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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 Cravitatis. Cap. V.
4. X R = 3 ∞ 2
Fis. vicacis d ra, distanicia, R. + 4v. R L3 N
6R+ q iide d F A, R + 6 R L 4. V.
100. Ongulaeque eidem Friangulo B VC insistentis, aciem habentis T A; momen-
tum respectu r a (oppolita) ZSN R = =25 ~3 (sire supra Centrum, live intra,
fucrit V punctum;) et respectu Aciei sua T A, ZS N R F35 X 7 R = L5 ~3,
(prouc lupra Centrum intrare tuerie V punctum) Centrique graritatis a r a (op.
6R + 4. + i a F A (aeic) R= 4 ~ R + 3 v
Polica) distantia, PJ. F X P + 3.x.
6R F 4. N
Acque haec momenta, momeneis Ingularum (respectire sumptarum) semiles.
menco BV a insistencium, Addica, vel Ablata, Drone Cupra intrare Centrum
fuerie V punctum; exhibent momenta respectira Ingularum Sectori BC A infi-
Rencium.
Puca; Onsula Semiteomenti BV A, aciem habentisr a momento respectu r a,
3a R - 85 R (= 8C R3) + 85V R + 13S R = 2 53V; (Ut S F.) A addatr,
vel auteratur, (prout supra intrare fuerit,) respectirum Ingulae Frianguli BV C
momencum, Es_ R2 =35 _ = R = 45 N3; HloC elt, (PTOPTEE N = R - v, Supra
Cencrum, addendum; ec x = -- R + v, intra Concrum, auterendum: adeoque
v3 = R 3 = 30 R = = 32 = R - v3 = R  = V R = = 5= R + 5= V, addendum; 8
63-
= R + 30 R2 = 3v R + v = - R3 F V R2 + s2 R - s2v, auteren-
dum; quae tantundem valent: Scd, N Z = R2 = 2~ R f v= = R = - 52; eltque
vel + x= addendum, vel - x auterendum, quod cancundem ralet:) Si addatur
35 R - 2 5VR2 -- 125 R f + s v: Hlabetur momencum Ongula sectori BC A
insiltentis, aciem habentis r a respectu r a, 3a R3  12 5 R3 = 55V RE. OE priuS.
Acque ejusdem Ongula BV A(aciem habentis r à) momento respectu F A,
3aR - 35 R3 (= 3e R3) + 35VR = = 5 R F = 53 V (uE S F.) B addatur
rel auteratur (prout supra intrare fuerie V,) momentum correspondens Ongulx
BVC, 2SN R? = =5N3; Hoc elt, (ob caulam modo dictam) s addatur L5 R.
25VR 2+ 253 R = 2 53v: Flabetur, Onsulae sectori BC. A intiltenris aciem ta-
bentis ra, momencum respectu P A, 8a R = 55 R. + 55V R. OE prius.
Ongulaque aciem habentis PA, momencum respectu ra; idem est alque illud
aciem habentis ra respectu Y A; proprer alcicudines et distantias ubique rect.
procatas.
Vnerilae vero intisteniis semileemento illiB V A, aciem habentis FA, momen-
tum respectu, aciei, sUIX PA, 3a R3 = 35R3 (= 3C R3) + 85VR2, 35 R
253V; Si addatur, vel auteratur, (prour supra intrare tuerit V,) momentum
correspondens Ongulae BV C, Z5 N R F3s N = R + 4 5∞3; HIOC ct (ob caulam
modo dictam) B addatur Z5 R3 - 3 5V k = F 253 R f 253~: FIaDCTUE momen-
cum Ongulx Sectori BC A intistemis, aciem habentis P A, respectu iptuuis F A,
Ba RET 245R 55VRE. OEPrIUIS.
Denique: Ex momentis eildem Ongularum Semiscemento BV A intistencium,
si auterancur relpectiva momenca intiltencium Priangulo B AV; habenur mo-
menta insistentium Segmento AB A.
Ouxe aurem Frianeulo B A V insitic Semiquadrancalis Ongula, acieni trabens
LA; CstPvramIS. Cujus vercex A, batis BV XV A = 5V; alcicudo, A V = V
adeoque magnicudo ; 507 = Z5V R = 353: Distantia CenerI Braritatis d I A, 32:
adeoque d Ta, 2 R - 3v: FF propierea momencum respectu T A, + 5V3 = 5V R2
25 R 253V; e respectu Fa, = 5V= R = 2 5V3 = 55VR 2- 65 R + +53V
Haec itaque momenta, momeneis respectiris Onsulae Semiscemento B V A infi
LtenEIS, (8CR F 35VR2 - 353 R = 2 53V, _3CR3 + 85yR - 453 R + 4 5V
per ST.) subducta; relinguune, Ongula legmento AB a inliltenis, aciem ha,
hentis TA, momencum respecta T A, 3C R3 = 35V R 2. = 12s. R; e retpectu
ra, 3eR3 +  sVR2 = = S. P: FC (propier magnicudinem, LC R2 = ESVR,, u
SN. prop. praeced.) ditancia Cenuri pravicaris d F A, exic L5 et 2 = 95u R + 28. e
1X
deR7 + 50R = 253
T2CR - 45V
12C. R = 4 siv
Ouaeque Friangulo B A V insistic. semiquadrancalis Uncula, aciem habens. 7 c. 5
idem