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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 774, page id 851387705:0794
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De Calculo Centri Cravitatis.
CapV.
Aa erectis 8R3 P + Ze R3 = av R2 F 4 5VR= = 3 a S2 R. REGUE HXC MOMenLA per
Magnicudinem dirila; extribene solidi bB2 diltanciam Centri gravitacis a plano
Aram =
P - 6CR - 65VR- 45
oleic 48 R2 = 24 V R = +25
i a planO TCN
R 4V R - 4s R F s2V
12 R - 60R - 35
ab Aa Plano, 3   + 10CR2 - 8av R + 25V R - 4a5
16R = - 8V R - 4.
Similitet, eum solidi porcio AKBa paralletogrammo incumbens, Magnicudi-
nem habeat ( ex ductu A a = 2 R, in a B0 = V R, Factam,) 2V R2; et Momen-
rum respectu plani A Ta crecti, (ex ductu Magnicudinis 2v R3 in distanciam
Cencri pravicaiis plani a. BV, a r0
R
(D per 6 O, O. prOP. 17.) ZC R.
=5VR2; _ respectu ran crecti plani, (ex ductu a C = R, dimidii longitudi-
nis pritmatis, in magnicudinem 2V R2,) 2V R3; de respectu Aa crecti plani, (Cx
ductu magnicudinis 2V RZ, in distanciam Ccurri graricatis plani a B0 ab A a, HOC
ost, in
eR + aD
3 Der SP, C. PrOP. 17.) = 2 eR F 2 av R (est enim
Prismaris centrum gravicatis in medio recta Cencra gravitatis batium oppotitarum
jungente, Per PrOP. T, _ 5 hujus:) Si ex his Solidi A K Ba magnicudine e mo-
mentis; auterantur Magnitudo ee Momena respectira Solidi A DBa; V R3 F Z5 R
et 3CR3 + 250R +553R; e ZV R = Z52 R2 = 3S VR; _ = ZC R.  aV R
=ESVR  Za S R: Tupra cradtiia: Relinquentur, Solidi ABK, magnitmdo, (hoc
est, ascresatum Omnium su, co spectancium, sumpris a arichmerice proporriona-
Libus,) VR = =s R = ZVR; Momencum respectu plani A ra crecti, (hoc elt.
Omn. = s, co spectancia,) iCRF 45V R ==5R; Momentum respectu plani
ran erecti, ZV R = 3s2 R2 F Z S VR = 3 V R + SSVR; Momentum respectu
plani Aa, (hoc est, Omnia a 5V, eo spectantia,) =ZC R F aVR L L SVR
=Za SR. Atque haec momenta, per magnicudinem dirisa; exhibent, Solidi
ABK, ditanciam Ceniri graricatis d plano A+ a, 3e R F 3SVR = 253
plano 2an, 160R = 8 s R. + 2 52
12VR - 65 =68
L3R +.
12VR - 65 =6v
=B2
32
i (adeoque, d Y A, 3 R -
30  3R + 3 h == ZV; et propiorea ejusdem respectu T A, momencum, hoc est
aegregatum Omnium ; 5~, eo spectancium, sumpris a arichmerice proporionali.
busu 523 R = Z~= R~ = ESEDR = ZVR = 3 sR =5SVR;) distanciamque ab
Aa plano, =3C R + 4 a0 R + 5V R = 2 a 5
+VR = 25 = 28
Trem; Portionis A L bB, magnimdo ee momenta, habencur ex Porrionum AB F,
es Ab B, magnicudinibus et momentis (respectire) additis: Vet subductis Por-
tionis b B0. B magnitudine ee momentis, ex magnicudine e momencis (respectiris)
porcionis AKBa: Vel etiam eodem modo quo habentur iptius bBa B magnuudo
_ momenta. Nempe ex ductu plani a B0 = ~ R, in AY = 2, habetur iptius
AR BB (pritmatis) magnirudo v R. Acque ex hac magnicudine in 5~ (ejuI.
dem CentTI BTAVITALS a P A rel b B distancam,) habetur ejuldem, respectu P A
vel bB, momentum, 5 v R. Duetaque in B = : v = 2 R = 3 v (dillantiam a
ay) ejuldem momencum respectu + an 2v R = E V R. Fademque magnicudine
ducta in Ceneri pravicatis distantiam ab Aa, = C R + a~; et d plano Ar an
CR. = 50 Cealdem nique quae sunes in a bo plano, distantia ab A C, d ra; )
habencur ejuldem momenia, respectu A a, a V R = c. v R2; e respectu plani A r a,
evR2 = = 5VR.
EE cinilicer de porcionibus alio, mucacis mucandis, sudicandum eric.
Supex ADa Semicirculo, crigi incelligatur Cylindri recti porrio; ea ratione,
ue super singulas B V ordinacim applicacas, alticudinem habeat respectivis b B 
qualem,
1C