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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)
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PrOD. XIX. De Calculo Centri Cravitatis.
Momencum respectu aciei Cuaer ; R2 P = 4 R2; respectu cermini oppotii, 4. R. FiB. 168
8K
Distanciaque Ceniri sraricaris ab acie lua, LP - ; ab oppotito cermino, 8 270.
Ongulaeque a Bo aciem habentis Bo, momencum respectu ra; idem est alque P.
omnium aB. planorum, iplam complencium, respectu ejuldem ra: Hloc cst, (per
S9. prOP. 27.) Omn. a e A E + a SV R: seu Omn. = a R = 4 s A + a 5VR: e0
Spectancia: Tumpris a arichmerice provortionalibus.
Sune aucem Omnes a: (aricthmerice proporrionales,) = : a3. Adeoque Omn.
2aR2: = da 2 R=
FcOmn. S: ( modo ostentum,) = v R. Adeoque Dmn. - + 5 R2: =  v R.
Trem Omn. SV: ( per SA. prOD. 18.) = EV= R = v R2 - 3 52 R. Adeoque
Omn. 2SVR = 5V R3 = = V R3 = 85 2 R2.
ErBO, Omm. 4 a R2 = = 5 R 2 + = 5V R: == 5a 2 R2 - 85= R2, (eU BCF R . OuOd
itaque est momentum Ongula aB0 aciem habentis Bv, respectu ra; Idemque
(propier diltancias et altirudines reciprocatas,) etiam aciem habentis ra, motmen-
cum respectu BV.
Hoc saque momentum, per Ungula aBv, aciem habencis B0 magnicudinem
(modo dictam) e R2 diritum; extribet hujus, 2 7a, distantiam Ceneri graritatis,
F= 8a + 35
ioterai
Edenique momentum, divitum per magnitudinem Dneulae as Bu aeiem habepiis
ra ZeR + 2 5VR (per S . prOP. 17.) extribet Ongula a Bo aciem ha-
bentis ra, Distanciam Centri Graricaris a Bv
Aa
a R = 2asR. + s R + 2a5V eR + rast
 adeoque ab
2a R = 25 f + Z, 5V 9099(1 1. Y
2aR = 25R + 250 ,11 2CR + 22
A a momentum, Za = R2
aa 5 R
e-
efR
ee propterea, ejuldem respectu
  asV de R 95b R:
Ouod iplum (propier diltancias _ alciiudines reCIprOCatas) el eriam mementum
Ongulae a50 aciem habencis R a respectu ra. Aique hoc demum per hujus Mag
nicudinem (modo dictam) e R2  av R, diritultu; cextribet Onsul aBV
a R - 245 R + SR + 2257
aciem habeneis A an distanciam Ceneri exaxicais d ru 8 a R = 85 X F 8a 
c2X = 2 a 5V
8ck + 8aV
colu
115e
ot
Fr Execiacim, Ongulae a Sin aciem habentis sn monienum respectu r az aciertive
habenes ra, momentum respectu sn; (PFOPIeT a = +P, ex S V = R,) 73 R2 D2
ER4. Aciemque habentis ra, momentum respectu Aa; aetemve habenLs A a
momentum respectui 24; 228 R2 F F 3R1. Irem Aciem habentis du, Distanria Cen
eri gravitatis a ra,  P F SR: Aciemque habentis A a, Diltancia Cencri gravitacis
D2 + 16 R
d ra, 
13t 1IE P2 = 26R
vicacis a du
B∞p: Aciemque habentis re Diltancia Ceneri. gra.
1 2R2
L p f 16B
∞i ab Ag, 
ejus
Wscton
In Ongulis ivicur expoticis, cum quae liguram sinuum vertorum, cum quae ligu.
ram Sinuum Rectorum, corumque partes spectant; decerminarimus cum Magnicu-
dines, cum Momenta; e Cencri graricatis distantias, tum d plano per aciem per-
vendiculari, cum d plano ad aciem recto; acque in quo cerrio per aciem plano
conlticucum (IC, Constat ex PEOD. 12. nempe in eo quae Onoulae alcicudinem bile
cdc. AdeoquE (per prOP. 26. Cap. praeced.) iptum in sinsulis gravicatis Cetlerum
determinarimus
Oux aurem de Onoulis craduncur, eadtem et Solidis convertione tactis, eorum.
ve Sedisolidis, aliitre impersecta convertione Factis, tacile accommodan 3 per
DrOP. 12, ec 2g. hujus. Nempe Semitolidi conrertione Facti, magnicudo, est ad
correspondentem Ongulam Semiquadrancalem, uc L P ad R: Fjulque Centri gra-
vicacis diltancia a plano quod conversionis axi rectum sic; eadem est quae Vnoula
Plano aciei sux recto: Adeoque momenca illius ad respectira momenta hujus,
respectu iltius plani, sunt ut ipsa magnicudines, nempe ut L.  ad R: Cenrique
Bravicatis