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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 734, page id 851387705:0754
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De Calculo Centri Cravitatis.
CiaD.1.
Fig. Fs autem (per prOP. praeced. 5 O.) Sphaerici Sectoris integri BCBA
c50, maenitudo, 60 P = SV RP; (adeoque semisectoris magnicudo, 20= P = SVRP;
260. e Ongula Semiquadrantatis, qui huic respondet, (incellise, qui Sectori circu-
en
lari BC A insiltit, aciem habens Aa) magnicdo : c2 R = 3 V R
Ducta isitur distancia illa in magnicudinem; Elabetue momentum Sphaeriei se
Etoris inceori BC B A (respectu AXIS motS, Planire FangenLS, 7∞,) 3C2R∞ +
166 B~ = V R= P =3VE RD = ZVR2 P +8s2 RP: Semilectoris, 5V R2
=16s2 RP: Onoulaeque Semiquadrantalis, 2 2 R 3  3 52 R2
F respectu ipsius T a, momencum sphaeriei Sectoris incegri BC B A, 5C2 RX
16C= BP = 13 V R2 P = 5V=RP = LV R= P = 5s RP: SemilectoriS SVR= Y
ios RP: Ongulaeque Semiquadrancalis, 5V R. 3 52 
Et speciarim, qux tori Semicireulo intistic Semiquadrantalis Ingula aciem ha-
BenS Aa; (DFODIET V = 2 R, e s
0,) etZR3, e solidum convertione ta-
ctum, hoc est, Sphaera intcora, 3 R2 P: ee Semisolidum, seu Hemispharium L P. P
Diltancia Ceneri graricatis a r a vel. Y A, R: Momencum Ongula respectu ra, vel
EA, 3 RE; Sptiara, Z R3D; Fremisphaerii AD~; ZR3P.
Deinde (Der PrOP. PracCd. SR.) Coni intcori B BC, (conrertione Prianouli
52 ∞
BYC, circa Aa,) magnicudo est 
29
L∞: Ongulae Semiquadran.
calis, Er. HLOC ett, Si V CC Cupra C Centrum, P s P,  5 P, R 52: Siue in
P
tea Cenirum; . 2 ∞ v- R 2∞ V k
6R
22
R
72R
Est autem (per 6 hujus) Cencri gravitatis d D C distantia, ZN: FTOC CR
R = 2V, SI FuPra CCHErUM; _ 30L ER, E intra Cenrum. FF utroque casu
uldem 2 r a dictaniia, 2R - 3V = R = Z N: AIque a LA, a R + Z = R F3 v.
Ex proprerea (ductis magnicudinibus in dillantias) Momencum, respectu ixtius
Ton Coniinceeri BCB, 5.L 5 P L ; Semi conis 1. L 5 X + =
a
8R, 
drancalis Ingulae Eus. P L LV2: vet
Hoc elt; si tupra Cenrum,
SSVR 55; Si intra Centrum
5  + 35vR + 551.
7R 3V
2+R
R
7R - 30
1522
N = qua 35 2g
18 as D, 2s R = ENSV.
P - 40R - 35.
148 X
52P, -SR-
7X + 40 R + 35 ∞ = 7 N + 40 R + 35
24.R
48R
EE, respectu iptius FA; momentum Coni inceeri, semi coni, dt Semi.
2
52
Qactrancalis Oneulae, 3 x S P + 8R. 3 L N S = P + 26 R 3dX s R F B ~ S: vel
R + 30
24 R v 524 R + 30
48  + s P, 3. 4 s R + 8  5 v. HOC et, Supra Centrum,
R2 4V R + 35
24 X
3. p, e =40 Re + 35 . 8, iis  - 55 v  + 3s0; vel
Intra cencrum = R + 4v R = 35 29
+3522R - 15a 24 R
R + 4v R - 35 5 8
48R
us R
Flaec itaque momenta Coni, Semiconi, Ongulere, BBC, BV C; momentis de-
ctoris, Semilectoris, Ingulaere, BCBA, BC A, respectiris; Subducta, Additare
prout vel supra vel intra
Sulaere, BB A, B V a momema respectu iptius r an LV R2 P= 3s R P + 6 v 
E
+ 8P, 6VR2 P = i s RP + i s vD +
51 = 5v R + 3s v R + 552.
16P, 50_ = 1 s2 R. + 3 5. v R +
D.