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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 242v, page id 00068201:0484
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Juterm hac acterRabue ver si quae sunt in nuneris extrahi possunt u stampioe
et possicunt a Sichotenio prasciplum est; ad literales verd aequationes non serviunt, nisi
literae ad numeros rationales irrationalesque reducantur un
Si sinel habetur nethodu
LH
Methodus
3 aet 7 ps an 4. () at =  l. an p Bp a Y
fier ay p dal (+ a S -an) +31 à V- a l s- an, + 2a (5 a 
et( à Lan
(ab + an J-an
+35() à 13+ a l S-an, - 2a ls an a ln
a y - 2al 25) Al( VS an) Al. Laan)  3aIn + ams au
Xqu
a lp). ant an
ja  l S. an) J an talm alque
B sa vocemus 13- 3aln H94, et 17 anssfa
si Et quodrm Do cubando a -GXa ) Yquit  agstuns on    ga t atlanasn
.71) il Lan) ( 8i) alu = 27 an S an
fas-an
YA(7 d (271 1 an) + 27 aln = 27 an Juam
Jiii 54 (a = X2a - 54 a n appellemus Va  5+  a
et ga + fas- an appellemus
=9X + 27X 3 ea
brevius X  Aph + K. Unde
ta  X - hp K. Ergo X - 3Xh + 3X h - W  K3
Ex puire Xp KY va l + axte
et mnehijolicatis omnibus per , fit: 3X b3 - 3 X t  H 2 ati 
hep K x + h + 3X h, exquem valorem inserendo
1d1X
in posteriore, fier:
+ 3X - 2 X h  (3 Xt to) p. 3K ht BXTh) + h+ X eritque
sie tam Ergounk X - 6xhid - 3X3 4 3X
6Xth - 3 xta p3 + 3X C 3 H 3) 
3MX + het ada
125 X H etc
1: cub a 3K3+h3
tier a L-an  X F axb- la Fta brb
et avaetae eta
4.54 an
fiei: -9ua D ea +. 27p D Ca  va, fier.
S0 eae
Ergo 3X h = 3X h.  K3 - x3+ h
3XK3
Lvoce
a vat -2va + l’at explicet
2per cubum ab ∞ +b, separanda tandem
3X3 + hi
sie H, (3NX) (C XH) ( H DXK) x
3K3 + H3
3.Xha + 17X ta vaer 1 quin et -9Xi + 27xh iuah
Ergo h  vah - 27X h3
inseratur in prioue, fier: - 9  ha  - 31 (a 81  aX H3 va X
rt
hi AvaX +or axh
in duas, ita ut si fieri potest, valor ipsarum xerb sine
+9+a+ 3a
is Eetracionibus imaginaris obtineatur, tai enin =ani p Xb( X +6X b (42X9Xb2+ (18 Xb  64b (t bD ab
- 2X3a 2l - 6 X bael - 6xb a l = 2b a l = l at. Vrdendum q
I X + b noundo y esse rudicem cubicam, et et a esse quadraticam,
 X + 3x d  2Xt + B pro y ponamus ar, et pro X ponamus ea
aequatio dissui possi
in duas, ut liceat et
fier: aV Ea X + 3Fab. = 3Xb + b3 sive a 6 - 3Eab - b X. Ergo purum tractabilem
Ea H a = 6aVXb 2 a vb rgs al a  5a + 32
2 a + 68 ab + 9bZ
unde
(+65 ab + b.
5a +68ab 96  aa a b a   ab
et ordinando a ua 3bac + 3Eab  = b5-
  av- 6 a 2b- 2ab,  V.
sive as- b+  y 1 a - 6a xb 2ab3 Explicetur jam b ita, ut ex radice porit
extrahe radix cubica, quod non difficile ope aequationis planas indeterminatione
ponendo b  expercando b per duas quantitates, atque inde destructiones comminiscendo) 3t ab - b
aequatio carens radice cubica, si pro y substituatur ejus valor nempe b  ac 3F ab - b3
 potndo at -b 10. fit aequatio ejusdem cum eodent Z a +li
Za + 36
opem ita) inti provemientem licebit
de fal1362
sejungere in
mas, sive altentiam arbitrariam
tandum aeq. 8 dividi posse per x + b) et fieri: x- b 1Va = a b 263 explicare quam licet commodissime, ut valor
2a- 0a5l. (3b3 Ea (346) + 3 xb  (- b)
ie val a 1o npt- l X L 1 Xb sanibu laratr at
quasitus habeatur ipsius V. aequatione vel planam
les alora quo, su Mnoris geomretire Hoactabiti
sive X
b, vel ipsius x, et
tandem per ipsas ipsio