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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 325, page id 851708439:0349
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rum sic a maxima, e minima, idemque communis excestus; omniumque nume.
rus n: Est, inquam, naa, = a an F e in a f b F c + d f en = 3 in a a + bb
+c6+ dd + c6.
DE M ONS TR A FFO
Adeoque na C = a a.
Tiem, a =d = C 6 + 20 = a + 30 = c + 4c.
TToc est, a = B + e = c = d = d f c = c + b.
Adeoque, na = a + 2.B + 2c + 2.a + 2c.
1t
aa = F Bb = + 65 = + ad = + ec
ec + ad + cc + 60
+2Cb + 2dc + 25d = 2 bC
+aa = aa...
..
aa +bB +cc + ad  eet = E
 nac =  + ee + ad + cc +bb5
l1805
 2eb F 246 f 2Cd f 2be = e
a= 2eb + 4ec + 6ed  8ec = B
B = e in, 2b + 45 + 6d. + 8e
F c in, .. . . . a F b f c.  a  e
7 = e in a + 3b +50+ 7d. + ge
=d
Le in, a F 2B = 2c + 2 a = 2C (= na C) = a l 2
Lc in,. .. b + 26 2 d + 2c =
e In, . . . . . . . c.  2. d  2.C =
e in, . . . . . . . . .. d.  2c =
Fc in, . . . . . .
....
e:
= aa = bb + cc + ad + eet
8 =. 2a a f 2. bb + 260 + 2d d = 2eC)
n = 3 a a F 3bb. = 300 + 3 a a F 3ec =d
B = 3 1 aa + bb + c0 + a d + cc=
e =n aa, F a an F c in, a f. b. + c + d + c.
duod erac demonstrandum.
LGIIILIEZL
COROLL ARLVH.
C3 in, aa + b + ec + ad fcCZ
1. c in a. = b + c + a + e = (e in a + 2B. +25 + 2 d + 20 = a a =) 2 aa.
Hoc ct; Duoniam (quo tiat omnium criplum) actumendum aliquid ett, sed
minuS quam 3a a.
Arehimedes Ec enuneiat. Freo, quadrata omnium aequalium maxima, minus
Cunt quam trictum quadratorum illarum inaequalium, (nimirum, quia altumendum
aliquid est quo tiac criplum,) sed minus quam criptum omnium exc epto quadrate
maxima (quoniam, quod sic altumitur est minus quam criplum maximi quadravi.)
Duodque de quadratis aieitur, pariter valet de aliis fieuris inter se somilibus, ait
eas rectas similiter descriptis: (co quod Fgura planae similes sime inter se uE
quadrata lacerum homolosorum,) Ec talibus erat ille. Post usurus.
Monendum hic est (quo constet archimedis propotirionem cum mea coinci.
derc) quod Arehimeais illud naa F aa idem est cum meo m LL (adeoque F ejus-
dem est = ; m 1I.) Nam illiusn F F est meum m, (qui repuro = O in nu-
mero terminorum meorum qui in numero cerminorum Archimedis non numera-
tuT.) Ejusque a est meum h (maximus terminorum acictumetice prOpOrtiOna-
rimm. ) Fjulque e in a + b +c + a + e, idem est cum meo 3 m. 1, ladteoque
5
S ejuldem
Cap. L. XXVIIT. A L G F B R A.
Nam ne = a.
2
Trem
bb