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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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e
De Calculo Centri Cravitatis. Cap. V.
eorum d duabus in eodem plavo rectis, non inricem paralletis, distancias,) ipsa
GravIcaTIS Centra.
Eademque mechodo, de aliis Circuli porrionibus, corumque Momentis, ee Soli-
dis convertione tactis tier iudicinm. Puta, ( pro lectore BaA, (ad verticem ter-
minatO) exponeretmr sector Da B, aliulre hujusmodi: Cum enim cum Sectoris
Ba A, cum D a A, magnitudines de momenta (reliquaque quae hinc dependent)
jam extribeancur; etiam sectoris D a B (qui illorum vel difterentia vel Cumma (ic)
magnicudines et momenta (adeoque et quae hinc dependenc) Facile extriberi po-
terunt.
Trem; eadem methodo qua momenta, verbi gratia, semilesmenti B V A, a recta
Ta, ad rectas FA, vet BV, transteruneur; possune limiliter d recta Aa, ad FT,
vel B a cransterri. Caque, quae hric craduntur, mille modis aliis ampliari.
Oux aurem de Circulo ejusque portionibus dicta (ImE: eadem ad Elliptin, nujut
que portiones, tacile cransterentur. Nempe, si incelligatur Axium ellipleos alter
Aa, alEF DA: MaDENTE, VE pEiUS, A a = 2 R; (adeoque A V =- V, V a = B;
Crit D a in ca ratione ad 2 R, qua est ad A a; adeoque B V in cadem ratione ad 5.
Adeoque ubicunque BV, aue hinic parallelae in caleylum veniune; pro s, substi-
uenda exit quanciras quae sic, ad5, I ca ratione qua cst D a ad A a: (majore
quidem, Si Da Sic axium major; minore, si minor;) Adeoque, pro s; quanci
Latem quae sic ad hanc in duplicata ratione rectae D a ad Aa: et Cimiliter, mucatis
mucandis, in reliquis ejuldem poreltatibus.
2
PRO P.
Sectoris Sphaerici Contrum praritatis, eM in aris Cui illo puncto.
quod a Cenero Circuli dictat Fribus Ouadrantibus Racii, minus
Fribus Octantibus altieudinis Superticiei Currx: Seu Fribus Oua
drantibus Radii, minus Fribus Oetantibus sinus VerH: Seum quod à
Centro Circuli distat, Fribus Octancibus altiendinis residuae super-
feiei currae; seu Fribus Octantibus sinus Versi residui.
Hoc est, in Femisphaerio; 8 Radii.
Acque hinc Segmenti Spharae (plano ab(ciM) Centrum graritatis col.
ligicur: Ex in aliis porcionibus similiter. Pt quae hine dependent.
Nempe; Si ponantur Symbola ut in proxositione praecedente; erit,
Semiguadrantalis Qnoula torius lemicirculi aciem habentis, A a
(unde de Solidis conrertione factis, e Semilolidis het indicium,)
Magnitudo 3R3; dictantia Ceneri graritatis; sive a F a, Sire a TA,
R; momentum respectu + an rel TA, ZR.: Distancia Centri sra-
ritatis ab A an  P; momentum respectu A an SR P. . 1
Aciemque habentis ra, Magnicudo ; R P: momentum respectu Aa
3R; distancia Cencri cravicis ab Aa : Momencum respectu
ran isR P; respectu T A, 13 R P; distantia Centri pravitaris à 7a,
ER; d FA
Aciemque habentis Ta, Magnicudo : P. P; momenrum respectu Aa,
ERa; Distancia Ceneri gravitaris ab ao, : Womentum respectu
Ton BR P; respectu TA, E R. P; distantia ceneri gravitatis a r en
2R; d FA, 3R.
Semiguacrantalis Ongula, Sectoris BC A, aciem habenris Aa, (unde
de Solidis conrextione factis, et semisolidis, tiet judicium;) Magni
tudo, 50 R; dittantia Ceneri gravitaris d DC, 8B; 2 ra, R F 3B; 2
Ta; R - 3b; momenrum respeetu r a, Zv R3 F 3SR3; relvectu ,
2V R
A.
FiS. 165.
ibo