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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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PrOP. VI. DeCalculo Centri Cravitatis.
Complementum Parabolocidis Cubici, (proprer hujus Parabolocidis ordinatim.
applicatas, in suberiplicaca ratione diametrorum interceptarum; adeoque ordina.
rim. applicatas Complemenci, in Priplicara ratione diametrorum, sire dictanciarum
a Vertice Complementi;) est Scries Ter-
tianorum: Puta, ut OP, IP, 8P, 27P.
Ec. Ulque ad P; adeoque summa omnium
d
263
de
UC =N P; per F hujus; (hoc est, ad Pa OdP, +d p, 16d p, 8F dY
ralleloorammum circumseriptum, ut F ad
+:) Cum itaque Diltantixe CnE Ut Od,
E d. 2 d 3 dus _c. ad. D: NIOmenta CrUNI
ENDP = LNPxAD.
UE Oap, E d p, 26ap, 8E ap, usque ad DP. FE Cimut omnia (per L hujuS) ut
ENDP =ENPXSD. Et Diltancia Centri graricatis; ZD. Per 24 C aP. 4.
Acque, ad candem formam, mutatis murandis, in aliis Paraboloeidium Com-
plementis, aut etiam solidis eorum convertione circa Axem Tuum factis: aliitve
lecundum ejusmodi alias series.
Parabola, BAB, Fig. 127. (Propter ordinatim axplicatas in subduplicata ratione dia. L.
metrorum:) est series Sublecundanorum; cujus Index Z: Duta, VOP, VEP, V2P,
V3p, ecc. ulque ad P: Adeoque simul omnia, ut ZNP; (nempe ad Parallelo-
grammum cireum (eriptum, Ut 2
ad 3,) Der F hujus. FE PrOPteF
diltancias, uc O d, 2 d, 2 d, 3 d.
VOD, YEB, V2P
Odqe
Ed
Sec. ulque ad D; NOmenL C. OdV p, 2 d V p, 2 a V 2P,
TUnE, utOdVP, EaVFP, 2dV2D, dVoP, aVD, dvop,
3 dV 3P, ecc. vel ut a V Op
aV FP, d V8p, d V 27 D, eC.
ulque 2d DP: quae est, Peries
ZNFDF = ZNPXZD
Cuborum Sublccundanorum; cujus Index TZ vel 3. Adeoque (per F hujus)
Omnia, UEZND P = ZNP XED. EE distantia Centri graritatis, 3D.
Paraboloeides Cubieale, (proprex ordinarim applicatas in ratione diametrorum Cis
Tuberiplicata,) est leries Subterrianorum; cujus Index z. Puta Ut V COP, V CP,
V c2P, VC3P, _c. ad P
E. L OMNIUI LUMMA, UEZNP;
Der E hujus. (hoc clt, ad
VcOB VCTP YCZB,
Parallelosrammum circum. Od V cOP, Ld V Cp, 2 d Y C2P, 34Y C3)
Seripeum, uc 3 2d 4.) Et,
proprer distantias, uc Od,
2d, 2d, 34, etc. ad D: NO.
menta erunt, ut, Od V COp,
aY COp, aV CP, dVC+OP, aVCBEB,
ZNDP= Z NPM3D.
a
DF.
TdYCEp, 2aYC2P, 3dY C3P, eC ad DP; sire, ut dY Cop, a Y Cp, d Y C26p.
qYCB+ p, ecc. ad DP; Series Biquadratorum subtertianorum; cujus Index F.
vel Z. Ec Cumma omnium (per L hujus) ut ZNDP = E N PXZ D. Pc diltantia
Ceneri gravitatis, ZD.
Et similiter de aliis seriebus judicandum.
Nempe, univertalicer; Si Index seriei Ponderum sit S; adeoque (per L hujus) HL.
cumma corius, ue   NP: Index seriei Momencorum, erie S. + L; adeoque
norum summa, ut =  = NDP. Ouxe per summam Ponderum NP di
vita; exhibet  = D, distantiam Centri pravicatis d verrice; nempe, ad distan.
tiam maximam, ut S. f + ad 5 f 2: Adeoque reliquum distantia (quae est di-
Pancia Cenuci oravicatis L Bati) ut g.  D. EC propterea, Axio potrio ad Ver.
ricem, ad porcionem ad Balem, ut 5 f 2 ad 1. Quod exat demonctrandum.
Modque