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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 773, page id 851387705:0793
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PFOD. XVIII. De Calculo Centri Ceravitatis.
35= R2 F 352 VR, ut prius. Acque huic momento, si addatur momentum POr= FiP. 169
tionis BBa B, habebicus momencum porcionis Ab Ba; eadem qua priuS. L. M
Idemque Solidum ABB, eodem sicu potitum, si respectu rectae Aa considere. C.
EuT; Momentum ejus est asgregacum omnium aB. planorum solidum complenti
um (hoccst, omnium v R, eo spectancium,) in suas relpectire cencrorum grari.
cacis distancias ab Aa; (hoc ett, in = e R + a
Hoc est, Omnium = ek = F av R, Ccu Omnium - a R 2 F s R? F a V R; Tumpeis
 arichmerice proportionalibus, ulque ad Veorum maximum.
Suntautem Omn. a. (sumpris v arichimerice proportionalibus;) iptum planum
ABB; hoc cAt, = c R = aV, Pes EB. PTOP. 17. Adeoque Omn. a R2 = = e R3
 aV R=
EC, Omn. 5. (hoc sentu,) iptum Semicirculi segmentum ABV, J e R + Z5V;
per S F. prOD. 25. Adeoque Omn. SR3: = ZC R3 + ZsV R 2.
Trem, Omn. a2, Cunc ipla bB rectae, planum ADB complentes, in suas respe-
ctire a P A distancias V; Hoc elt, Plani AbB momentum respectu P A; Hoc est
40R3 Fav F 250R = Z252: per GF. pFOP. 17. Adeoque Omn. av R: 
CR3 = aV R = + 4SVR 2 = = a 5= R
ErSO, Omn. = a R2 + s R2 = avR: = 3C R, + 2 50R2 - ; a 52 R. Ouod 11a.
que eltmomentum solidi ABB respectu A a.
Idemque momencum, per magnicudinem v R2 = ZS2 R (SB) diritum; extii
bec ejusdem diltanciam Ceneri gravicatis ab A a, 3e R F 35V R - 2a5
4VR = 252 = 2v =
Huic aucem Solidi ABB momento sic reperto, si addatur momentum Solidi II.
bBa B; habetur momencum Solidi A bBa respectu A a.
Elt aurem bBa B Solidi magnicudo s2 R = v B R. per SB: Ejusque ab A a di-
Ptancia Cencri graricatis, (idem quod iplius a Bu plani, PEx PFOP. 2, 5. hujuS) Cst
e R + a2
3 Per SC. PrOP. 17. Frgo ejuldem, respectu Aa, momencum est,
=cb R + avB R = - 20R3 + cv R + a s R = -= 20 R. + av R = suR.
as
Hloc iiaque Solidi ABB momenio (modo reperio) ZC R 3 = 2 sV R 2 - , a 5 R
addirum; exhibet Solidi ABBa momencum respectu Aa ZCR3 + aVR2
5~R2 + Eas= R. (Adeoque rocius Ara Solidi, cum lic in hoc calu,
2 = 37
 = 2 R, 5 = 0, _ e = a = 5 = a = = P, mOmenEum respeCt A a,  3 R37 1
PP =SP P.) EEmomento per magnicudinem vK + =S2 R (S A) dirilo; hahetur ipsiuis
Absa solidi, dictancia Cenri Graricaris ab A a, = seR + 4av R - sV R + 2a5
que in incegro A ra Solido, 3~.
40 +25
. (Adeo-
Arque hoc (sire corius Ar a Solidis sire iptius porcionis ABBa) momentum
respectu Aa, est agerexarum omnium a sh eo spectancium; Tumpris a arcv b15 3
richmerice proporcionalibus, usque ad maximum A. Sunc enim, rectangula (cu
parallelexipeda bBo, summa omnium sh (ur s A dictum ell,) corumque ab A a
dictancian Ba = a, respectire.
Ouxque de his Solidi porrionibus duta luntu lacile ad alias uBI OpuS feril
transterentur: Ouarum tum magnicudines, cum momenta dt Centra graricatis,
ab tis quae jam traduncur tacile derivari poterunt: Pura, Porcionis BBT, aui
ABR,
Si enim ex corius Solidi Ara, magnitudine Z R3; Momento respectu ray in Fi8. 170.
crecto plano Ara, 3R3 D; respectu ra in erecto plano ran, 3 Xa; ee respectu
plani luper Aa crecti, 3R. P; supra craditis: Auterantur Magnicudo, & relpe-
ctira momenca Solidi ABB, V R = = LS R; e Z CR F  5D R2 = 3s R; e
VR3 + 352RZ = = 52~R; _ = ZCR3  a
25VR2 +  as R; lupra
tradica: Relinquentur, Solidi bBr, magnicudo, 2 R3 = v R2 - = s R; Momen.
cum respectu ram in erecto plano A rO s R3 P = = C R3 - + 5VR2 = 65 R; rC
spectu ra in plano ran crecto, 3Ra - 3 V R3-
E cccc:
S R2 = ZsV R; respectu plani