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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 469, page id 851387705:0489
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PEOD. CXCI. INETNLTORUM.
erie eorum ab invicem disserentia (ee propierea uiriusris a justo) intinice parra,
hoc clt, nulla.
PorrO; Duoniam, numero e sic in intinicum aucto, illa Onicari adjuncta pars
Sui aliquoca, sucura est intinice parra; exique, sive Y L =, sive Y =- =
3 Can.
cundem acque V I, Sive 1, (proprec eranescencem parrem intinice Barram,) qua
mulciplicando nihil murar: Dicimus, Fractionem illam 3r3r5 X5 ~ 7 X7 X ec.
tey
On25X49 XBL 8C.
8x24X48x80 80.
2X4X 4 X6X6X8x _C.
in intinicum concinuacam, este ipsistimum quaelicum nu-
merum e praecile; ad quem ita se habet F, ut Circulus ad Onacratum Diametri:
Vel, (E id masis placeac,) ut cst iltius Fractionis Denominator ad Numeratorem,
sic esse dicimus Circulum ad Diametri Guadratum: F.G, uE Numerator ille ad DC-
nominacorem, sic Ouadratum illud ad Circulum; Nempe ue tactum ex continue
mulciplicatis 9x25 X4.OX BF eC. (quadraris numerorum imparium,) ad Factum Cx
8 x 24 X 48 x 80 ec. (eisdem quadraris unicare minucis) in antinirum conci
nuatis.
Si quis aucem curiotius inquirat, quousque continuanda erix illa musriplicario
continua, uc eandem ad differenciam datam, sire ipla minorem perveniatur: J. Neni
De ue numerus julto major, numerum justo minorem, iptius parce quamlibet exi.
Sua (vel ne illa quidem) Superec: Id hoc modo investisabiturs
Ouancitas major dicacur m, minor n, licque earum difterencia, iltius pars fuan.
tumris exisua; puca  m =m =n; et quaeracur quousque concinuanca eriu
operacio, hoc ell, quis tucurus esE numerus S mulciplicacorum (simplicium) maxi.
mus, un illa differencia (ret salcem ipsa minor) prodeat.
Ouoniam igieur M = n = = M, exic n = M M; e m. n:: M. m- m::
112
m. -, = m: : B. B = a: : 8. Y: 2 = F. (per modo demon strata.) Ideoque
BV: 2 = 2: = b2 =a 3. Fx (verinque quadrando) b 3 B2 = b ~ + a2 2
=2ab2. Acque (delondo urinque 3 ~, e reliqua cantponendo,) 2aB 2
= a 3 = V. Ft denique (uerinque diviclendo) 2 = 2 ab =  2. Flujus: Egitur
numeri radix quadratica, (s Fuerit mumerus par,) vel saltem, (si vel fracts vel
Furdus sit rel numerus ImpaT,) par numerus illa radice proxime major, futurus
est mulciplicatorum maximus, ut altignata disterentia, vel ipsa salrem minor, pro-
veniat. Ouod crac inrestisandum. B  i
Idem Aiter.
Post hanc autem noltram, iptius quancitatis e designationem; libet etiam aliam
Tubjunsere, quam a Nobilissimo Viro, atque acutistimo simul Greomeera, Dom.
Guliel. Vicecom. e Barone Bronnoter, accepi.
Cum illi progrestionum aliquot mearum propoluerim, es qua lege procederent
indicaverim, id interim rogans, ut qua forma quancitatem illam commode de-
sixnandam pucareri, indicaret; Nobilistimus. Vir ille, re apud le perpenta, me
Mhodo item Infinicorum sibi peculiari quancicarem act
tranc Formam commodissime designandam judicarit.
Nempe si unicari adjungatur Fractio, quae denominato-
4 = 2 4 3 13 13 12 c.
rem habeat continue tractum; ca lesc, ut parricula. lE
rium Fractionum PumeratOres (InE F, 9, 25, esC. numeri quadrarici imparium
Eg 3, 5, c. Denominacor rero ubique 2 cum adjuncta tractione, et sic in infini
tum. Hoc simul addiro, ut ubicunque candem placeat consistere, pro ulrimo
numero 2 cum tractione deinceps insecucura, ponatur horum aliquis (prour 10.
cus ubi consisticur postularerit) 3, 5, 7393 etc. (deinceps ab T, numero inteero,
Arichmerice proporcionalium;) nempe li in primo loco lillacur, 3; si in lecundo,
NR N 3