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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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PFOD. XVIII. DeCalculo Centri Cravitatis.
ErGO; Omn. Za R 2 = 35 R2 + 3 5V R = ; 53: HOC est, Momenum Solidi FiB
ABR, respectu F A; Clt, 242 R - 385 = R2 - 3VR3 = 55 = v X.
269
Adeoque, propiex iptius magnicudinem + a R = 2 s  R, (per SH. ) Distancia 270.
Ceneri Bravicatis d T A, P - 80R - 45 R + 45V
20, R f. 80 X - 4 5R+ 450 - p + 4v R + 452
da2 -95
cf
P-408+ 450
Spectu ra, momencum, : a 2 R2 = 18 s R 2 + 3, V R= +  52V R.
Si aurem Solidi hujus ABK momenta, ex respectiris Semicylineri A Z Ba mo-
mentiS auFCTANEIE: Relinquuntur respectira Solidi A B Ba momenca. FIt autem
Semicxlindri hujus magnicudo (ex ductu Semicireuli AD a = = RP, I aB = a,
a P; Centrique graricaris diltantia d TA, vel ra, AC vel C a = R. Adeoque
iplius respectu J A, vel ra, momencum, =a R2~. Onde subductis, Solidi ABK
momencis, modo tracitis,  a = R = - 8s R2 - Z V R3 - 3 5= V R; _ = a2 R -
385 R 2 = 3VR3 = 3s V R: Relinquitur Solidi A bBa momentum respectu TA,
a R2 P - = a R= + 565 R = 3y R3 f 5 52 VR; e relpectu ra  a R 2 2 - = a 
= 38S R2 = ZV R3 - , s= V R: Fujusque propterea Distancia CenEri GraVI-
catis (proprer magnicudinem L a RZ = = a2 R + à s2 R, per B R.) à FA,
R + d~R 4 5 R + 4. 5 V
da  - 9a F 952
4V R = 452 V
OaP = dC)
=R +. +2 R + 45 V
92 X = 9ef id 20,R.
80- 4 s R + 4 52 2
daD - 9a + 95
Si vero eadem solidi ABI momenta, ex respectiris seomenti semiestindri
AKBB, auterantur: habencur respectira Nomenta Solidi, ABB. FR aurem
Tegmenri semicirculi A B V magnitudo = e R F Z5V (Der S F. PrOD. 25.) quae
ducta in bB = a, exhribet maonicudinem segmenti Cylindri AKBB, : C a A
FEa50: Cenrique gravicaris diltancia (urpore eadem quae sexmenci demicirculi
ABY, Per SC. prOB. 5.) a FA, R= 3C R + 35∞;
Sck + 350
Adeoque momentum respectu FA, = ea R = (= = a R = = = a 5 R =) =  a 5VF
= = a 5; respectu 7a, =C a R = F = a 5VR  3 a S; (eadem quae plani A BV mo.
ductis respectivis solidi ABIE momencis, mode
ribIcIS, 2a2 R= = -85 R = = ZV R3 = 35 VR, et 4 a R
585 R= + 3~R
+3 sV R: Relinquicur Solidi ABB, momencum relpectu TA, (hoc cst, Omnia
a5v, sumpris 2 arichmerice proportionalibus,)  a R = = a5 R + 565 R f 3~ p
f325VR F3 S V R = 5 a 53; _ respectu 70, (hoc elt, Omnia a sB, Sumpris V
arichmerice proporrionalibus,) L a R 2 = = a 5 R  = 36s R = ZV R + ; a 5V k
==Sv R + 3a5. Adeoque (propcer magnicudinem, a a R = 3 a sR + a s: se
F3a5V, per SL.) Solidi ABB, distancia Centri Gravicatis d FA, R +
8V R -4 52 R2 F 4 S V R - T2a5
Da R = 1BaS R. F 9s2 R ( 28aS∞
A
4V R 2  4s2 V R = +2 a 5
96 R F. 18aSV
ro,R
8V N- 4s R + 4S2 VR - +2 a 5
92 R - 18a5R + 9 5e R f. 18a52
Fommone Rra Solidum, (.Sive SpectetX uE ABBO, SiVC UL ABB, perinde est;
momentum habet (prOpter a = = P, v = 2 R, 5 =0,) respectu P A, i5 R 24
f3R2; respectu 7a  R D2 - 8 Ra. Centrique Graricatis distaneia a Y A,
est. R + O4 R3
982i d 20 R.
64 R3
22
PorrO; eadem ABV Segmenta plana, dollaun Ab R complencia; leu, Si 1
BCR = 35V, (per S F. prOP. 25.) ab Aa, diltant ipsis bB = q arcubus arithine.
rice proporrionalibus: Adeoque corundem omnium, hoc est ipsius AL K Solidi
Momentum respectu Aa sunt Omn. Z e a R + Z a5~; seu Omn. 1a R = 3a5 H
F Za50: Sumpris a arichmetice proportionalibus.
Sune aurem, Omn. a: = 5 a (Der PrOP. L.) Adeoque Omn. Z a R: = 3 2 P.
Et Omn. a S: hoc e, Omnes s, nilineum a B. complentes, in an coruncem
tEFL