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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 290r, page id 00068201:0579
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Y4 CZ  cbt en
Vs e
PCoV
(7
erit   _
d5
+5d92 + 10d97 + 10d9 2 + 5d9+ Z + g
d. + 4d9 1649. + 4dg. +94.
la toB.
3d9
26d3
2d9
36d
3dg2
6bd9
b243
Eudqe
364
4bd 4bg
5
(2)
662d
iob
n
1648. ab331.  
93
66d9
3649 3b 9
3b92
b6d9
342
6629
36
26289
412 4b39
10b
(7)
64d
5 b
lg
649
(6)
Jam id agitur ut tollantur terminus secundus, simul et quartus
delis arbitrariis, d. g. b. ponatur dgH E b. et dividendo
columnam secundam suppositam 0 per b. fi tollentur
simul 9 et b. ex col. 2 et haberi poterit absolute valor ipsius
d. itsque  sumendo pro cognita,. Et ta poterit haberi d
pro cognita, jam ex columna quarta posita . fiet aq
et explicando d9 in ea per eb, et dididendo per b. fiet aequalio:
in ea b per d9 fie: eoanescet b. et g. etiam
10 elgs + 4eb9 16pbbe t 993 +59 b9s eb in alteri quod luntile
10d 9 + 4 d93
Quoniam tamen explicatio ista semper
in potestate est itaque faciendo 3)b9 d +rb dnD
ive Bp - 399. tunc in columna quarta evanescet d, extra d 9
adeoque in columna quarta non extabit nisi du seu non nisi e
nempe ponendo  b et 9. cognitas aut arbitrarias ibique assurget
e ad quadratumo et ope aequationis quadraticae invenietur, e
et ita e haberi poterit pro cognita et ita sola d restabit
M +n men b+C-  et nny bcpY
restit ME+ n + b5+ C5 1.
 n. 6n F
+n 2 14 Y  seu renca Y4b3 B9
in glteca aequatione priore ex columua ida, quod explicando experiemur: et  aS  +   bBC
Columna pa dabit: SC d + +ped + 1+ +ged + 2 +2rC + 5d -sr + 4sd +st 10)
columna  dabit: 10 et 294 + 4 e 34 AEp C  37 (+9) +69 e 2 + 99
(13r 2 - 34) +bre 2 - 139 (+ re - 2192 4) + 5 a99 r 4 5 - 279, + + 2 27 q S
usim
Posteriore ergo aequatione inveniemus ipsam c e. absolute. Et ita c. erit cognitas adeoque ejus valore in prioreo
aequatione inserto, non nisi una ibi restabit imognita d, ascendens ad quartum Faut (si datae sindesolidae terminus
secindus sublatus sit ad tertium gradum seu si pto) ad tertium gradum.
Habemus ergo methodim generalem
cujus ope ex qualibet aequatione surdesolida tolli possunt termini incognitae adipares dimensiones ascendentis
porro valorem ipsius e, compendii causa ita
sit jum X +9X +sX + t, vel X + quo X +f B F Scribemus:
Xemn ME + Gm n + 10 Mn + 10 m n = 5mn + n
eu X (+5mum + 5 Cum HN +CC2M  + S mN + n
s
sive cciccardi
-simn X
S
+mn ... . + ma..
-imn..
.
- mn..
=vma im3
ergo X 5ma X - sm E X + m
+ 5mn X  - 5m n X
+umn
+ smn m
seu yn A3
Emusus XB
comn in
Vidoamus quid fiat si aequationem Cubicam meliplicemus per X - 3mnX = vipo. ponendo scilicet  X - m - n po.
multiplicemus per X +m X
+on
b.
+m produetur cusus aequatio cultca, qua si seu  vantitas ee. quae ipsi X - smnX a 5mini Xam
addi potesta eodem omnia omnes aliae aeq vationes inferiore multiplicari
e prodicta eidem addi Possunt, summa erit aequatio , cujus radix ∞ + in 
et quae habebit omnes termiras completos, et plurimas arbitrarias, cm et in qua
nulli m + n vel m + n vel m + n vel m +n, non reperiantur 8
m +n non extet nisi in ultimo termino, ac proinde solvi poterit aequatio data per
aegratio as eudem gradus, ut Xam ex pr X + da X + Bm extractionem radicum Eepuanum in cubo. X . dun X  po produtamus, nim alio undo
ai
X
Birin
t
e
omur
0. Cun
sit X  d 3 + 89
+ b
v d272 + 4 492 16d9 2 44d5 3. g
co
+
2
d75 4d393 edz Z 1dg19
d+75 + 4d2977 +6d92314d9 21981z
+d B. +4d 9b 16d96. 409 b. 19
v2 4Z +3d92 + 3d 7 + 92
V rpco  quo  + YO + sux + 
a373 4349 7 1dg 23 + g n
co) Z + 2b7 + b
+2bd 6bd9. +6bd9. +269)
b42. 3bag +3b8. +b9
v
0
42Z2 +2dgZ +g
1Z3 +3b Z + 5bZ + b2
1173 2d9  93
3bd 6bd9. 3692
3b4 6bg. 3692
b2dr. 263,, 69
+g
C174 + 4633 a66Z + abZ +b
abd. 4b94
66d. 6bgL
4V. 4697
5 bd. bg
- 10
33
2
= smn r 3mna m
in 21 ma am.
+ 10 nCma m
in
Ergo X 71
m
v nn 3m
N + pN2+ qXFY A +sX +t H
+Dm
82
+ m
=Pman
n
30. uomn.
+ d
fict: X3 te
u 1.