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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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Cap. ZL. IV. A L O E B R A.
C A P. XL IV.
Fujus usus, pro Resolvendis aequationibus Quadraticis.
OC axtificio (de Addirione _ Subductione instimenda in radicibus non-
dum cognicis, adeoque Tublatione secundi cermini) aequationes Ouadra-
ciex Atectae, ad quactratieas simplices reducuntur: OE Tola radicis qua-
drarica extractione vorro opus HI. Exempla haec LUME.
AEquario aa - 2ba = + cc;
POTito a = e = b; Adeoque f ee = 2BC + BB = + a a 2
Fit
=2b0 = 2bb = = 2b a5 = + c6.
ee = + bb +66. Cujus radix e = = V: + bb + cc.
Adeoque a (=  + e) = b = V: + bb + c6.
Ftorunique valorum radicis a reperietur alier Actirmatirus, alter Negatirus:
co quod V: bb. = cc: major ct quam B = V bb.
Aquario, aa + 2b a = + cc;
Pohito a = e - b; adeoque ee = 2BC = Bb = + aa 2
Fic
= 2bC - 2bb = + 2ba5= +66;
ce = + 33 +00. Cujus radix (ut prius) e = LV: + Bb + cc.
adeoque a (= - B + c) = - 3 + V: + 3B + cc.
Ouorum valorum (ue prius) alter AAirmativus est, altex Negacirus (ob cau-
sam modo dictam.) Sed hoc calu, Major est Nexarirus; in priore, Minor.
Aquatio aa -- 2ba = = cc.
Potico a = e = b; Adeoque ec + 2bC + BB =
Fit
aa2
= 2bc = 2bb =- 2ba5 = c6
ee = = bb =cc. Cujus radix e = = V: L bB - cc.
adeoque a (= = B. + c) = + B = V: + Bb-cc.
Ouorum valorum a (modo sit postibilis) ucerque est AHirmativus: (propter
V: bb =cc: minus quam B = V bb.) Sed Fieri Potelt, ut calus sic Impossibi-
lis, adeoque radix a Imaginaria. Nimirum, Si c major sic quam b; adeoque
bb -cc negatira quanticas; quae radicem quadraticam non admitrit.
Aiquatio
aa = 2ba = = C6;
POtO a = e - b; Adeoque e0 = 2bc. + bb = + aa2
Fic
+ 2be - 2. bb = + 2ba
ec = = bb - cc. Cujus radix, e - + v. + bb - cc.
Adeoque a (= - b + C) = - b =V: + bb - 05.
Ouorum