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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 282v, page id 00068201:0564
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Jam ergo ut calculum de integro ordiamur,
data
Sit, aquatio
W X - 39 Cd +25 96 - at  0.
erit ea intractabilis per regulas Cardani, quoniam  a q
riente termini secundi 34  cTubus 4, major est quam qb - a+ +2
quadratus a q - a +, semisse termini uttimi, 2 Sq- aF
Ponatur jam Ce p Y + 29 13
-39
+3Sq. a F)
 =4N3, y +3, 4, 39V
y +6953
et fiet aequatio
+89.3 B3
- 34, 2953 (6 8)
+21q - a +
+189313 (49
+259 - aF +2S
ubi sed video, a me erratum esse, in calculo, debet treri
Aequatio data: Cd X - 9 q Cd  , 224 - a t H quae aequatio
est intractabilis per regulas Cardaniu nam cubus triens a 94
qole cognita termini ul penultim est 34 ejus cubus est
t2 surq aF)
Cd ei
(15)
y A - 2 9 13.
ut ante, fiet:
(3, 295, Y +3, 493, ) 892
99
+ 2794)
.92913
2 Jvig at
6qu 3
=ril 279. a
prtam sacisim potestates In qua aequatione si faciamus tantum, ut
duae radices, 13, et 1279- a  eodem signo sint
 ita iss
affectae, quod in nostra potestate est erit signum
termini secundi et ultrmi idem quod si ergo suam
molem exhibent, sie affirmativa intelliguntur habebimus
aequationem ex data factam, omnes radices habentem
veras, quia signa alternant; et talem ut a
3413. semisse termini secundi factum quadratum,
993 sive 279, aequetur ipsi 279 cognitae quanditati
terminipealtimi. Quod desi derabatur.
haec aequalio cum
fier ergo ex terminis ultimis:
m+ +(2243 ⊓ (6 qa 13) + 2aY 279- at
M12 + 160e9 s3 m + 64a962
2a279 - aFF2
et signa radicum s 
conferatur jam
hacl.  ay-omne +ominay -no 
C fiet mn B aq s3, et ne aq S3, et n6 2ra g
M 1 274606
mt
= 2796-a
(+ 16a4 r2rg- a F
1oZ abg
+279247
166
O3 aq() 13 nest
adeoque
=, 3, 16a9 (279- a F2
2449
quae aequatio est semper possibilis Ment C B3 4at79F sig 1 q6 - 1316,
et erit m. 6a 43. β3 = a Sirf. at. + sug
41 221
= 15, 16a9 527 96- a2 +. quae semper et postitili. 
14qui utique major quam 279 - a F quadra Aebet ergo aequatiaii () termini
tum a 274- a4+2 dimidio termini ultimi. Jam
faciamus
-0q0
L adeoque 9m n p 9a93 1 279 a
modoq sit masir gerim
quantitates
characterem portant
sunt formutae quae
affectionis ut
sunt
quae characterem.
portant ambiguitatis
et quarum signa pro
arbitrio, aut rei usu
atque exigentia variare
dicet, ut radices
quad raticae, vel
aliae parium dimensionum
Cterae omnes quantitates
sunt o in differentes
non portant affectionis
characterem.
ex terminis
secundis et
tertiis