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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 Ccravitatis. Cap. V.
F18. 166, HEm, u B~ H, respectire; ea est quam habene omnium illorum criangulorum ut
168, 173. La P, in distanciis respectire z bB F ZBV Cuspentorum momenta, ad momenra
corundem in distantiis respectire ZB V Suspensorum; seu, ut omnia Y a V in 3BY
ad eadem in ZBV respectire ducta, acque insuper uc eadem omnia Y a P in 3bB,
ad eadem in Z BV respectire.
Cumque lic cadem ubique racio criansulis ue Ta P, in 3BV, ad idem in ZBY:
adeoque s omnium ad omnia; nempe ut 5 ad 2: Sed non eadem ubique ratio
Prianguli, uc Y aP, in 3bB; ad idem in ZBV; propeer cum Priansulorum su-
per aequales bases inxqualem alcicudinem, cum aliam acque aliam racioren b B ad
BV, hoc elt, arcus ad linum: Proprerea, rationi sad 2; alia consocianda clt
Duam nempe habeant omnia respectire criangula ut P a P in 3 bB, ad eadem in
EBV; scu, quam habent omnia in 9bB, ad eadem in 2B V, respectire: Hoc est,
Duam habet Noncuplum omnium b B, Scu B0, (hoc est. B A areuum arictimetice
proportionalium,) aur his aequalium BC Friangulum a rc tig. 170. complencium
in respectiva Lriansula l a P, Teu (proprer aequales omnium bales) Trianeulo
rum altitudines Va respectiras, (hoc est, sinus vertosarcuum Ba, qui cum BA
complene Semicirculum,) Icu in, iplis aequales, bB, leu minuta paralleloeramma
his proportionalia tisuram Sinuum Verlorum seu Prilineum Resticurum H8. 270
complentia: Ad Duplum omnium B V CSinuum Rectorum corundem areuum BA,
aur hris aequalium B0 (complentium rqu tisuram Sinuum rectorum cocius Semi
circuli tig. 270.) in eadem respective Triangula leu Priangudorum Alitudines.
aue minura Paralleloeramma iplis Proportionalia: Hloc elt (in Frilineo Reltirure
tig. 270.) quam habet Concuplum omnium bB in B6, ad Duplum eorundem BB
in B0, respectire.
i. 170. ACBB, in BC seu ea ducta exhiber iptius b e momentum respectu Rei; ade.
que omnes bB in respectiras B6 seu Ba exhibent respectu ejusdem Aa, momenta
omnium bB, hoc est momentum Prilinei Ara; Adeoque Noncuplum omnium
bB in B6, elt Noncuplum Momenti Prilinei Ar a respectu Aa. Ve similiter in
porcionibus: Puca, Noncuplum omnium bB porcionem bB a B A complencium, in
respectivas B6 seu Ba ductarum, (hoc elt omnia dah, porrionem b A a B A spC.
ctancia,) elt Noncuplum momenci porcionis bB a B A, respectu ejuldem A a.
Fis. 168. Aeque omnes eadem bB in B0Hi3. 270. seu in BV tig. 168, 169. Lixhibent Jri.
169, 170. plum Momenci Semicireuli ADa aur ipsius Sectoris B a A, (prout de Priangulis
rocum Semicireutum, auc iplius tancum Sectorem complenebus, intolligatur,) re
spectu Diamecri Aa; per B A. PTOP. 18.
adeoque Daplum omnium b6 in Eo, est Persuplum momenci semieirculi a D a
respectu ipsius Aa: Aeque, in partibus limiliter, respectire sumptis.
Adeoque Concuptum omnium bB in B6, ad Duplum carundem DB in BV, cA
ur Noncuptum momenti Trilinci Belticu ATa, (ejutre portionis b B a B A,)
fi8. 170. respectu rectae A0; ad sexruplum momentum Semicireuli AD a (ejulve
Sectoris respectiri Ba A,) respectu Diametri A∞: Vel, u P riptum momenc il
lius, ad Duptum momenei hujus.
Flt aurem (per SC. prop. 17.) Trilinei Restienti A r a H3, 17O. momentumre.
spectu Aa, S RD2 = 2 R3; adeoque hujus Friptum ZR ∞ 2 = 6R: Lt momen
cum Semicireuli, respectu A a, pEr SO. PTOD. L5. 3 R3; hujulque DupluM 3R3
Llt erso Triplum illud ad Duptum hoc; ut 3 R P 2 - 6R3, ad 3 R3; hoc est
dR∞2 = 144 R3, ad 3E R 3: Sen ut 9Z2 = 144 R2 ad 32 R2. Acque hac de
mum racio (uc supra ostentum est) rationi 5 ad 2, hoc est 80 R ad 32 R2 con
juncta; exhibet rationem momenci semiercloidis Nra, admomencum Semicireui
A Da respectu ejuldem Aa rectae; nempe, ut 9~2- 64 R ad 82 R . Cum
iaque momencum illud Semicirculi sit 3 R3: Fric Semiercloidismomenum respectu
P2- 64 R
Aa. (seu corcespondens Onpula Semiquadancalis,) =
R3
R = 3 R2.-
Alque hoc Momencum per Semiey eloidis magnicudinem  P ~ (S B.) diritum:
extribet ejusdem ab A a Ceniri gravitatis distanciam, a P = L0∞
L
ox iadeoque, d r F,
d lteruendo maenicudinem,) ejulectu respectu + Y momentum
16R F
204