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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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c 11G
cionet
velo
vis la
1a
Icet
1O1CV
91
Cap. X
s. A L C E B R A.
 AL P. XXZ e1
De Aquationibus Quadraticis.
Fcundum Methodum jam expolitam: Ostendit FCarriotus, In quaris aqua-
e tione Ouadratica, modo sic possibilis, (hoc est, modo calus proposits, non
sic impossibilis catus,) duas Temper esse Radices, reales; (tor nimirum quot
Lune dimentiones in ejus lupremo gradu) ue quae tiac ex duabus aequationibus
Simplicibus inter se mulciplicacis. Nempe, vel dux Atirmacirae; vel dux NC.
sacirae; (eaeque rel aequales rel inaequales;) vel dux quarum altera SiC ACIr-
maciran altera Degacira; acque, ex his, nunc Afirmacira major estr nunc Ne
fatira, nunc inter se lunc aequales. Ouippe omnes hi casus occurrere pollunen
in duabus aequationibus simplicibus, sic incer se mulciplicandis. Verum (I ca-
Tus expolita aequationis sic Imposlibilis; Radices illa dux non Reales erunt,
sed qua dici Colent Lmacinariae.
Exponic item, singulorum horum catuum Exempla; dualque simplices inter
se musciplicando, ostendie, Oualis sic, in quoque calu, quae inde relultat aequa
eio Compolita. E consequener; expolic aquatione compolira, ex quibus lI.
uctous oriri centenda TE.
Exposici catus Fres Tunt,
d=-0.
 = O.
Vide dect. 4. proP. 2. 22 - ba
=ca = Bc. = 0.
Leacticco; Fb c
Vide Sect. 4. Pr. 2.
=
=0
c =0.
d a = - ba
u Ca = b6 = 0.
d. b = 0.
a = 6 == 0.
aa Fb a
F ca F b6 =0.
In casu horum primo, radix utraque est AFirmatira. In sccundo; altera
AAirmatira, alcera Negatira: Sed non apparet, in hac Forman uira duarum ma-
Jor sir. In cerrio; utraque est Negacira.
His cribus, duos alios addic (in procestu operis) catus speciales, quas A qua.
tiones rocat Camonitas Secundarias,
IV. aa = +B5. 44 - b0 =0.
V. aa = - bc. aa F BC =0.
Radices; = V bC, = VbC.
Radices; = V - BC, - 1 - bc.
Oiarum prior, est Specialis sub casu Secundo; posterior, sub casu Primo vel
PextIO.
FX primoribus illis Casibus cribus; Patet, In Quadrarica squatione (nOn
impossibili) auas este Radices; quas appellabimus b, c.
Et quancitatem absolure cognicam (bC, in omnibus; radicum illarum Rectan.
sulum elle, seu Factum ex carum inter se mulciplicatione.
Foraque aequatione sic ad unaS pArtES FeVOCata, ut nihilo aquetur; de lupre.
mus radicis practus attirmatirus, et ab attectione immunis; prout in aequacio.
nibus
Radices; =b- 6.