLII a = = 2 -E, 
B = R = 1,) in 3~ R 2 = 3 E, R 2 = 35 R 2 + 3 5 A2 - 2 5 _ R - = 5 feri, in 8 Y R2
= 3ER 2 - 2 5 4 R = 3 5d; Dempe BER = D = = E2 R  = 2 E 5 N R = 3E, S: RCLIB.
quicur porcionis des, Momencum (respectu eju dem Ta) : 52 R - = R. +. : 5 P
=3∞ R = = s X R + 3G5 N R = LE5
Xic. 170. Hloc icaque, per magnicudinem, (modo invencam,) divisum; extribet ipsius
deg (porcionis solidi) distanciam centri gravicaris a 20
DE2 P2 - 9 R2 + 952 R 2 - 8 + R = 4 5. a R + 18E, 5  P + 12E5
9E R = 1855Y + 95 R = 9R
8 ∞ R3 + 4 S N R == +2 E5
95 R = 1855 X = 9s R = 9R,: Adeoque d Cd,  8  P. + 4 s a R -= L2 E 5
OE2 R. F 18E5 N f 9s2 R 9p
Duod in magnicudinem ductum, extribet solidi des momencum respectu cd,
3a R3 + = se X R = 355 (BOSItIS, E = DF. H8, 169. = c8 =07 = aE fB, 17, 0
et N = CZ = E0 = 47; e s = F Z;) Vet (Tubstituro s pro s, qui Tc linuS ar-
cus Ba tig, 169. = ES f3. 170.) momencum timilis solidi a0y respectu ad,
3 N R = 3 2 ∞ R = L E,03.
Fi5. 182, Et consequenter; similis solidi A07 fig. 283. (ex ductu rectarum oy in 79
183.
respectire) momentum respectu AS, (uipoce prioris sexdecuplum, propier cum
lingulas dimentiones, cum distantiam, ut 2 ad F,) 33 ∞ R3 f 18 ∞ X R = 15, 503:
HIOc Cll. (Dotito a == 2E, propier arcum semicirculi duplum respectiri arcus in
quadrante; et c = 2 x, propier chorctam arcus an duplam sinus recti dimidii ar-
Cus; de X == 20, propter subcentam complementi arcus a ad semicirculum, du
plum linus complemenci dimidit arcus ac quactrancem;) 18C R3 = 3X cR - 3a X
Hoc ilaque per 2 Pe divisum; hoc ost, 30 R + 50X - ; extribet (uc jum
oltensum elt) aexregatum omnium a s, seu rectangulorum o7v F5. 183. adeoque
(prOPIer A7 = ZR a) hujus duplum, est aeoresacum omnium a s, leu rectan-
sutorum Bbo fis. 182. Ec propcerea hujus duplum, seu illins quacruptum,
BCK + 367  12. a
E =Omn. 245: H8. 182. Adeoquem li rotam A F (pC
Cemus (Propter 6 = 2R, e X = 0) eruine (qua co spectanc) Omn. 2 a 5:
64 R3
BiB. 177. FrEO (proptex Omn. a: = 2 a c = 16CR +, 8 a X R; _ Omn. 5: = 38
2F0NI e OMM. 2a 5: = 336 R2 + 50X 2-
2 aX
3R ut jam ostentum
S.) Omn. a 2 +. 2 a5 + s2: = 2. a. 9 4 3c3 -- 136 R + 30 21 + 8aX X
= 227
0