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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 798, page id 851387705:0818
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DeCalculo Centri Cravitatis. Cap. V.
Fi8. 169, Trem; Omn. 35V2: = 8V3 R = 3VR3 - 3 s2 R2 =3 s v R, (per BT. PrOP. 18.)
Adeoque Omn. - 3 502: = - 5V3 R = - Zv R3 + 35 = R2 + 3 s2 V R.
ErgO, Omn. Z5VR - = 5V 2: (= Omn. Z 5Vh: = Omn. 353:) HOC est, mo-
mentum Onoulae aBo, aciem habeniis ar, respectu ipsius ar rectae, est, LV2R2 -
323 R, hoc est, 3V R3 = 5 s R= + 5 s2 V R. ut prius. Aique hinc Distancia Cencri
Graricatis ab ar colligitur, ut prius.
FG speciatim; Ongulae ad n aciem habentis ar momencum respectu iptius ar
(PrOPtCEV = s = R; e a = + P, ) CAZ R; ejusque magnicdo rs R= P; CeNEI
que pravicaiis ab ar distancis, 32 P
Ongulaeque torius arn, aciem habentis r a momentum respectu ra 2 R4; (ipLius
adu duptum, propter duplam masnicudinem:) Diltanciaque Centri graviratis a
eR
ro eadem, nempe: Fc quidem (Per PrOB. 5.) suver ipla du recta; hoc est,
d F~, vel Aa, +P; e proprerea ejusdem respectu Aa scu IF momentum,
(propter magnicudinem sA= P,) elC, = R P2: Quod itidem est aciem habeniis
FT, vel Aa momentum respectura; propter alticudines se distantias reciproca-
tas. Adeoque (proprer hujus magnicuainem =R2Y) Diltancia Cenrri graritaris
27a, 162
Similicer; Ongula aB0, aciem habentis Bo, momentum respectu Aa; SUNE
omnium planorum aEo aCv, ec. ulque ad a Bv, (ungulam illam complentium)
momenta respectu Aa; hoC CA (DerS 9. prOP. 27.) Omn. = C R 2 + a V R: seu
Omn. = a R Y sR + a V R, eo speclancia; sumpris a arichmetice proportiona-
libus.
Sunt aurem Omnes a, (arcus arichmetice proportionales, eo speclantes;) Za2,
(per prOP. L. hujus:) adeoque Omn. = a R 2: = = = a 2 R 2
Ft Omnes s (eo spectanies) hoc est, iptum a B0 planum, ett Vv R, (Per SO.
PrOD. T7.) Adeoque Omn. 5 R =: = V R3.
Tiem Omn. a0 (Tumpris a arithmetice proporcionalibus,) Funt ipsus A BK
plani, momentum respectu Aa; hoc CH, Z a = R = a 5 R F V R2, (Per S FL. prOP.
27.) Adeoque, Omn. aVR: = = a 2 R 2 = a5 R2 = VR
ErgO; Omn.  a R2 = sR= F aV R: = 2V R = a s R. Ouod itaque ett
Momencum Onoulae a B. aciem habentis Bu, respectu Aa; aciemre habentis Ae
momentum respectu Bv.
Duod quidem momencum, diritum per Ongulae a B0 aciem habentis B0, magni-
cudinem e R= PCu a R E - s RE, (Per S O. PrOD. 17.) exhibec ejusdem Distanciam
Centri pravicais ab A a
2VR- a5
a-5.
;adeoque d BV, a = 2VR = a5 a = 2VR. cjus.
que Propterea respectu BV MOMentM a 2 R 2 = 2 V R3.
1 S-
Idemque 2v R = as. R2, per Ongulae a B aciem habencis A a, magnicudinem
=e R + av R (per S G. PrOP. 27.) diritum; extibet ejusdem distantiam Cencri
Gravicatis d B0, 2V R2 = aSR
R = 5R = av
=2VR
2VR 2 = a5R
hujusque propterea, respectu Ao, Momen.
tum, = a  R2 = 2a5R2 L a v R = 2V R
F Speciarim; Ongulae as n aciem habentis su, momentum respectu A d; aci.
emre habenris Aa momentum respectu Sn; 2 R 2 - = R3 P: Ongulaque a Sn
aciem habentis s’un momencum respectu s u, 1 3 R 2 P= - 2 R: Aciemque haben-
tis aan momentum respectu Aa, L R3P = 2 R.. Centrique gravicacis, Ongulxe
8R RT
adn, aciem habeneis su, distania ab A o ∞ - a R
-32
4P - 16K: Aciem.
que habentis A a, distantia Centri praricatis d S u, 2 R - = P; ab A a, 2 P - 2 R.
Ongulae autem coriusa r n figurx linuum rectorum torius semicireuli, aciem ha-
ventis lire Aa, Ere YT, (PTOPTeT a ==ZP, V = 2 R, 5= 0,) Magnnudo, E R P:
Nomentum
0
R + 2a5 R + a
aR + sR + av = = ek F av