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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 822, page id 851387705:0842
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De Calculo Centri Cravitatis. Cap. V.
Fi5. 166, - 3C R3 + 3aVR2 - ; 4 52 R + 3 si R 4 5 a s v; et respectu bBY, 30R.
70.
= = aVR 2-  25V A2 = = aSt R = 2 s R =  5aS V; per S F. PrOD. 1D.
Ergo Ongulae Segmenci Semieycloidis bV A, aciem habentis T A, momentum
respectu TA, C =, 2CRP = 3a~R2 4 85VR 2 - 3 a s R - 385 R = 5 a s2 V
+53V; e re(DeCtuL nan = 2 C R3 + 3aVR 2 + 350R= = 3aS R = 53 R
f = a s V f Z53 Vg. _ respestu BB V,, 120. R 3-  3a V  f 35D R = Z a s R = 35R
3as2V =  V. Adeoque (proprer magniuidinem, - e X F a v R + 35V K
2a5 = = 5; ver S F, C, prop. Placect) Distancia Ceneri Pravicatis d Y A.
=15C R3 = ∞6 av R + 815DR2 = 48 a 5 R = 385 R - 2445 v = 1850
 sustonDC R  72 aVR + 545. V R = 36a 5 = 24 5
=8R
650
23 F sR C = 3f0 R) - 4 a 520 = 3532
=3eA7 + 12aV R + 95VR- 6a5 = 453
22CR3 + 48a v. R7 1Y 27 50 R2 = 24 a s R - 105 R = 24 4 52 2 = 18530.
15. 111
184R3+. 72. a V R = 545VR = 36a5= 245
3 fV R - 4 26 V - 35~,c
=3 a BE+ T2 avR + 95V R = 6 a 5: = 4 53:
a bBV,
25CR3, + 30 av R2 + 45 50R = 24 a 52 R = 26 5 R = 12 a s2 v - 653V
= v-
= 18CR + 72 av R + 54 5VR = 36a5 = 24 5
3fV R = 4 a5~ = 35 V
=3CB + 22 avR + 950R = 645= - 45. =
350 R -4 a 5V = 3 53V
=3C R3 = 12 av R, H3 V R = 6a s = 45; Demisolidique correspondentis
circa TA, magniendo ad illud Ungula aciem habentis Y A, ut Z Z ad R. Mo-
 Cenerique sraritatis di-
sancia in semilolido, ast illam Ongulae ut 2 R ad = f
Similiter, Ongulae Seementi Semicirculi BV A, aeiem habentis ra; momentum
respectu ram eltus de R + 85V R + i s R - = s2 V; e relpectu bBY,  deR.
F3aV R F 3 5V R2 = 4 5 R + 1SV; per B F. PTOP. 16.
10c
Uneulaeque Tritinei bB A, aciemr habencis ra, momeneum respectu  a, Es R3
E5bR 35 R, 3a B = = 3CR 4+ ZaVRE =5VR + 3aSR  5 R
=5a s2v; e respectu, bBY, 3fR 3 abR = 5BR 35 R - = 5B2 R
DCOD. 19.
3C R3 A,  4V A E + 3 5V R7 = 3a 5 R + a5 5 R t 6a5v; Dex BF.
Adeoque Dngulae Scomenti Semieseloidis BV A, aciem habencis +a monien-
cum respectu rb,  3 C R3 + 3aV R + 55V R + 3as R + 285 R = 3 a s V
= = 53V; e respectu BBV,  C R = 3a V R 7 35D R2 - 3 a 5R = 3 s R
=5a 5 V. f ∞ sV;  relpectu T A, (idem quod aciem habentis Y A, momen-
rum respectu re,) C R3tSaV R2 + 350R 5 aS R = 35 R L 5 a sV
F 253V. Adeoque (propier magnicudinem, 13C RE = a V R + à sV R
Y 3 25 f 353; per 8 HsC. DFOP praeced.) Distaneia Centri gravitarisy X Xa,
=d7o R, + 9640 , + 95D R2 + 96 a 5 P + 58 5 R = 24 452 v = 18 500
a bBV3
2TCR
54c R2 F 72 aV R = 18 sV R + 36a5 + 24 5
= 42aV R= = 625VX = 48a S R  85 R + +2 a 5 v + 65V
54c R + 72 aV R f 185V R  36a5  24. s M v 1,
iZ eRF 48 aVR F27 5D L 24 aS R. 185X f24 a 5 D + 18sV
d. F A ∞ 115
5C R F72aV R  185V  2 36as F24 55  11.
Semisolidique correspondemis citca r a Magnimido ad iplud Ongulae, ut L V ad R;
Momencum respectu axis sui ra ad illud Onsula, ut 2 dd L; Dictantia Ceneri
Braricaris d 2o ad illaur Csnsutascub Z se ad : 8. Let dire. ologues
Simlliter, Ungulxe Segmeniti Semicirculi BV A, aciem habenris b B V, momen-
tum
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