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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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E C 
B R A.
=bbCbC a = = bbbCCa = BbB a aa = a a a a 4.
F bbabcd
FCcbbCd
cCabcd
 a2bbcd
ddcbca
F 2 bCdbcc
b + c + d
 bbbada = C66 4 a a
FCCcbba = addaaa
 bbbcda = bbc a a a
+cccd d a - bb d a a a
-cc0b da = cc b a a a
dd dbba-ccda44
addcca
b
aa
addbca- ddcaaa
F 2 bcb cba = bc d a a a
= 2b abeba
=2b abcda
b+c +
c + d
a
C A P. XI.
DeFTarrioti Sectione quarta: Deque numero
Radicum Realium.
NSectione quarta, de Radicibus Affirmarivis speciarim agitur: Ibique de
monstrat arriotus, in plerisque omnibus casibus jam memoratis, toc e tales
Me Radices (assirmativas incellise) quor ante declaratum est.
Ouodque de Astirmatiris oltensum est, de Negatiris pariter ostendetur. Ouippe
mutatis lionis (ut supra ostensum est) qua jam lunc Nesatirae, cum tiene Altirma-
tirae; adeoque quoc cum fucurx funt Affirmatirae, tocidem ee tales jam lunt Nega-
cira. Indeque constabie, quoc tunc omnino Reales; e cOnlEgUENtEE, quOT LunE
tancum Imaginaria.
In Canonieis Primariis; id ex ipsa Constructione constat: Caltem, eas esse Ra-
dices; quamvis non eam liquet (absque demonstratione) non plures este. De Se-
cundariis Canonicis, id ex ejus demonstratione Hc eridens.
Demonstrationes ejus, pro lingulis calibus, (quamvis Tubtiles Patis) non omnes
repetam. Ratus utique susticere, quod ad aequationes supra memoratas (plerasque
Taltem) ad oram cicarerim eam sectionis quartae propolitionem, ubi demonstran-
tur Radices illa. Ouas Lector, si libet contulat. Paucas camen, uc reliquarum
Demonstracionum specimen, hic Tubjunsam.
T. AEguatio hujus Forma,
radicem habet a == b.
 b lb nn b6d
Nam, potito ubique B pro a; lixec prodibie, 6b -bb
in qua aequalicas est manitesta.
+cb = bc.
Sed non alia quaevis (affirmativa.) Nam A C, (aucalia quaevis, puta d.) proa
substimuatue; habebitur,
Cc = bc
=F Cc = Bc.
 Ca =60
HIOC  cc + c0 = bc. = BC. auc dd. L cd = B d LBC.
Adcoque (dividendo illam per c. + C, aue hanc per a. H 5,) 5. = B, aut d = b.
Nimirum, c. +6 = c +c
in c. In b.
vel a +c = d +c
in d. in b.
Adeoque c = b. _t a = b. non aliaa b ve supponitur.
auE ad - bd
TI. Aqua-