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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 301v, page id 00068194:0602
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Quoniam igutur V = (∞). _t ergo etiam oportet
aequari jam. X = ly + mm,: ytn ut diximus. Ergo fiet
Z = l0 +aim: _v+n adeoque EV + nE = l0 + mm, seu
m = mm - n8,: 5- l. et eodem modo
quia (3) = 1(V) tum, :, (V) +n fiet (2) = mm - n(8), : (5) - l. Ergo
fiet si v = (V) fet mmf) ( n. 5(5  mm HIns = min 5 ( Imm -n B .)  Y
ande v quir ponia seu nn E - B) + ln (5) - E 20 ex seu lb mim - ln, 8.
et uia Unde oportat vel esse = - (E) =0 seu _ 8 = (5) contra
pypothesum, supponimus enim fonmutam non habere duas radires
vel oportet facere  mn - In  =0  seu mn = ln
sed ita X firiet constans, quod etiam est contra Hypothesiu
nanfieret X = ly + ln,:, ytn id est fieret X = l. Uonde
colligimus fieri non posse ut V et (∞) aequentur
nisi hoc unicus, casu quo (2) v = o et Nam etsi
fingeres vellemus esse V = 0 et etiam (V = 0 fieret
mm = n ) n8 = 0 = nin = n (E), ande rursus 3 et (E) aequa-
rntur contra Hypothesin
dideamus ergo quid licveat
X = Ryy. + M nam y. + _ n:
si faciamus:
si fingam formulam X + bb X. + C esse aequationem
aut
et esse  2 X - E = 0 at X - (8) = 0,  X - (2)
seu X = 5 vel (5) vel () et firri similiter et substituto
itaque altius assurgendum est. Fingamus _ formutam.
datam esse aequationem, seu X + bbx + C esse = o Hoc
no)
enim posito  factores dabunt valores ipsius X, nempe sint ejus
tres factores X - E  A, x (8), X - ((5) pea fiet
X = E vel = (E) vel = ((E) si j sit jam
(4t) X = Ryy+ Cy tmm,: _ yy + Epys App:  patet numeratorem
3tid,
si is valor substituatur in aequ. 1. prodituram aequationem graduum 6, tempe
(56) V +.. y +.y + .y +. gy + 9 4..y =0  quam per suos
itaque ut extralibilitatem hobis utilem obtineamus, oportet bis adesse
duas redices aequales id est esse y   =() verbigratia
((2D = ((VD quod an liceat
per q acremmodata
vos
atae
liino
y= V 0 = (v) pt
ad certam radicem fiefono) E = f vC = l~ + mn,: V, BV + 2pts + pp seu fie
(7 mo.)
Ex aequ. 4 re
vi deamus  obaeq. 7. fiet cum sit
seu fipt + Y (yW + 2p ∞) + pp E = 0 e et () eodem modo  4(v0) +, 1 20
= h
h tan
fit (1mos
omo) = h
=hI= hum
+x, v0 + 2p0 +p -0
Ergo si sot  V = (0) per B.E
radices vel factores exprimendo fiet y - V, y - (V), y - ((V), y - ((V)), y - ((17), y - (0((6)6) =0
(6to
nacc
lio
ind sficopua