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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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LARITHMETICA
F Sic deinceps, continue multiplicando numeros Arichmetice proportionales
(quousque gradus po: eltatis poltulat) d 2 e 3 concinue binario crelcentes.
P R OP. CXIX.
Corollarium.
TProPterea Conveics (vel Pyramidoeides) Semiparabolae laut etiam
Parabolae) circa asius ordinatim applicatam aptatum, erit ad Cylin-
drum (vel Prisma) ejusdem basis e alticudinis, ut 8 adt 15.
Nempe ut Ouadrata reliduorum seriei Aqualium
muletata serie Secundanorum, (ad rocidem maximo X-
qualium.) Nam si volvendo Semiparabolam A DO cir-
ca iplius ordinatim axplicatam DO, uE axem (vel
etiam alias, UEPTOP. 9. Con. Sect. diximus,) FOrMEtIE
Conocides (vel Pyramidoeides) Cujus Vertex O: erUNE
plana illa Conocides (vel Pyramidocides) consticuen-
cia, ut Ouadrata serici Aqualium serie Secundanorum
muletara. (Nam recta in Semiparabola ADO diame
ero AD parallela, lunt relidux Aequalium ablaris Se-
Candaris, in complemenEO A Y O rEpertIS, VIE PaLCL EX
dictis ProP. 23.) Ideoquo ad coridem maximo aequalia
(hoc est Cstindrum rel Pritma,) ut 8 ad 25 per praecedenria.
SC TTOL YV M. 0.
Et parr modo de Conocidibus vel Prramidoeidibus ad Paraboloeidis cujulvis
ordinatim applicatam aptatis, judicum tiet, ope sequentium proposicionum. Puta
in Paraboloeide Cubieali ratio erit ut d ad r4; in Biquadraricali, uc 32 ad 45;
in Supersolidali, ut 25 ad 33, eec. ut in tab. PFOP. 126.
P ROP. CXX
Corollarium.
Pinde, Si nnita serres Aqualium mulitata serie Primanorum, in
eandem seriem AEqualium eadem serie Primanorum auctam, respective
ducatur: Rectanculorum (vel Duadratorum aut etiam similium quarumvis
feurarum, ipsis aequalium, aut quidem proportionalium) Aecreratum, ad
Accrexatum tocidem maximo N. qualium, rationem habebit cornitam. u
Alque idem accidet, si Duadrata seriei mulctara ducantur in Quadrata se-
riei auctae; e Cubi illius in Cubostrujus; (5 sic deinceps.
Nempe cacdem prodibune rationes quae in PCOP. 178. NaM, A NREBE  Y
1 2C 1
in R
Pacic D- a5
C: R
D: R V a:  R, 2a.R F a 7. 1 1. 1L C MC 5(IL LC 1
a
 C: R.  a. = R.
Fuct. BB FAi e OtiX.
2
22 = a
3aR2 = 3 a2 R + a
Cacit R = 3 a 2R + +
ec
5
ee sic ip lineulios cerminio cujutvis pocestacis; ur mulciplicaneto patebic
PFOp. CXIX.
3aR=+ 3,4 d
5