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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 425, page id 851387705:0445
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primana, e in iplis Reliduis si auterantur Subquintana, led e in Ouadraris si au
ferantur Subsecundana; Irem in Tonanis I auterantur Subprimana, _ in ipsis RC
liduis h auferantur Subnonana, sed et in Cubis li auterantur. Sublecundana, e
Ouadraris Ei anterantur Subtertiana: Trem in Oetaranis si auterantur Subsexrana
e Sexranis si auferantur Suboctarana, sed e in Decimanis li altetattu Sugum-
cana, ec in Ouincanis Rauserantur Subdecimana: et sic alibi ur ex tabella patet.
PFOP. CXXNIIT. TNEENETORUM.
Sed _ etiam alias idem aliquando accidie, puca in Super solidis s auterantur Sub.
PROP. CXXXITI
Theorema.
CTexponalue Lelus Flmanorum mulctara serie Secundanorum; Re-
siduorum Ouadrata, Cubin Biguadrata, erc. ad seriem squalium, Fa-
tionem habebunt cognitam.
Pata
Ouadrata
20
2bD.
_c. usc
Relidua
dc. usque ac
DD-
ZAD 5
Cubi.
a D = 3a D + 3a D -
pe
83D3 = 3UD  3b3D -B
BB - 30D F 3B51- ∞
AD - 3 AD f 3AD - 3AD
+3 = 20
C3D3 = 3c4D 2 = 363D -c
ecc. ulque ad
4X5X6X7 840 140
30 273 4X5 6x7 140
Ft sic deinceps; continue mulciplicando Numeratores per numeros quadratos.
et denominatores per binos continue sequentes Arichmence proportionales.
2LL. CaAaIV.
Corollarium.
Deoque; Si series Aiqualium mulctata serie Primanorum respective du
catur in seriem Primanorum: Rectanculorum (aut ipsis aequalium, vel
etiam proportionalium, Quadratorum aut frurarum quarumvis similium)
accreratum, ad accrecatum totidem aequatium, rationem habebunt coenitam.
Aque idem acvidet si Duadrara seriei illius in Quadrata hujus: Lt Cube
illius in Cubos hujus, C3c. respective durantur.
Nempe cadtem prodibune rationes quae in PrOP. praced. Nam si ducatur
D - a 9: D - a: = D - 2a D. + a C: D - a: = D - 3 a D. + 3 a D - a
Fet a D - a
ec.
M a2
in a
a D = 3 a B + 3a D = a
ec
aD - 2 a D + a
ec.