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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)
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A L C E B R A.
Cap. XL IV.
Ouorum ralorum a (modo sie possibilis) uterque est NegatirS; (propter
J: = bb - c0: minus quam b = Y bb.) Sed (ob causam modo dictai) uier-
que Imaginarius, si c major Tc quam b.
Ouod Sufticie resolvendis omnibus aequationibus Ouacraticis.
IIle aurem hane Polurionem non Polet adhibere; led pocius illam alteram
(ut ec post cum, Pellius) complendo Ouadratum. Ouam ille Mechodum mox
achibet ad AEquationes ZIF _ ZIII mox sequentes; et nos supra expolui-
IUS.
Sed quacunque sit processus Forma; sire complendo quactratum, sire 10l.
lendo secundum terminum; sre quam ego supra primo loco memoravi; leu
quaeris alia: res eodem redic (quacunque ria eo Derreniatur;) Nempe,
Agnationum,
Radices.
a a = 2 b a = F c6. a = = B = V: bb + Cc. Major AHirmatira.
aa = 2b a = = cc. a = - b = V: bb f 66. MInOT ATirmativA.
aa = 2ba = = cc. a = = b = V: bb = 5c. Viraque AFirmatira.
aa = 2 ba = -- 0c. a = - b = V: bb =cc. Viraque NegatIVA.
Attamen: Oroniam Coeficiens (quam nos 2b dicimus,) quamris Fractio
umc
nOn (IE, Possit camen esse nil
Ouando hoc concingit; commodius eric (pro vicandis Fractionibus in procettu
operis) rem lic delignare (polico f pr0 2b.)
Aquationum,
Duplae radtices.
aa - fa = +66. 2a = + f F V: ff + 4cc.
aa +fa = +C6. 2a = - f = V: ff. + 4Cc.
aa - fa = - cc. 2a = + f = V: 5f - 4Cc.
aa +fa = - c6. 2a = - f+ V. 55 = 4CC.
Duplaeque radicis sic inrentx, dimidium sumere pro valore a. Hoc es a =
s= V. F5 + 45C.. pocius quam a = + 3 f = V:  55. + c5. Ft similicer in rC.
liguis.
Acque ob eandem rationem; Ouando suprema potestas radicis a altecta fue.
rit coesticiente; puta ma a - 18 a = f n d d: E m calis FIE, ue non divictat s
a
_ n d d absque Fractione, quo tiant S. =f e  = ec numeri integri: Com-
modius omiatur solica praeparatio (dividendo omnia per m, quo fiat a a ab
altcctione immunis,) rem ica delignando;
Aquationum,
maa = 13a = = n a d.
maa = 15a =, + n d d.
m a a - 18 a = - n d d.
Mulcipla radicum.
2m a = = 18 = V: II88 + 4m n d d.
2m a = - 18 = Y: 2188 + 4mn dd.
2.m a = = 18 = V: 1188 = 4.M n d d.
maa + 1ea = = nad. 2m a = - 18 = Y: 1185 4mnad.
Acque cum eandem radicis mulciplum diridendo per 2 m, quo habeatur ralor
I188, n dd
amm m
2M
E V.
Ouamvis enim valor utrobique idem ; operis tamen pro.
cectus sic minus erit impectitus.
Alque hactenus de quadracieis ARectis, ad quadratieas simplices reducendis,
Tublato secundo termino.
CAP.