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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 1r, page id 00068229:0001
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Sed pro iationalibus Cubicis pert altiorbus altius altrus
assurmendum esse est, ut si sint Va. + b +  patet quamlibet
harum habere tres valores unde videri possit assurgendum ersset ad
 nonum. Nam si nesradices sint A A a L. Et vel B. 6. β
siet A + B vel A +B vel A+ B vel q + B vel a + b vel a + B
vel a + B vel a + b vel 2+ β. +. Considerandum) est tamen
an non duae aliquae radices ipsius a solis differant
signis sit.  X - v =0 fit X b = 0 et
XX + XV + vV =0 et et + XV + 1 rn = + vn - VD - - 3 on
seu X + L B = -  B Y - 1. seu X = et - + v - v f- 1 vel X = - 1v+ v F1
unde patet duos illos valores non coincidere, ac proiade posse
ne in aequatione quidem coincidere, ergo tres diversos valores
esse hibendo, nan sive YV valere v vel - : v -v S. 1 vel - LV +VY.C
Nihulo minus tamen video s libla
Si a+ b multiplicetur in  a+ b  ab prodire a + b3
.
 Unde colligo, s  in aeg. X V  u
liberetur X a suis radicibus seu ambignitatibus, mul tiplicando
per ipsum radices seu ambigutates ipsius V, prodire non
alios novas valores  pro apbsocnti, sed eosdem cum
obu
praecedentibus. Itaque pro i matuonialibus 2. Cubicis trabus obu
tollendis assurgendu ad radices  tres, pro n tolledis
dimensiones
tribus assurgendur ad radices see seu novem seu 3 Peo
tollendis, quatuor assurgendum ad radices 3 seu viguniti septem, dC
( sane, cum sit X - V = 0 erit etiam x = v
ergo etium X I = VVI jam CY
S1 = 1 vel 2 - 1- 1 vel - 1 + f - 1. Ergo loco
aequationis x - v 20 scibi potest : X - B = 0 vel X + 3 + f - 1B = 0
vel X + + - 1∞, V = c
At inquies sub quolibet horum valorum cursus duci potest in tres
ipsius YX seu in  X vel X - 1 - 1  vet X X
derum ayt huna redire aequationes simplices
verbi gratia si scubamus-1+S
redibit X - v =0 si scibamus X -+ si
fiet: aedi fiet X - p - 1 - 1.1
V
V - 1 - L.=
1+5. =0 seu tam numeratorem quam
nominatorem mulliplicando per - 1 - s. 1 fiet X - p + 2s. 1 = 
in pradit quod mirum
priores
1 + sey
c
X - B - 1
novus valor
est fesce intolerandus seu falsus hoc est neque magmanus nequeprealis
0
si sit X. v -o tunc Ausi X V - _v Si = 0 sed ex hoc sequitud
ideo tautum licet scribere: X - v 
alerum hac Methodo
O
seu
qui tamen
2.- s.
+- vs. 1
be