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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 834, page id 851387705:0854
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De Calculo Centri Cravitatis.
Cap. V.
Fi3. 166, Vel etiam Sc colligitur, ejusdem b Ba. V Ongulxe, aciem habentis Aa, respectu
iptius A a, Momeneum.
Rectae Praperium complentes, ab a B incipiendo, usque ad bV; Funt , A s,
AF 25, A F 3s, _c. usque ad A F S. Parumque puncta media, seu graritatis
centra, distantias habenE, 3A, Z A F 35, 3 A +35, 3 A +35, ecc. usque ad
EA+ =S. Oux in rectas illas ductae, exhibent carundem momenta, Ceu Frian-
sula rectis illis infiltencia Ongulam complentia, 2 13, Z A2 = s A + Z52, E A2 +
25A+ Z, 52, Z A = 35 A + 252, _c. usque ad 5 A + S A F 3S2. Fadeque
Friancuta, ducta in carundem respectire distantiam centri gravitatis ab A a,
nemDe Z , 3  = 35, 3 A = 35y 3 A +55, eec. usque ad 3  = 3S; extribent se.
riem Momentorum, corundem Friangulorum, respectu A a; Z 13, Z 13 + 5 A 
S A = 353, 3 A + 25 N + 45 A + 35, 3 A = 35 A2 F 9s A + 2353, 8c.
usque ad 3 A F S A F S A F 35. Ouarum omnium aGGreGATuM (per PrOP.
T.) PEOPIeE V a =B, clb, SB A3 + =BSA = sBS A+ BS. Seu (recti.
cuco ralore minuscularum,) Za3B F Za  SB- F 5a 52 B -f =53 B. VE prius.
2+ Su in Z A + Z5, = Z A2 + 5 A+
2
A + 25, in = A = Z5, = = A + 25 A + 352.
A + 35, in 2 A + 25, = : N + 35 A + 35
Sec. usque ad
1+ 5, in 3A+ Z5, = 3 ~ + S A + 352
3bA + 1b52F 1b52.
EA= 3S, In3 A F 5 A + 352, = 3 2+ 5 A + s A+ 353
A = 35, In 3 A = 25 A + 3527 = 3 A3 + 25 A + 4 52 A.
34+ 35, 12 = ~ + 35 A+357 = 52 + 35 A + 95 A + 35.
cu ec. usque ad
1+ 35, in  4 F SA + 35, =3 1 + 54 + S A + 353.
B a + 1b5 N + b5 A + ib 5.
Duod quidem noula BBa V momentum, =a 3h f Z a 25B f Za 5 2B. f ,553h,
Teu L. prOpter B = 2R - 2,) Z a R = 3 ad V + a 5 R - = a 5V + 3 a 5 R - = a 5= V
F65  = 253V; ex Ongula ABBa mOmenIO, 22 C R3 =3 aV R2 -85VX2 +
Ea3R + 3025 R + 3aS = R + 5653 R, (modo tradito,) Subductum; Relinquit
Ongula Ab V, aciem habentis Ao momencum respectu A a 2CR3 = 3 a V R-
5SVR2 = 5a R + 5a  5R + 5as R +. 555 R + 5 a 3 v + 5a 5v + 5a 52 v +
2530.
Acque hoc, per hujus Ongulae magnicudinem, - 3 0 R 2 = ; a R + : a 5 R. +
SP = 5420 + 5a 50. + 552 V, (per SK, L. PrOp. praeced.) divisum; extribet
Ongulae AbY, aciem habentis Ao, distantiam cenri pravitatis ab Aa,
870F = 96avR = 95VR = 12 a R + 36a 5 R + 12a5 R + 25 R + 240 2 + 36a 50
24 a 522 +653v
= a8 ve - 28a R + 36asR f 65. R. + 36a v. + 36as0 + 1250:
Semitolidique conrespondentis Momentum respectu axis convertionis sux, du-
plum est Momenci Ongula respectu aciei sux: IIiusque distantia ceneri cravita.
iis ab axe, ad hujus distantiam ab acie; ut 2 R ad ; P. Or Capius ostentum est.
Figdemque Momenta et Distantiae, sie acthue alias investisaneur. Nempe, Mo-
mento Ongulae AbV per se invento, sine ope Ingula AbBa: Hinc iplius
ABBa Onsula Momentum, reliquaque deduCUntuT.
Dirisa recta A a in parres intinue exiguas, inricem aequales, in punctis S, C, 2,
Sc. hoc est, sumptis v arichmetice proxorrionalibus: Ouae Semicreloidem A + a
ejusre scomenrum Ab V, complene reeta bV; sunt Omnes a F s, eo spectances.
Cuaque
168.