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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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De Calculo Centri Gravitatis. Cap. V.
ratuE SS2 R = 55 = V, vel addatur = 5s2 R = 352V; habetur Semisesmenti BV A
Nomentum (vel Semiquadrancalis Ingula) respectu iptius A an ZV R 2 - 552R +
552v. Adeoque Solidum illius incegra convertione circa A a deleripeum ZV R2
P + =: de Semiconvertione, 30 PD =  52 P +
2
T2X.
Cencrique
Graritatis, eju(dem B V A Semisesmenci distancia ab A ∞, (divilo MOmenIO pEF
magnicudinem SF inventam) erir 30X =3s R + 5s2 2V = s R + sv
3aR = 25 R + 1 52 , 3eR = 35V
AUE CtIAM, PTOPIEF 2VR - s = C7 - 5 ==2; MomentM CrIE SV R + E5 V. Solidum
convertione integra lactum si P +
ert
i e
x;ec, convertione dimidia, 122X f. 
22. R
VR] 52V VR (52
distancia centri pravicaris ipsius semiscemenei BV A, ab R7 20 R  250 ZR + 250
Si autem, ex hoc Semisegmenti B V A momento 5 92 R. F 55 =V, auteramus mo-
mencum Frianguli B AV (respectu ejuldem A a) 5S2 V (est enim Balis AV = 2.
alcieudo BV = 5, Cencrique Gravitatis d tiate diltancia Zs; adlCOquE MOMEHEUM
s2v:) relinquiene Sexmenci AB A. Crespectu ejuldem A∞.) momenum, 502 R.
Oeprius.
Sumiliter; Distancia Cencri graricaris Frianguli BCan 2 recta Aa CA (per 6
hujus) SBV = 55; ejusque magnicudo =s R. Rrso illius (respectu rectae A a)
drantalis Ongula, est 55= R: Adeoque Solidum inteera
convertione circa Aa Factum, SS= P; et convertione dimidia-  28
Priangulique BOo momencum illid 5S2 R, addicum Sectoris B C N momento
(BO reDetcO) LVR3 ==5C2R: exhiber Secloris D a A (respectu eju sdem A a)
Momentum, rel Semiquadrantalem Vngulam, 5D R = F S = R 50E R. H2 5e R
Solidumque incegra conrerlione cirea _ a Factum, ZV R P  L52 ∞ =. 2C2P + Es2 4
et Demisolidum, 8V. RP + B 52~ = (EOEP + 152 illivie e
Auc eciam; Propter Prianguli B V e magnimidinem ZsB = 5 R 35V; et Cen-
eri graricaris ab A a. distantiam Zs; erit ejuldem, respectu Ra, momentum Zse B
S2R - 552V: Ec Colidum ejuldem cirea Au’inceora convertione Factum,
53B∞ 1IeV 1t
12 X A352P-
5N = 3SP=; Semisolidum,
22
vZ
Triangulique B r a momiencum Ilud ; S X = 3sEV; semileomenti B V A mo-
ento ZV R= =  5= R = 5S =V (B R rePertO) additum; extribet Sectoris Ba A
(respectu ejusdem A a) momentum, leu semiquadeantalem Ongulam :VR F Z52 R.
Cc prius. Adeoque (uc prius) Sosidum, ZV RP = 55 2 D; e Semisolidum SVRF
Fricque (momento per magnicudinem : a R F E s R = 3 fR, SHI inventam, di-
riso,) Sectoris B a A distantia Ceveri gravicatis ab A a,
VR2 F 3SR 20R + 5
3a R + iSR
Decerminarimus ieine (inter alia). tum sectoris D C A, tum B a A, cum Se-
miseemenci BV A, Cenera graritatis, (per corum cum a r an leuif A, seu BV,
seu DC, cum ab A a, distancias,) quaque hinc dependent.
Arque ae eandem tormam, murais mucandis, de aliis cireuli portionibus judi-
candum erit.
Potine aurem hac eadem, quae rectam A a spectane, (SD, R, S, tradica,) hac
adhuc alia methodo explorari.
Sunt utique (Per nollx Arithmetica InfinitOrUm, DFOD. LIZ, 22E, 223, _EC.)
Ouadrata ordinarm applicatarum in Ouadrante, (vel Subtenlarum in Semicireu-
lo) Series A. qualium mulctaca serie Sccyndanorum. Pura, ut R 2 - 0, R?
qu R= = 9, ec. ulque ad R2- A2. HIoC ell, ur Plana Cylindri Conice
exCaVAII (Per PEOP. X13. ejusdem;) Veh (per ejusdem PTOP. X72.) ut Rectae in
Semiparabola diamerro parallela.
Si enim Ouadranti ADC, circum soribatur AOD C. quadratum, quod Diaso.
nali
115. 159
Fie
463.