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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 792, page id 851387705:0812
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11
De Caleulo Centri Cravitatis.
Cap. V
Idemque 3 a R2 f V R = Ss R= momeneum, per Ongula ABBa, aciem ha-
bencis ra magnicudinem, 2 f R = f Z sB R = Z a R2 = 25 R2 = = SVR, (8 D.
ProP. 17. inventam,). diritum; extibet hujus Distanciam Centri gravicaris a BB,
2a. f 80R5a5 R + s R + a52
6a R + 205 R = 25V : adeoque ab A a, : a - 80 N - 5as R. + s’ R + asv
6aK = 1OSR- 25V
ejusque respectu A e momentum, 3a R 2 = Z a5 R 2 = = a SV R = V R3 = 8s R2:
Idemque est momencum Onsulae AbBa aciem habentis Aa, respectu ra; prius
exhibitum.
Duod quidem 3 a2 R = Za5 R= = = a 5VR = V R. = 5 s R momencum,
per Ongula A bBa aciem habentis A a magnicudinem = a  R = a s R = v R=
(Per S LL. PrOP. 17.) divitum; extribet hujus Distantiam Centri graritatis d 7a,
2V P F sR + 2450 4 a5R
4u = Bas- 8vX ; adeoque d FA, 3 R  2V R + 5. R + 2 a5y - 445R
42  das - SuR
ejusque, respecta TA, Momenum 3 a P. L 3 as R - v R F Bs P2 + + d5VR:
aciemre hahentis La, momencum relpectu A∞.
Atque hoc demum 3a2 R = F3a 5 R2 = ~ R3 f 35 2 P2 + = a 5V R momeneum
per Ongulae AbBa, aciem habenis F A, magnicudinem Z f R= = = sB R = 3 a R
45 F450 se (ED. PCOP. 27. InVenIam,) diritum; exhibec husus Bultan-
tiam Ceneri gravicaris ab A en L a - d~ R2 = s2 R = 3 a 5R = a 5~: adeoque d
b8: 3a-
10a R F 65 R + 250
80R 2 = 5 = R = 3a 5 R = a 5 2
10aR + 65R + 25V: Ejusque, respectu bB, momencum,
Za= P2 = vX3 = 55 R2; idem quod prius repertum es momentum aciem ha-
bencis bB, relpectu F A.
Adeoque; Si cocius Ara Ongulas spectemus; (PrOPteT a = Z P, V = 2 R.
5 =0;) Eric Ongulae Aro, aciem habentis Pr, magnicudo, 5 R D2 = 2 R3: MO.
mencum respectu r0, 3 RE ∞2 + 2 RE; respectu Y A, E R2 D2 + 2 Ra: Distan-
4 R
uia Centri eraritaris a ra, 3 R F p. + 16R. i a FA, E R p. + 16 7
Aciemque habentis A0; Magnicdo, S R D = =2 R: Momencum respectu 20,
ER=∞2- 2 R4: respectu T A, 5E RE D2 = 2 Ra: Diltancia Cenrri graritatis a
en 3 R.
+ R
P7 - 26 X. d FA, 3 R + p, - 16p2
Aciemque habentis =a; Mlasnicnco, 3R2 P; momentum respectu F r. 3 X2 c
F 2 R; respectu Aa, = R2 ∞ 2 - 2 R.: DictanCIA CenIrI BraVICaTIS d FF,
∞ + 26 R.
34; ab A a + ∞ 16 R2
Aciemque habeniis F A; Magnicudo 3 R, P: Momencum respectu F Z, . N. ~=
= 2 R2; respectu Aa, E R = P. - - 2 R.: Diltanca CenerI GravitatIS d F~
2 f 26 X
5D i ab A0, 1∞ 16 R
Fademque per se poterant, eodem modo, caleulo exquiri; quo Ongularum
porcionis Ab Ba momenta prius exquirebantur; quaque inde dependent.
Ex his iem sic tradicis, Ongularum portionis BB= momenca (quaeque hine
dependent) haberi porerunt. Nempe; ex Momentis Ongularum tocius Frilinei
AT a Cubductis respectiris Ongularum portionis AbBa restanc Momenta respe.
ctira Ongularum bBZ; sive respectu iplarum ra, FA, sire respectu iplarum
A∞, FY, _C. Acque ex cognicis aliquibus reliqua facile derirantur.
Sed et eadem poltunt per se eodem modo exquiri, quo in iptis A b Ba Factum est.
FIL MLIquE (PET SF. prOP. L7.) plani cujusque bBr, momentum respectu 7 a
a R2 - 35 R = + sB R; Adeoque Omnia, 2 a R 2 - 2 5 R = a sBR; (HOC es,
momenta planorum omnium Ongulam bBr, aciem habenrem bB, complencium;)
Tunc iltius Onsula momencum.
Sed Omnes an larcus aritimetice proporrionales, ab ipso an usque ad maximum
seu rB = _y) CumEs l PEr PEOP. X. husus, ) 1 a 2. F1B0, Omn. 3a R2: = 8a = R.
tcem
160
7C