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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 86v, page id 00068049:0174
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in Pacto ex X+N. X+b. X+C. X+ C
X +a et X +b radices fiat X =  y + nn et fiet
+mG + RN et my+ nn
+ ay+ pa
y + p
b3+ pb seu radices erunt y + untpa et 94 HNF pb
inta
fiet nntpa, :mta = un+ pb,: m+ b, adeoque fiet
num, + nnb + pam (+ pab) = (numt una + pbm (F pba
et sit nn = Pm, b-a,: b= a et fit nn = pm sed
tunc fit X = mytum seu x = m. Videamus an sic
y + p
liceat X = myy + ny+ p,: yyt qqy+r2
fit + myus + ny + p in
+ agus + ady + art
my + ny + p3
by + bgG + br3
sed tollere licet
yt quae pro-
veniunt quia
lollere oportetet in radicibus vel summm vel ulluum terminum
ande
quoram utrumque supponeret esse a = b. saltem vicleamus
an licatulium. Videamus an saltem efficere
liceat ambas radices extrahibiles, fiet
N F2nnag + uqqu = mph +mar + ap + aarr
en+2nmbq +bbqqu = mp + mbr ZBp + bbrr
n-mp= ua Mr+p Lunga + rr- q9 aa
N-mp-
Mr + p - 2nnq b + rr- 99 bb
Id qua ineo quod video obtineri posse neque enim inde sequitur
ut neas ex quont quo quod a et b sint aequales sed solum
quod sunt radices ejusdeu aequationis. ope harum duarum
aequativum tollamus m, fil m= n + 2nnaq + auque = ap - aarr,: p +atY
p
fit (B7
Znnaqp+ aaqquep- ap= aarrp n brf 2nnagbr aaqybr
apbrr aarrber = n p + 2nnbq B + bb9q p - bp  p3- bbrr p3
Sed quia restant
ntar At2nubus art boggarL bparr- bbrrarr
duae radices necesse est tertiam quoque esse extrahibilem, et item
habebitu novus valor ipsius M. ubi tantum t pro a vel Doccurrit C
Et iamvementus duns ex  eris ra hests qualua literis n, P, qra 2taque
et m
m+ b