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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 778, page id 851387705:0798
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De Calculo Centri Cravitatis.
Cap. V.
Fig. 170. ab Aa distantias ductae; Tune eju(dem aBo momentum respectu Aa; hoc cst
(per SP, 8. BCOB. 17.) = e _ + av P. Adeoque Omn. = : aSR: = Z e R
EaV RZ
Fiem, Onn. a 50: Sunt ipsum A b K praecedentis Solidi (ex ductu rectarum B.
in bK respectire) momentum respectu Aa; hoc cl, - Ze R3 + aV R7  = 5VR
2a5 R; per B I. Adeoque Omn. 3 a 5V: = = 3C R3 + 3 a v R + 550 
2a5 R.
Frgo; Omn. = a R = = a5 R F = a 50: HIoc es ipsius AbK Solidi Momentum
re(Dectu Aa; elE, 3C R (= 5a R3 = 35 R3) + 35D R2 + Z a3 R = = a Sl.
Hoc itaque per iptius magnicudinem,  a R = 3 S R (Der D K.) divisum; ex
hibet ejutdem distantiam Cenri eravicacis ab Ag, 3C P + 350 k + +a - 6a5
6a = 65 = 6c,
Hndque Solidi ABK momencum, ex momenro Semieplindri AL Baq Subdu-
ctum; hoc estu ex magnicudine ; a RP (SM. octensa) in Za distantiam Cenrri
Graricatis ab Aa (peT PFOP. 2.) ducta; hoc elt, ex s a RD Tubductum: Relin-
quit Solidi A bBa momencum respectu eju(dem Aa, 3 a R P - se R3 - f5VR 2
5a  F: aS R. Adeoque (proptes magnicudinem : à RP - + a R + 4 s R,
Per SK.) Distancia Ceneri graricatis ab A0, 3 a P = 3C N - 3 5V R- 4 a + 6 a s
6a = 6 a F652 =6a = = 6cf
Idemque Solidi ABK momentum, ex momento Solidi A R BB, subductum;
hoc elt, ex magnicudine Ze a R F Z a 5V (SMI. ostenta) in La (Diltanciam Cen-
tri graritatis ab A ∞) ducta; hoc ett, ex =e a R F L a 5v: Relinquit Momen-
cum Solidi ABB, respectu ejuldem Ae (leu Omn. L a 5: eo spectantia, Tumpris
2 arichmetice proportionalibus,) = se R3 = 85V R = 5 a 3 R + + C a R
2a5 R = 3a250, Teu (PTOpter C = a = 5,) = 5a R = 35 R) = 85VR
= a R = a5 R  = a SR f = a5V. Adeoque (proprer magnicudinem : q p
==aSR  L5E R F = a5V, per S L.) Distancia Ceneri graritaris ab Aa, et
= 3e R3 = 35V R 2 = 2 a R - 6a 5 R + 645 R + 6 a 52
6a R = 12a5R + 65 R (= 6e R) + 12a5V
Tommyne A ra Solidum quod spectar; (sire contideretur ue ABBa, sire VE
ABB, perinde est,) Momenum ejus respectu Aa (prOpter a = = P, V = 2 R, e
= 0,) est  R ~  - s R. P: Dillancia Cenari sravicatis ab Aa, 5 F - 
Denique; Fadtem A BV scomenta plana, Solidum ABK L3. 170. complencia
Cenera sraviraris habent rancundem a plano Ara distancia, quantum ab A a di-
lane corundem Cenera in H8. 169. Forumque omnium sespectu A a f8. 269.
momenta; HOc est, Omn. 3 V R2 = 55R = ESV: (Der SR. V. DEOP. Z5.) TuINE
iptum solidi ABK momentum respectu plani Ar a crecti.
Sunc aurem Omnes v, (sumptis a arictimetice proportionalibus,) Hoc est, 2r-
Cuum arichmetice proporcionalium sinus versi, eo spectantes; idem acque Al KR
blanum; hoc ett, e R, (per SB. DFOP. 17.) Adeoque Omn. ZV R2: = = 0 R3.
Ei, Omnia s, eo spectancia; Dupium Momenti iptius aBo respectu ra; hoc
ells hC R2 + 3 5V _, (per GO. prOP. 27.) Adeoque Omn. - 55 R: = - i e 
=13SV R
tiem, Omn. S. v; sunc Duplum Momenii Solidi A B K praecedencis, (ex ductu
rectarum BV, in B K relpective,) respectu Plani (erecti) Ara; leu Ze R3 = = 5V R
18S RR.
ErsoOmn. 3V_ = 55 R + 35 V: = Z C R - 1 s R = Z a R = = sR3 - 155 R.
Ouod inque est Solidi ABK momencum respectu crecti plani AT a. Adeoque
(propier magnicudinem, i a R = = se R = = e f H, per SK.) Dictancia Ceneri era
vicais d plano A r ey eAt 2 a . = 12 5 R = 25 - 12C R - 25
da - d
def
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