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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 826, page id 851387705:0846
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FiB. 16C
De Calculo Centri Cravitatis.
Cap. V.
68, 170 lid a r0y E R - =2v R. = 30 as R = 8 s. R + 25 as0 + 752 v
27 a + 54a5 = 24 V R + 15 s2
2R + 12.V R 2 = 30 as R - 85 R = 25 a 5V = 7 5.
27 a + 54 a5 - 24 V R = 15 52
2 TA,
Adeoque ejusdem re.
spectu T A, momentum, 8a  R = F I= a5 R2 - Z V R3 + 73 52 R2 + 2 a 5V R
f 3652 V R.
Ouod ipsum, est eriam Momenium Ongula porcionis Semiercloidis ABBa,
aciem hrabentis T A, respectu Aa. Adeoque, si per hujus ungula magni
cudinem 2 fR2 = E sB R = Z a R2 + 2t 5 RZ F 1Z SVR (DeF S D. PrOD
peaeced.) diridatur: Elabetur ejuldem Dictantia Cenrri graricatis ab A_
af 33as R. + 195. R -- 32v R + 15a50 + 145V 63a R - 1 952 R + 320 R2- 145V
226a R +665R F 305V
126a R +665R + 3050
Si isitur cocius Semiereloidis Ara Ongulas spectemus: Juoniam hoc catu
CAt a = Z P, V == 2 R, e 5=0; erit Onsula Ara aciem habentis ra, momen-
rum respectu Aa 3 R. p. - 15 P; Magnicudo, 3 R2 P; Cemrique sravicaris ab
Aa distantia, 27 128 k=
aciemgue habencis Aa, momentum respectu ran 3 R.  2 - 13, R 2; Maeni-
rudos 3 R ~ = - 3 X; Cemrique fravicaris distancia à r 0, 3 R -
32R.
32. R3
d∞- 64 R2
a TA, 3R + ∞2 =6q R2: Momencum respectu T A, 5. R2 ∞ 2 - 3, R2.
Aciemque habenis TA, momenrum respectu A a, : P, ∞. - 9 R; Maeni.
cudo, 3 R = P; Distancia Ceneri Bravicatis, ab A a, +∞ - 64 k
637
Si autem ex Ongularum Forins Senrieycloidis A ra Magnicudinibus et NO-
mentis; auterantur respectire Magnicudines ec Momenta Ongularum ABBa: IIa.
bencur Ongularum bBr, Magnicudines de Momenta.
Pura, sI ex Ongula Ara aciem habentis ra, Magnicudinc Z R 2 F; _ NO.
mento respectu Aa, Z R 2∞2 -s R+; modo extribitis: Auterantur respectirae
Ongulae AbBa magnicudo, Ef R= + Z sBR = Z a R2 + 235 R2 = 35VR; 
momentum respectu A∞, 3a2 R = F 23 a SR 2 = 3 a5V R - 8VR3 F G= 52R =
= 35 S V R; supra tradica SC. Hlabetur Ungula portionis Semieycloidis bB2,
aciem habentis ra Magnitudo, 3 R P - Za R = = 23 5 R= + Zs V R, Teu (PrOP-
Dex  = = P = a e B = 2 R = 2,) Za R = - Z5 R2 - 3sBR; ejusque, relpe
Etu Aa momenium, Z R= D= - 3 a R = - 15 R a = 8 v R3 - 23 a sR 2 + 3 a 5V R
22S2 R2 = 2b 5= V R: Adeoque Cencri gravicaris ab A a distantia, a +
45RD2 = 180aRP + 180 a R = 512 R3 + 256VR2 - 164 5 R + 565 v
180R ~ - 360 a R = 6005 R. F +205V
Si ex Ongulae A r a, aciem habencis P A, magnicudine, 8 R2 P; e momento
respectu Aa, + R2 ∞2 - 8 Pa modo cradicis: Auterantur respectira Ongula
A bBa maxnicudo, 2 f R 2 =  SBR = 2 a R2 F I= 5 R= + Z5V R; _ momen.
tum respectu A a, 3 a R2 = IE aS R 2 = 3V R3 + 13 5 R= + 3a 5vR + 3 s V R:
Tupra tracica SC. Flabetur Ungula bBr, aciem habentis TA, magnicudo, 3 R 2Z
-2 a R2 = 1 5 R2 = 1 2 5VR = + a R2 - 2 5 R = + ZsB R; ejusque MOIENtM
respectu Aa, 3 R2∞2 =  R+ = 8 a2 RZ + 3V R = i asA2 = 22 52 R
Za SVR = 365 V R: Adeoque Cencri graricaris ab Aa distantia, a +
63R D 2 = 252. a R F = 256R3 f +28V R = + 252 a R = 765 R - 565v
252. RP - 504 a R = 264 5 R = 1205V
Si ex Ingula A54, aciem habencis A a magnitudine, 2 RD 2 - 2 X3; No-
menco respectu ran 2R, ∞. GPL; e respectu F A Z 2 ∞.- 5 pa; modo
tradicis:
820