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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 123v, page id 00068198:0246
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formula trium radicum aequata quadrato
indeterminata saltem e vinculis liberata
ciples aequalitas pro Eredeterncinatis
Xta  L2MNP X+ b = LM X
2
X+C = LMN
N4D2922
et Xta, in X +b, in X+C = L+ M N
LX
2
 L2MNP - a  X = LM N 92 - b X = LM N R - c
e
Ex valoris t 6 et 7 fit L= b -c,   M NE= M N R
ex valoribus set 6 sit LZ a = b, :, LMNp - M N92; quos duos ipsius L
s
(10)
valores aequando, fit: L Mb-c= Mq a - b = NR a - b
et
e
mgmic +MgaCM
et exaquo fit L = MZ a = C = NR a b,: v b.2 qnem valorem aequando velori 8
fit:   seu faciendo p = MN B fiet L = , M Q a- C - NR a - b, : M N b-C5
12)
quem valorem aequando valori B, fit x bc  C
(14) 
et
4
oe CaNR a m
fit _MN5 b-C= a + a MZ
+b
sit s sit 5b-E = HZR et ex aeg. 15. fiet:
5,
+ b- a N R + a -c M
(17)
+c
16)
O
2
quae ut sit extrahibilis fieri  -2a +b + C - H = 286a 2  b-a, a- c
quae unica est determinatio hicassumta restri
potest.
seu H = 1 -2 1b - a, a -c 2a + b +C (adeoque rfiet denique
(19)
2
= 0, adeoque
Sb-a NR  Ya-C MZ
ctio
seu M = - Nb- a NR:, ta- c2. Egregium, si verum, nec video ubi
 locu
N
10)
error haerere possit Notandum minon curare itrationalitatem
in quantit atibu determinatis, modo indeterminatae e vinculus
b Em
bua NRG. a -C.D - fLa N R: Ya- CZ
sed ita fieret L= b cri0 quod est aslrdum; seu con saltem
ipenerationem est
nectire
liberentur seu L= , b-CK K L N aR. 
permista. Licebit  venire ad aliam; si scilicet scribamus pro1b
L2 (17
tia
b= a F st N R + a =C Ny + +  -2a +b + C- H ? MN
et
(10
a
ffA
et fiat Nb-a +ff, a - c = - 2a + b + c = H. seu H = e-2a +b + C - 1b- a + ff, a-c
e
fNB ita quaesitum consequi-
18
2 (26)
mur sine restrictione, nisi quod supponimus ad usum nostrum f, adeoque H. esse constantem
et siet Yb- a +  NR + raC M
si fponitur = a reditur ad calculum priorem g  Ex 2 fit M= F∞r. atnR
a
Et ex per 21 fit L= b- 19
-2f 1b.q +f + b.a
quc
ba+ NR tanc Z
12c
NdR+, 2F + b - a- 25+b- a t H = ta-c f- sb _+
ex beta sed hinc video in valore ipsius X quaesito   ex 84. 7 per 21. 12
seu L(22)
-c acc
evanescere literas omnes inde incognitas praetert, vel ergo quaesitum
obtineri nequit, ()
vic cenerali calculo samus  Quo substitulo in aeq. 6 fit
usi) vel opptet fess inde
erunnata erv. sign. C