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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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PFOP XVIII. DeCalculo Centri Cravitatis.
Dlani AZC, = 3 C (3 F 3 aV R = 8a5 R = 185 R F 5a sV; distanria C entri
Gravitatis ab ATa planO = 120 R + 12 a v R - 6a S R + 25 R +6a 5V
de X + +8a 5V
Portionis ABR; Magnicudo, : a R = = 5 R = = CFR: MOMENEUM FCSpC. R. M.
Au FA, = a R = 85 R7 - 3V R3 - 3s VR; respectu 2a,  a R = 1 sE R
+30 _ + ; so e; dillantia Ceurri Pravicalis d Fa, - +V _ + 45. v
2 ra, R. + +v X F 4 F ~. Momenrum respectu Aa, se A. + ds vN + s a X N.
= as R; distancia Ceneri pravitatis ab Aa, 3C F +3 5uR + 4 a - 6 as
6a2 - 65 = 6e
Nomentum respectu plani A Ta, ZC R3 = , 8S R; distantia CeHEri STA O.
vitatis ab Ar a planO,
Portionis ber; Magnitudo : ae  = i PP: Momentum respectu 7a
a2R 7 = 38 5  R 2  ZBR = 52 BR; respectu Y A, a a2 R2- 33s2R ?
= 3BR3 = Zs2B R; respeCtA PF, + a R3 = 3 s3 f  SBR 2  3a 3 R
=as R; respectu plari ATO Z a R3 = 3sR3 = ros R; distancia Cen
eri Cravicatis d ra, R = 4 B R + 452B
ab A a
34 = 952 i a FA, R +
3 a R 2 = 35 R2 - 3 s B R  4 a 3  6a 52
12a R 2 = 225R2 = 25
6a2 852
P + 45 B
9a 95
i a plano AFO,
B
2
Adeoque exhibentur, in utroque solido; cum eo quod sit ex AF a R.
fieurae Sinuum versorum rectis bB, in B0 Fisurx dinuum rectorum
respectiras rectass tum eo quod hE ex Ar a Figura Arcuum rectis
DB, in BV, respectiras semicirculi rectas, corumque partibUS OX-
Dolitis; Tum Magnicudines; cum Momenca respectu planorum
aliguoc expositorum; et Centrorum gxaritatis 2b illis planis distan-
cix. Ec proxterea proprer exhibicas Cenerorum craritatis distan-
tias a tribus laltem planis non parallelis; exhibentur (Per PTOP. 26.
Cap. Praeced.) ipla Centra gravitaris.
111
Ouae que de expositis dicta sunt; ad alia Facile porerune accommodari.
Et quidem quae de his solidis cractuncur, ad Prorracta, et Contractam
Facile transferentlir.
Ouxeque de solidis fieuram sintium Rectorum unius Ouadrantisre.
spicientibus, cracuntur; eadem ad Solida Fieuram Chorcarum Se
micirculi similiter respicientia, transferentur. 
Dper ora Fipuca linuum rectorum eries incelliealut seslindri (Pritmuitoe)
A
a recti portio; ea ratione, ur super lingulis B0, tiguram complencibus (arcuum Fig
arichmerice proxorrionalium sinibus rectis,) alcicudinem habeac respectiris Bb 169,
(corundem arcuum, eorumre complementorum ad lemicireulum sinibus verlis) 170.
aequalem. Auc etiam (quod eodem recidic) super Rra tigura Sinuum versorum
(Arcuumre) insiltens ad angulos rectos, in ra recta, Fipura Sinuum rectorum
erun promoreri incelligatur ad P A, solidum deseribens columnare (Cylindra-
ceum dicas, Prilmaticumre, perinde est,) Paralleloxrammo P Aa r incumbens; quod
sinvola superticie sinvola currae A d r ed angulos rectos insistence, secari POrrO
incellisatur, Solidum a dra abscindente.
Manitestum est, ex constructione, Plana Solidum hoc complencia, rectis bB
intiltentim Pacalletoriamma elte rectangula; ip lib. bB0 rectanertio abique equa
BCC CC +A1