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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)
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De Caleulo Centri Cravitatis.
Cap. V.
Atque haec demum, d BV, diltantia; in maenicudinem ducta; exhibet momen-
259, cum, respectu rectae BV, Segmenti BB A, 353 - a R f s R~ F aVR = 25VR
160. F52 = = e R f aVR - 55. PF semilesmenti BVA, = Z e R + Z aVR = 25.
=+ZCN R + 35ZV.
Deinde, Frianouli BBa, auc BV a distancia Cenri grariratis a 7a, est 2B
ER - ZV: adeoque d Y A, 2 R - Zh = ZR f 3V. Ouxe in magnitudines
(sB, ZsB,) ducta; exhribet Prianguli BBa, momentum respectu 70, 3sh = ZsR
352R = 35 ~2= 35 R = 3 5VR - 35; e, respectu YA, 2SBR = = 5B
= 35 R7 + Z5VR = 352= Zs R = Zs VR  Z53, e Frianguli BV a, momen.
cum respectu rectae T e 3s h = 3s R - 35V R - =5; _, respectu recta L A,
SBR - =5B = 2 5 R2 = = 5 ~ R +
13
Oux quidem momenta, addica respectiris momenris Segmenti BB A, e Semi-
seomenti BV A, (SL inventis) extribene Sectorum Ba B A, B a A, momenta re-
spectu carundem ra T A. Nempe, Sectoris B a B A momencum respectu r a,
a R F Z5 R = Z5VR = fR F ZSBR; d respectu rectae T A, a R2 f =5 R2
F35VR = fR = = sBR: EF Sectoris Ba A, momencum respectu rectae Ta,
2fR2 F 6SBR; _ respectu TA, Z F R =  ShR
Fodem modo; Frianguli BCaq Centrum prariratis est in recta a P, qux Z
puncto a ad medium rectae BC ducitur, ejuldem a e duas terrias verlus a abscin-
dens. Fst aurem ipsius medii puncti B, eadem altitudo supra ra, quam habet
rectae C. V medium punctum r; nempe ay = R = = X (prOuE Supra intrave Cen-
erum fuerit V punctum; ) hoc ell, (uctoque casu) a y == = R = =2. Adeoque
distancia Cenrri gravicaris TriansulI BC an d ra et 747 = R = 3 v; aeque 
EA, R + 3V.
Adeoqué (propier magnicudinem Frianguli unius BC a = = SR, ee simul am-
BOrum 2 B C. a = s R,) erit unius momentum respectu rectae r a Z5 R2 = LSVR
e simul veriusque sR2 = Z 5VR: FF, respectu rectae T A, momentum unius
25 R +55V R; e Limul utriuIque sR = Z SVR.
Duxe quidem addira momentis sectorum BCA, e BCBA, nemDC Z a R=
F3SR, _ a R2 =Zs R= (per SI.) exhibent momentum, respectu rectae ra
Sectoris Ba A, Z a RZ F 35 R = = ESVR = EF RE + Ssh R; e lectoris Ba B A,
fR2 + EsB R: FF respectu rectae TA, momentum Sectoris B a A, Z a R2 = ZS R
F55VR =Zf R = =sBR; et Sectoris Ba B A, momencum f R = 3sb R.
UE PriUS.
Aique haec demum momenta, per luas respectire planorum magnicudines (: F R,
SR,) divila; exhibene ucriulvis sectoris B a A, B a B A, Cencri graricaris diltan.
riam dr an R + ; et d F A, R -  p; Adeoque alcicudinem ejus supra Cemrum
C, vel CD rectam SB 25 R - 50
3a +35
Similicer, Prianguli ABV, magnicudo, cst = sV; distancia cenri gravicacis d
A, clt Z0; adeoque, d r aq 2 R = 3V; et propterea ejusdem momentum respe
etu 7a, 5VR = 3 502 = 25V R + 353: e respectu T A, 3522 = =5VR -=
5
Ouxe quidem momenta Subducta ex respectiris momeneis semisesmenti BVA,
nemDC, Za R2 = = 5 R2. F = 5V R = 3 53, per SL.) relinquit Scsmenti AB A mo-
menuim respectu Ta Z a R = = Zs R= + 65VR = Z C R2 F 550 R; et, respectu
PA, ZA R =5 RZ
55VR = ZCR E = E5VR.
Reque taec momenca, divisa per sectoris A B A magnicdinem, L C R (per 5G.)
extibent dillanciam Ceniri pravicatis dr a, R f =; _ d Y A, R - ; adeoque
supra DC,
5V
30 3a, 35
Pariter, de Scementoa Ba judicandum; puta, Pro areu AB. = a, substicuendo
arcum reliquum ad Semicirculum a B = a = =  = a: _ PrO LNuverSO A V = V,
Tubstimendo aV = h = 2 R - 2: item PFO T A tangente contermino arcui AB,
substiuendo ra tansentem concerminum ips a B; et, vice verta, T A prO Y a
Ouippe
F18.
1.