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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 807, page id 851387705:0827
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PFOD. XX. DeCalculo Centri Cravitatis.
lidum 2a R P F i 5 R P + 3 5 2P, et semisolidum, 3a RP + 2L 5 R P + 5 5V ~. FiB. 169)
Similiter, Segmenci Semicirculi a Ba, Momencum (vel Semiquactrancalis Sp
gula) relpectu ra, et Z a R 2 - =s R 2 = EsB R; e relpectu IA, : a R=
F3SBR; per SN. PrOP. Z5. EAque LegmenE Frilinci Restimei BB7; Momen-
cum (vel Semiquadrantalis Ongula) respectu 70, Z a R = -- 25 R 2-
A
e
respectu TA, 3 L R  - 3s R = + + SBR; Det BF. PFOP. 27. LrBO (quod ex v
trilque aspregacum est) Segmenci Semieseloidis bBr, momentum (seu Semiqua
Trancalis Ungula) respectu Ta, Za R2-  25 R2 = 35BR; e respectu F A
Za R2 = 2 5 R =  35BR. HIOC est (PrOpieK a = = ∞ = d, e B = 2 R - d
respectu 7a, 3 R= P = 3a R = 72 5 R + 35VR; e respectu T A, 3 A Y
Za R2 = = sR : = 2SV R. AdeOquE (PrOpTeC magnicudinem S B. invencam,
2 a. R = 25 R = 3 R P - 3 a R = 3 s R,) Distancia Ceniri gravicalis d ra,
X
28a = 185
205R - 55V
105 R-550
D2 = 18a = +85 2 F 1, 3R+
18a - +85
dP = 18 a = 185. Solidumque ejusdem cirea r a Conrertione tactum Z a R P
=35 RZ =  ESBP = ER~ 2 = Z a RP = 235 R P F 135VF; e Temisolidum
8a R - 85 RP - 2 SB R = 16R P2 = 3a RD - 375 R P +  5VD: AEque, Cir-
ca Z A, Solidum Z a RP = Z sRP + 3 sBP = 8 RD2 = Z a RP - =L 5R∞
= 352P; e semisolidum, 8a R P = 35 RP + 2 shD = 16 RD 2 = 3a R F
45RP = 4522.
P
Tiem, Segmenei Semicireuli BV A, Momenuum respectu 20, LC R2 = 3SVR F.
+ 35; e respectu TA, ZCR 2 f =5V R = =5, _ respectu bBV, - 2C R2
= ZaVR = 5S; Der SC, R. PrOP. 25. Momencum aurem Segmenti Trilinei b B A,
respectu 70, -- ZCR = + aVR = Z5VR L 3 a 52; e respectu Y A, - Z CR 2
= a~ R + 25VR = Za s; e respectu BBV, 3C R 2 + 35~ R = Ea s; DCt SF.
DEOP. 27. Momencum igitur Segmenti Semieycloidis B V A, (vel Semiquadranta.
lis Ongula correspondens,) respectu =a, - 3C R + av R + 45VR + 3a5 + 55;
e respectu Z A, = a c R2 + a v R + 35V R = = a 5 - 3 s; e respectu bBV.
aCA 2 + Z aV R + 2 sVR = = a 5= = 8 53. Adeoque (propter magnicudi.
nem SB. inventam, = = C R F a ~ f = 5~;) Distancia Centri graritatis d 20
=3ek + 12a0 R 4350 R +6a5 +45, a TA, =30 N f 12a2 R + 912 R- 6a5 - 45
-6C K + 12aV + 650
bBY, 3CR + 6a0 R + 950 R - 625 = 25
= 6eR + 12 aV +650
cirea ra factum, - 3 c RP + av P + : 5uX
=de R + + avP + 550X-
= =CRZ = a v~ = 2522-
+ Za0P +3508.
+ 5a0P + 3508
a52 D 53∞
4R 12 X
25
+R
452∞
eX
a5 P + 2537
522
2
53∞
E K
538
3
6ek f 22aV + 652
Solidum ejuldem convertione
S2F, 53∞
eA
3Xi ee temitolidum,
Eiem cicca TA, Solidum,
E; e semitolidum, = J C R P
L: Denique circa BY, Solidum : C R Z
6k
53∞
64
et semisolidum, se RD L : av X + 350X
Fadem habentur ope Fraperii BBa V. Ouippe si ex quadrilinei BB a A
fig. 266. auteracur Fraperium bBa V, reltabir Semiey cloidis segmencum b V A:
rijusque momencum ex momento Ouadrilinei subductum, relinquit segmenei
b Va momencum, hve respectu recta Y A, tire ra; unde et reliqua conte.
QVIEHTUT.