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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 735, page id 851387705:0755
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PFOD. XVI. DeCalculo Centri Cravitatis.
E respectu iptius F A, 30 P2 ~ - 852 P~ + 152V 4
13S=RF = 2 52 ~Z-
352 V R = 354.
4 
 33VR3 = 852 R2 + 65 = VR = 852 = EV R2+
Adeoque, momenta per magnicudines dividendo (puta, Ongula momenta, per
magnicudinem Ingula, SV2R F 55 2~ = 5VR 2 - 55 2R  5s E V, PrOP. praced.
S R. inventam,) habetur distancia Ceneri gravicatis Vngulax B V A aciem ha-
bentis Aa, (adeoque e Sectoris, vel Semisectoris correspondemris,) a ra,
P + 80R: = 4 5 R + 4 59:
TA, R-
8u R. = qui R + 45
8uP: - pe t 45  80N - 4. Pe + 4  + R - b
Vel (quod eodem recidit) a T a, R
20R + 3s
quk = a5 Vi d DC
6R 30
 q0R 45
4 R. + 4b + R - B-
6R - 30
qu + 4s
3h52
Boxe 4Rt q0
FA, 
360
4uR + 4 quR + 4 uB 4 R + 4B
4R + 4B R + v.
Ex (restiuendo magnitidines) momentum (respectu iptius BV) Sermenei
Sphaeriei BBA, 3V P2 D - 5 52 RP-
547
24C; Semileomenii BV A, SVR2~
1o: de corresponctentis Vngula, J V R3 - 3 52 R 2 - -1 54
Sed ee poltune haec eadem, sic alias haberi.
Cum enim (ur oltentum elt proP. Praeced. P. V.) Semi Ouadrata rectarum BV Fie
d huic parallelarum semilesmentum A V B complentium; linc rectis VB, dc. 164.
(tig. 264.) Parabola portionem A V B complentibus, proporcionalia; d quidem
iplIS VB, Cc. in E R ductis Sigillatim aequalia; acque in eildem a T an T, A, DC
distanciis: Eadem erunt respectu ixsarum ra FA, DC momenta Semiquadran-
calis Ongula (quam illa complene Semignadrata) Semisesmento AV B insistencis;
acque Prismatis porcioni Parabola a Ve insistentis, quam illa complent parallelo-
1
a
gran
Ci, e 73) ab iplis 7 an F A, D C, (planis) respectire. Hoc est (ver S hujus)
quantum inde distac iplius porcionis Parabolae A V B cencrum graritatis V.
FIt aucem Semiparabola AAC magnicudo (per 6hujuS) ZACXC A = Z R =
ejulque Cencri graricatis ab Axe C a distancia (per 8 hujus) SAC. = 8 R; adeoque
2 7 a, R F 3 R = SR; d T A, R = 8 R = 8R. Adeoque iphius momentum respectu
DCB, est = R3; respectu ra, in R3; respectu F A, 13 R3.
Icem Semiparabolae Bab, magnicudo ? abx bB = 2 V
3
24
3X: Centrique
Pravicacis d Ca distantia 8bB = 8. N: (adeoque d ra, P L3 X; a F A, R FB; prouc fuerit
Tupra intrare rectam C B.) Adeoque momentum ejus, respectu ipsius C.0.
ei Cui
addicum momentum parallelosrammi V. C. B B, hoc est (proprer PB, == _, 8 C b = X -
+ s
Cenrique gravicatis d C a distanciam, 3BB = 3 N: )
 extribet porrionis V BDC. momentum respectu iptius C. A
2 52 N
2. Hujusque propierea portionis V Ba C (propter
B N a d
magnicudinem v R - = =) distaacia Cenri pravicaris a C. A, est 12x R:  4 v
6 R2 - 3 ∞ 2
22.  - 4 4 V. Ade0q; d 7 a, R.
6N2 - 342
R2 - 3 
12R - q2 Vi d TA, R F 12 R - 4 
(DTOut
supra
A
160
4V R + 45
2 X  R2 -