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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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De Calculo Centri Oravitatis.
CapY.
Fis. ab A ae distanciis, similiter elicieneur acque priys. Ve non sic opus eildem ulteri.
263. Usimmorari.
Ac incerim haud eric incommodum hic loci monuiste; eadem eriam me-
chodo Friangulorum BCV, B a V, B Ca, momenra respectu iptius Aa, haberi
Dolle.
Cum enim lingularum B V rectaruim, (seu huic pacallelarum) Friangulum BCV
complencium, momenta respectu Aa; seu Priangula eildem insistencia, semigua-
drancalem Dnoulam (aciem habenrem Aa) complencia; sinc carundem BV, ecc
Semiguadrata: Oux quidem Semiquadrata, Pyramidem complene cujus Balis est
EBV 9 = 252, alciudo, CV = x; Pric ipla PyramiS (per 6 hujusi) HToc est
momentum illud, seu lemiquadrancalis uneula B Y C, acietm haberis Aa, L 57 X L N =
5S=N. UC priuS SR.
Tiem, (pari de cauta,) Momencum Frianeuli Ba V, leu huie insistens Semi-
quadrantalis Ongula aciem habens Aa; Pyramis erie, cujus Batis ; BV 9 = 352, al-
ticudo V == h; adeoque ipla Pyramis (hoc eM, Momenrum illud, seu lemiqua
drantalis Vngula,) Z5= XZB = 65 = h. OE prius SE
Estque Frrangulum BCa; idem acque B V a dempio dddicove (prouc supra in-
frave Cenirum C, sic V punctum,) BCV: Adeoque (respectu iptius. Aa) mo-
mencum Priansuli BCa; idem acque momentum B N, a dempro, additove, mo-
menco BCV: Adcoque Frianguli B Ca momencum (respectu iplius A a) leu SC
miquadrantalis Onsula eidem intiltens aeiem habens Aa; CA 6sE B + 65 E N. HOC
clt, ( prOPtex B = 2 R - V; e lupra Centrum, x= P v; auterendum; intra
vero, v = = R + v addendum; adeo que b F v = R;) 55R. OI priuS, 55.
Eadem ilem ostendenEIE ex PTOV. LF2. Arictim. EnFin.
Cum enim illic oltendatur, Rectas in semiparabola, Biametro, vel Axi paralle.
154. las, cliC ut Seriem A. qualium serie Secundanorum Muletaram; (Tunc enim Omnes
Vs, parallelogrammum AC as complentes, series Aqualium; omnelque Bs
complentes Semiparabola complementum AA S, series Secundanorum; FrgO, omnes
reliduae V B, Parabola diameiro Ca parallela, sune series A qualium muletata le
sic Sccundanorum:) Eloc elt, DEquadrata ordinatim applicararum in Cireuli qua-
drante; ut modo oltentum elt.
Si ipituru super eadem A a recta, (ut communi Base,) deseribatur nim AD a
Semicireutus, cum ADa Parabola recta (cujus Axis C a aequalis sit ip(IC D cir-
culi Radio:) Fc ordinatim applicata in Semicirculo qualibet BV producta, oc
currat Parabolae in B: Frunt omnes V B Recta, omnibus Ouadraris V. B respectire
lumpris proportionales.
Adeoque ductis omnibus VB rectis, (sire coram Parabolam, sive iptius segmen-
cum ut A V B complentibus,) in communem aleicudinem R = C A = CD: Frune
omnia V B in R parallelosramma (Prisma, Parabolae, ejutre porcioni, insiltens
complencia,) aequalia omnibus V B quadratis (et tingula singulis respective sump.
cis;) Hoc est ( per ance demonstrata) Duxlo momenti Semicirculi ejutre cur
insistunt porcioni, respectu rectae Aa; seu, Duplo semiguadrancalis Ongula COr-
respondentis, aciem habentis A a. (Sune enim HXC ParAIICIOSTAIMA, PFOBEEK
communem alcicudinem R, iptis quibus insistunt Rectis V B, proportionalia; adeo-
que, per jam oltenta, provortionalia ipsis V B quadratis: Sed e prOPter CD =
C. A = R, Parallelogrammum, C. A in R, aequatur ipsI C. D quadratO: FrGO et re
liqua reliquis respectire.) Fademque, V B in Z R, (urpore illorum dimidia,) ipsi
Momenco plani A B Y respectu ipsius Aa; vel semiquadramali Duxula correl.
pondenti aquantur.
Siigimr, Paralletogrammo A V S P; auteratue A BS S vet AA B5S (hoc est
Semiparabolae Complementum AA S dempeo acdicore ABS, prour supra intrave
cencrum tucric V punctum;) habetur P’arabolae texmencum AVB = AV s =
A AS F BAS.
Est aurem (PrOprer AV = v, ee Y S = R) Parallelogrammum AVSS = ~ R.
Icem; (propier Semiparabolae Complemencum, subcriplum circumleripii Paral.
lelocrammi, PeF PrOP. 23. Arithm. Infin. vel proP. L. hujus; rectamque AC =
C a = R;) demiparaboae complemencum A AS = hA.
ri
Trem;