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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
# Folio 428, page id 851708439:0452
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A L G F B B A.
Cap. XCIX.
deoque (per doctrinam aequationum) a - V.3 F apr. + 2. Fr p - V. 2 t ger. + 2
Sed (ut prius) 2 = ap. Adeoque = = p.
Ergo = =p - V. 20 + apr: + 2. Arque hitune limices
Sedhoc, omnino non estimpossihile. Nam, Sic Lumi pottunt Z, a, duo numeri
rationales incegri, ut sic = minor quam p, sed rancillo deticiat, ut desectus (IL altie.
naco minor. Adeoque cam exieuus, ur V: 2 2. + 4pr: F = sic eo major. Calus ereo
temper est pottibilis. Nam, aequacionum in hac Torma, Radix (attiemmaciva) nun.
quam est impossibilis.
Si de astumpro Lemmace dubitetur; sic demonstrabitur.
Certum est, numeros incesros z, a, Sic lumi posse, ur = sic Fractio (in rationali.
bus) minor quam propoticus (irrationalis) P; Led co tam prove acceclas, ut de.
tectus s daco minor. Fisto minuus hic detectus y. Adeoque = F y = p. Requiri.
cux porro, ue t  + y (= p) - v. 2~ + 4pr: + 2. Fsto  L y + x (- p + v)
Y: 22 + 4pr: + 3
a
2+v Y. 22 + 4Br: + 2
Ec22 + 20 = Y: 32. + 4 pr: + 2. Ec ~ +20
=V: 2~ f 4pr. EF (Tumpeis quadratis) 22 f 4 2V + 402 = 22 F 4 pr. HIoC
Cll; 2V + vv = pr. Adeoque (quicunque fuerit ralor 2 actiratirUS,) erit
V: 22 + 4pr:
Tumprum.
2 =v. Ouod omnino est possibile. Adeoque Lemma benC aL.
Si Forre contiperie (quod aliguando contingat) 3 == 0; (ut puca quando a p non
est major quam L;) hoc neuriquam turbat proceltum; quippe, eo calu, ralor Z ubi.
que cranelcet.
DE MON SF R AF 1O.
Cum numerus n TIC ( ex hyporheti) non quacratus: erit (radix ejus) Vn Curdus.
Ectom numerus intexer proxime major quam (surcus) Vn. adeoque exceltus,
minor quam I. Hloc ell, m = Y n = +.
POnamS B = M = VN. FIY =
eodem major. Hoc CM, = = p = Y: 22. + 4pr: + 
jam demonstratum est.
2a
v. 22. + 4pr: + 4
24
Tum, proptes = = B; adeoque 2 = ap: eric a p - 2 policira quanricas, seu ma.
Jor quam 0.
tem, propior p - Y: 2. 2. +. 4 pr: + 2
erit 2 ap = V: 22 + + Dr: + 2. EC
2ap = 2 = Y: 22 = 4 Pr. Adeoque (sumpris quadraris) 4. a a pB = 4 a p 2. f 2 2
=28. + 4Pr. EL 4 aa PB = 4 a P Z = 4PY. HOC est, aap- a2 r. FC ap. 2 =.
Hoc