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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. _ F B L A.
Aiquationes.
a a = 2 b a - a = 0.
aa +2ba = a =0
a4 - 2. b a + a = 0.
aa = 2ba + a = 0.
Racices.
= B F V: BB- F a.
-b =F Y: bb + a.
Major, Afirmatira.
Major, Negatira.
FB F V: BB -a. Veraque AFirmatira.
=b = Y: BB -a. Vicaque Nexacira.
Vel (potiris 8 pro sieno cujulris membri, sive si f sire =; _ B pro con.
trario) ad hanc Unicam, (in qua s tit b = 0, decst cerminus medius.)
aa 8ba 8a =0. SB = V: BB Ba: =0.
In quatuor formarum duabus posterioribus, contingere potest ut Radices sint
(quae dici Solenc) Lmaginariae. Sed, in duabus prioribus, semper TUML Reates:
Afirmacira puta, vel Negatira
Acque ad ealdem tormas spectane requationes omnes, in quibus funt (ut Ouch-
credus loquitur) tres termini aequaliter ascendentes in scala. Hoc est; in quibus
numeri dimentionum isnorae maxnicudinis sunc in Prosrestione Arichmetica. Puta,
27 τ, O. aut 43 2, 0. aut 6, 3, 6. Ft Similiter.
Ouales fune
AUE
Similesque.
cece... . 2bec.... a =0.
po ..-. 2b.... 0.
Oux quidem non alix sunt quam Aguationes Ouactraticae, ex Radice plana,
Tolidas pluriumre dimentionum.
Nam, POSIEO de = a, aut p = a; aequatio est, ut PriuS,
Fjusque Radix,
aa 82ba 8a =0.
8b = V: BB Ra: = a = eC = yyy.
Ouod si porro desideretur iplorum c, y, valor simplex; habebitur extrahendo
radicem consruan, iplorum e’e, yyy, c. (puta quadraricam, cubicam, aliamre,
Prout numerus dimentionum poltulac.) Adeoque
V2. 3B = V: BB Ba. = Y a -.
V. 3b = V: Db Ba. = V a = y.
Et in aliis similirer.
Aquatio Cubica, Radicem semper habet, faltem Unam, Realem: Reliqualque
duas, vel Reales ambas, vel ambas Tmaginarias. Poteltque (abjecto, liquis l le-
cundo cermino) ad harum quatuor formarum aliquam reduci.
AEquacio.
Radix.
e + 3ba = 24 =0. f V3. + a = V: ad = bbb. - 13. - d  V. alt 1000. - d.
aaa = 3ba + 2d = 0. - 3. + d + V: dd  B0b. + v. = a + V: dd + b0b. = a
aua = 3Ba = 2d = 0. + 13. + d. F V: da = b63. + V. + a - V: dd - 0bb. = a-
aud  3ba = 24 = 0. = 1. + d = V: dd - b66.  V. + a - Y: ad - b86. = a
Oua Radix semper Realis ell (attirmativa auc necacira:) quamvis in duabus
Formis posterioribus (quories obb major est quam ad) utrumque membrum (se
Paracim sumptum) Sic Imasinarium; (eo quod V: ad - bbb: Et, hoc eatu, radix
Ouacrati Pregatiri.) Nam, hoc non obstance, (membris imaginariis se mutuo
propter contraria ligna destruencibus,) Aepreacum (sive Attirmarirum sire NC.
tl
pacirum)
Vel (Dotiris S _ B ut prius) ad has duas Formas reduCentUT.
Cap. L. XXII.