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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 806, page id 851387705:0826
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500
DeCuuu Centri Cravitatis.
Cap. 1
Fjo. 167 coridem Lliangulis siguram circumseriptam complentibus, Wt O a A, Ta X, _c.
268, 173, aur ecam tixuram inseripex ec circum seripiae intermediam (uipore parcim inscrip
Caus partim circum eripiam) complenribus, uc Y a P, eec. (qua rectis aZ, etc
ut illorum axibus repraesententur:) Intelligenda erie Similiter Semierclois ex 10.
tidem constirui Ouadrilineis A aEX, X56Z, ec. vel etiam (quod eodem recidie
sectione in intinicum continuata,) ex corideur Fraperiis tiguram inscriptam com-
Plencibus, ut O ZEa PZ 6E, _cc. aur circumseriptam complentibus, ut A9E a
X 155, dec. aut quae tisuram partim inscriptam parrim circum seripiam compleni,
Uc Dy dE, _c. (quae rectis 26, Scc. ut eorum axibus repraetenLEntUT.)
Cunque haec Frapezia lingula, ex Friangulo limul e Paralleloprammo con-
tistunt: quorum illud est respectiro Semicirenti Frianouto aequale, hoc autem
respectiro Parallelosrammo Frilinei Resticuri fig. 270. lunique in eildem lire a
a sive aT A diltanciis: Praperii cujusque momentum sive respectu recta 20
sive respectu rectae T A, (aliarumre hisce parallelarum) aguabitur Nlomentis li-
mul sumpris eorundem quibus aequantur Trianguli Parallelogrammique.
15. 166, Cumque hoc de lingulis obtineat, obtinebit de de limul omnibus complentibus
167, 168, vel cocam A ra Semieyloidem, vel iptius portionem aliquam, ue ABBa, DB7,
bBdd, ecc. Puta Momencum Porrionis Demicyeloidis DBa V A respectu rectae
a vel TA, aequale erit momento Sectoris Ba A, et Ouadrilinci tig. 170.
bBaB A, (respectu rectarum r a vel F A respectire,) simul Tumpris.
Tec similiter ostendetur, Momentum Scgmenti Seneveloidis AB V, aequale mo-
mentis Sesmenti semicirculi AB V, et Segmenci Frilinei H8. 270. ABB, (re-
spectu rectarum ra, Y A, vel hisce parallelarum, respectire,) simul. Aequalia
liguidem tunt, acque in eadem diltantia.
FII autem Semicireuli ADa, respectu TA, OMenEM, a R2P, (DeF SI.
PrOB. 25.) Ec momencum Frilinei Resticuri, ejuldem sesquialterum seu ut Z
ad 2, hoc est 3 R2 P. per SC. prOP. 27. Semiescloidis ipitur, respectu ejusdem
Ta momencum (urpote illis simul sumpris aequale) ad illud Sectoris, ut 5 ad 2
hoc est 3 R2P. Cunque hujus magnicudo sic (ver S B.) 2 RD; distantia cen-
tri praricatis Semiereloidis d ra, erit 3 R. Adeoque à FA, 3 R. Ejusque re-
spectu T A momencum (magnicudine in diltanciam ducta) 8R2 P. (Ouod X
quale est momentis semicirculi Frilincique Reltituri, DrOD. 15. ec 17. inventis
limul Tumpeis) Frgo et Semiquadrantalis Ongula eidem insistens, aciem habens
ra, et 8 R2 P; aciemque habens Y A, Z P3 P. Solidumque ejuldem conrertione
eirea ra tactum, 8 PP; e Semitolidum, is AP3: Arque eirea Y A, Solidum
ERP2: e Semisolidum ,B R F2
Acque si ex Paralleloerammi A P ra momenco respectu ra vel Y A, hoc est
ex R24
(proprer magnicudinem Z P X 2 P = PP, distanciam que Ceneri grari-
catis R;) auterarur Semiceloidis momentum jam inventum; habetur, Comple
menci AT F, momentum respectu ra, 8 R? D; respectu TA, S R = P. Adeoque
propter magnicudinem modo inventam, a RP,) Dictancia Centri graricatis ejus
dem d 78
R; acque d T A, ER. Irem Semiquadrancalis Ongula cidem in-
liltens, aciem habens Fa, 8 R = ~: aciemque habens F A, 3R 2 8. Solidumque
guldem convertione cirea ra tactum, 8 RD2; ee semisolidum, io RP: Acque
cirea TA, Solidum s RP 2; semilolidum, S RX=
Icem Sectoris Ba A momencum respectu r0, cAt Z f R 2 = 3sBR = Z a R2
+35 R2-
50
momentum Z fR=
DeT SMI. PrOP. Z5. Et Portionis Frilinei resticuri DBa BA
=E SB R = 3a R2 F Z5 R 2 = = SV R, Det SD. DrOP. L7. FYBO
Portionis Semieycloidis bBa V A, momencum respectu ra (ulpote ex illis aggre-
Bacum,) 35 R = = i S BR=
Ea R2 = 235 R2 = 3 5V R. (Idemque eAt e Vn.
sula Semiquadrancalis eidem intistens, aciem habens ra.) AdCOque (BFOPIEF
magnicudinem SB. inventam, 3f R = 3 a R F 3 sR) Diltantia Centri gravica-
iS 2 74, est 8R + 5 sB
25a R = 255 R -
5SB 2Ld A  115 A F 552
8
18a = 185
550: Aeque d F A, 3 R -
18 a F 285: Ejusque respectu F A momentum, (vel Semi-
quadrantalis Ongula eidem insistens, aciem habens T A, ) 2 f R 2 = 5 5 B R = 2 a R
F I2SR2 +, E5V R. Solidumque ejuldem convertione eirca r a, 3 a R P + 23s R F
25uD; et Semisolidum 3 a R P + 34 5 R P = 2SVP: AIque CirCa FA, 50.
lidum
174.
170.