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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 7
# Folio 10r, page id 00068220:0019
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1
 sit Aequatio data X + bX  cX + dX +C a q. 0.
quae divellenda est in duas partes utrobique extrahibiles, quarum
latera sint X + lX + m  et n X + p, se de et fiet
X + lx + in aequ +n X + p. depressaque erit aequatio. Est autem
(2) X + lxam aequ X + 2lX + 2m X + 2lmX + m
+ U
et IelAnX +p aequ np XX + 2np X + pp
et fier X + 2l X + 2m X + 2 lmX + mn aeg. 0
comparanda
e
+ U - 2np  = pp
un
fiet laequ b: 2 et m aequ c: 2 - b: 8 + nn: 2
et rursus m aequ. dett  d . b + 2np: b. Ergo paego bc: 2- b: 16 +nn: 4-do~ r. n
Ergo P aequ. bce - b A8 +. bnn:  - d_: pIn
per compendium c: 2 - b: 8 vocemus f, et bc  - b:- d Quocemus g.
et sunt enim cognitae fiet: maego f + un:r et paequ g +.bnn : 2n
Resta t aequatio: mm- ppaequ. e. Ergo fiet:
f2 + fnn +n - _9g- gb nn -- b nt: ann aequ. e. unde n - +. b H =gbn aequ. 90
dd
Unde denique siet n  n b nn aequ. F99
sen
44f.
..
Hic enrons alculi conigendi  exproredentibus , aue correctis
-B2 n4 +9
e
1
f2c0
62
b
=2
bC
n aequrisb
+ CC i
++b d.
+4C.
b+c
_Vd
+b c2 Et explicundo
= bcd
+ dd
quae aequatio servit ad resolutionem, aequationis quadrato.
quadraticae cujuscunque. Inventa enim n per
aequationem praecedentem fit:... Xex + + b +f
sive, X + = B X X
ag
eit
+M.  +2C
Hic adhuc errores +: nn
calculi conigendi
L1 13
ex praecedentibus -2b
Zin 2+nn aq.0 sive
divis. per  + n
jam correctis tsds
Ebn
. +n
bn
qua aequatione resoluta, posita = esse = et + esse +
habentur duae radices; posito vero = esse + et + esse-
habentur duae radices reliquae aequationis quadrato. Quadraticae
propositae. Quod si poras b aego seu abesse terminum secundum in data
siti. n +AC N Y Cchi aequi dd. et se n X + efe aeq. 0 Et p. Mp ponendo  yy
denc 
 pro  ponendo  y prodit
nn
+4f 4452.
qe
0
++ Eequ 8 cc- Gebri bt
=9buq. A- L. b C +  b  bd
daq. eb. 75bc
+bdt
4bc. 12
1a
1
16
u