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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 390, page id 851387705:0410
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ARLTAMETICA
erop. LIF.
inchoatarum; (puta VO, VF, Y2, Y3, _C. YCO, VCF, VC2, YC3, _c.
V990, rgqF, Ygq2, V9433ec.) Ouas appello series Subsecundano-
rum, Subtertianorum, SubguarEanorum, etc.
Exempli oratia. Si exponantur ejusmodi infinita numero Ouadrata Arichmetiee- pro-
portionalia, lire juxta seriem Primanorum; quibus in Tabella altignatur ratio + ad 2.
Forum Laceribus, (hoc elt, seriei Tubsecundanorum) conveniet ratio E ad L =
(Tire 2 ad 3;) quia F, F3, 2, Tunc Arichmetice proportionalia.
Trem, si supponantur ejulmodi intinii Cubi Arichmetice proporcionales, Cire
juxta seriem Primanorum; quibus conrenit in Pabella, ratio F ad 2: IIlorum
radicibus cubicis, (hoc elt seriei subterrianorum) conveniet ratio X ad F3 (vel
3 ad 4:) ec harum radicum quadraris, ratio + ad 23 (vel 3 ad 5:) Ouia Lcilicet
F, F5, +3, 2. Tunc Arichmerice proporcionalia; sicur Onicas, radix, quadratum, e
cubus, sunt Geometrice proportionalia.
Ft pari modo, s intinira Biquadrata, Supersolica, dec. constitura intellisantur
juxta leriem Primanorum, quibus convenit ratio F ad 2; eorum radicibus Biqua-
dracicis, Supersolidalibus, ecc. conrenient rationes 4 ad 5, 5 ad 6, ecc. vel 1 ad F7
Zad F= _C. quia nempe F, X2, +4, L3, 2; ieM I, L5, F5, L3, +8, 2; deC. fUINE
Arichmetice proporcionalia. Adeoque.
P ROP. LIV
Theorema.
F incelligatur series intinita quantitatum, a puncto seu o inchoata-
Drum, et continue crelcentium pro ratione Radicum quadraricarum,
cubicarum, biquadraticarum, etc. numerorum Arichmetice proportio-
nalium; (quam appello seriem Subsecundanorum, Subtertianorum. Sub-
quartanorum, 6c.) Frit corius ratio ad seriem cotidem maximx aequa-
lium, ea qua sequitur in hac Tabella: Nempo
Subsecundanorum
Subterrianorum
Subquartanorum
Subguintanorum
Sublextanorum
Subtexcimanorum
Suboctaranorum
Subnonanorum
Subdecimanorum 
Lit he dCinCePd.
Patet ex praecedente.
R O P. LV
Corollarium.
RBO Planum semi- parabolae (vel etiam Larabolae) est ad Paralleloeram-
mum circumscriptum, ut 2 ad 3. ( consequenter ipsius complementum
est ad idem L’aralleloerammum ut X ac 3.)
Fst enim Planum Semipara-
Bolae (aur etiam Parabolae) Sc.
ries intinita sublecundanorum
(Der 8 PFOD. COn. Sect.) Pa
rallelosrammum autem leries
coridem maximo aequalium: F r-
80 illud ad hoc uE L ad x3, vet
ut 2 ad 3. (et, consequenter,
ipsius complementum, nempe
Eata) decamimi reliduum, uc
PKOP.