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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 758, page id 851387705:0778
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De Calculo Centri Cravitatis. Cap. V.
Fis. Aueciamfiguram inseripia de circumseriptae intermediam (ulpore partim in-
269, Seripram parrim cirenmseripeam) complentibus, uc Y a P, _c. (quae rectis a Z,
170. aT, eC UE IlOruM aXIBUS RCPEXSenTENEUE:) Incellisenda erie similiter FiguTa
Sinuum vexlorum Ar a ex coridem constitui correlpondencibus Onadrilineis ut
AEX, XE62 _c. Sectorum illorum duplis; vel etiam (quod eodem recidic, le-
Etione in intinicum continuara,) ex cocidem Parallelogrammis, tiguram inseriptam
complentibus, uE Z XEa, D265; ac. ant circum seriptam complencibus, UE A 9C a
XI55, Sc. aut quae tiguram partim inseripiam parcim circumleripram complent,
qualia Dy dE, _C. (qua rectis 25, 26, dcc. ut eorum axibus repraesententur; qua
criangulorum aeguealiorum a 2, aZ, _c. dupla incellisantur.)
EIt aurem Diltancia Centri graritatis in Parallelogrammis EX, 62, ec. ad Di
stantiam Cencri graricatis in Priansulis aequealtis, a X, a Z, _c. (d recta Fa;
uc Z2d3; seu, uc 3 ad 4, C per prop. 6. hujus.) Adeoque (propter magnitudi-
nes ut 2 ad L;) Frunc momenca Parallelosrammorum (tune linoulorum, tum (.
mul omnium,) ad Priangulorum respectirorummomenta, (cum lingulorum, cum
simul omnium; ) uc 3 ad 2, ( prOPIer Z+3 =3:) Adeoque Momencum, Prilinei
ATa, ad momentum Semicirculi ADa; gulque portionis, (ut A BBa, (Cu
XEd d, seu bBr,) momentum, ad momentum lectoris correspondentis, (uc BaA,
seu XaD, Teu legmenti a Ba,) respectu rectae ra; ut 3 ad 2
Fs aurem Semicirculi A Da respectu ra momentum (propter magnicudinem
PR, ee Ceniri gravicaris dictantiam, R,) ZR2 R; ergo Trilinei Ar an respectu
ra momentum, Curpore ad illud Semicireuli, uc 3 ad 2,) 8R2P. (FTOC ett
omnia = h2, scu =V= rocius semicireuli, seu semisumma quadracorum linuum ver-
Torum corius semicirculi, sumpris arcubus arichmerice proportionalibus.) Adco.
que (propter masnicudinem LP R,) distancia Centri sravicaris d Ta, ZR; adeo-
que a F, A, E R; ejulque momencum respectu L A, 3R= P.
Ergo et Semiquacrancalis Ongula eidem insilteno, aeiem habens ray 3RZ P
e aciem habens F A, 8 R? P: Solidumque ejusdem convertione circa r a Factum.
EX DE, et Semisolidum 8 R D=: e cirea Y A, Solidum 3 RZE; ec Semisolidum
6R∞:
liem; Sectoris B a. A momencum respectu Z a (per SM. prOP. 25. ) : a R2 +
35 R= = SSVR = ZfR2 FSSBR: FrBO, Portionis BBa A, momentum respectu
Fa, ZA R  = Z5 R - + sV R = 2fRZ + aSh R; (idemque cAt Onsula Semiqua-
drancalis, portioni bBa A inliltens, aciem habens s a:) Adeoque (Propier
magnitudinem, a R f s.R = fR,) distancia Ceneri graricaris portionis bBa A,
2 50, 3 R +
si e d FA, E R - -; e Propterea ejusdem respectu P A, mo-
mencum ( seu semiquadrancalis Vngula,) 3a R 2 + 35 R2 + = 5V R = 2fR 2-
SBR. Fc consequenter, Solidum, porcionis bB a A convertione circa r a Factum,
Et P p
sbP: e demisolidum, 8 f RP + 55hP: et, cirea Y A, Solidum
25bP; e Semilolidum, 3f RP - 35BF
Liem; SEGMentI ABA, MOMEnCuM resPectu TA, (BEr SNV, prOP. 15.) est
a e
65VR = = C R 2 = fSVK; ergO, Frilinci A BK momentum
respectu PA (vel semiquadranratis Ingula aciem habens F A,) est 3C R2 
252 R: (HIOC elF, omnia 302; seu semitumma quadrarorum linuum verlorum
accuum ariitimeriee proporcionalium, ab A, usque ad AB.) Adeoque (Proprex
maxnicudinem e P) distancia Centri eravitatis d Y A, a R -   ideoque d
Ta, ZR + ; ejusque respectu ra momencum, Z0 R = L SVR: Fx consequen.
rer; Solidum ejusdem convertione factum circa Y A, C R P = =52P; et Semilo.
lidum, 3C RP = 352P: _ cirea ra, Solidum, Z e _ P + + S2 P; e Semilolidum,
SC RF = 35VF
Similiter; Scgmenii aB a momentum respectu r0, L a R = - = 5R 2 - G5BR =
R2P = Za R = 85 R2 + 55VR: ErgO, Trilinei bBT, momentum respectu
7 ay ZaR 2 = 3s R2 - = sBR = 8 R2 P - Z a R - 35 R + =sVR. Adeoque
(propcer magnicudinem. R = . _) distania Ccuuri pravicuis 2 r a, . R.
40 - 4. 3
ideoque