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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 163, page id 175905688X:0185
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=185
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COMMENTAREE EN LIBRUM I.
163
Eritque reliqua P ML aequalis y, radici quaesita: Ita ut frat Y
∞ - = a +. V = a a  bb.) Veriim aequatioy y ∞ = a 7- L bb
admiceir adhuc aliam radicem, minorem quam nihil, quae per li-
neam OM delignataita exprimitur, Y ∞ = = a - V = a a F bb.
Cujus demonstracio ad exemplar praecedentis tieri potest.
Nec aliter fit, si proponatur X + ∞ = a X X L bb, P MI M
enim esset XX, e haberetur X ∞ V = = a + V = a a + b b.
Duonia enim x + ∞ = a x x F bb, cransterendo = a x x in al-
teram aequationis partem, eriex F F ax x ∞ b b. d addica utrique
Parti f =aa, Proveniet x + L a x x + = a a ∞ = a a- f b b. Tam vero
extracta utrobique radice, invenietur Xx L Z a ∞ V = a a L b b.
ac proinde tronsponendo. L= a, ut x x unam constituat xquatio-
nIS PaKtEII, CTIEXN∞ = = a. L V =a a F bb. UInde extractâ ruI-
Sus uerinque radice, tiet X D V = = a L V = a a + bb.
Eodem modo lihabeatur Z + ∞ a Z7 F bb, exit
DV: at V : a a F bb. Nam Cum Z + ∞ a Z = L bb, erit Per
cranspolitionem Z+ = aZ 00 bb. Addatur jam utrinque  aa,
Fetque Z+ = a Z 2- F = a a ∞ = a a + bb. CInde, extraCta VETO-
biqueradice, prodibit Z . - = a ∞ V = aa F bb. hoc est,
(∞: an) V = aa F bb, e per consequens
DV: a L V + a a F bb.
Similicer (1 (IE Z+ 2 a 
2 -bb, erieZ ∞ V = a-  V = a a =- bb,
necnOn Z ∞ V = a = V = a a = b b. Cum enim Z+ aGuCEuF
aZ = bb, e pertranspolitionem Z+ = aZ 2 ∞ = bb; addatur u-
erinque = a, tietque Z + - aZ 2 + =  a ∞ = aa - b b. JUarC Cx -
tracta urrobique radice, emerget Z  - = a ∞ V = a a - bb, hoc
ett, Z ∞ :a. V = aa - bb, ac per conlequens
∞V = a- L V = aa - bb. POrrO, quoniam radix ex Z+ = a 72
F = 4 a eAt quoque = a - Z, hinc _ = a - Z D V = a a -- bb,
hoc ett, Z.W : a - V = aa - bb, ac per con(equens
DV = a - V = a 4 -- bb.
X
abl