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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 107r, page id 00068201:0213
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X   10 arb + (3 b
XB +b + 3b X. adeoque X arb X - b e sb. et quadrando utrobique; fiet.
N - 6b X  - 2b X, +9b2 X + 6( X +b Y est autem b. quantitas
affirmativa:
Haec aequatio duas minimum habet radices reales, ob sb Sed matum in eo consistit
quod non nisi una habetur arbitiaria b.
An c An rectius ita C
XN 1O. LY + Sir + 4 + 10 + 1r + sirrus
XH ZS r + q 4q X sed adit determinatio cipionis Ferrei. Aliter.
X N 3 r
X r
: rq t
ult +......
X +ZY (-  =r + 90
+ r + t...
221 L 6 7 13
7
0.
i
4Sr 14, 2tir
1li 19
summae Ergo bE HC
Eoce notabilem formam duarum radicum d
quadatranum, quarum quadratum est numerus
Pro 24. compendi causo ponanus v. fiet aequatio
X2 - Y A0
Rectius ab initio ponemus: X + v B ..... et fiet X + 2XV +V A..
Serve adhuo rectius faciemus X ponenda, sed malum in eo praevideo quod ita duae radices fiunt
aequalis. Vi d eamus tamen pro V. = Y ponamus f. fiet aequatio: X - f 1.
Cx pro _ X ponendo Y + n. fier: _ + 2n y + nt B0
comparetur haec aequatio cum
aliqua cubica data,
+ m
+ ings + n y
m. rmm. m
mas
y + p y + aqy 4 aer pjo. fiet 2n +m pP unde paras aq. sue np P n
sed manifestum est eam comparationem esse impossibilem, nisi alteretur datu, et ejus loco
scribatur: y + 3d72 + 3Y
+d3
+apd. =pA2 B unde comparando:
Sed haec inutilia arbitror.
m 3d +p - 2n.
tar afp n + hdu + 2pn = 4n - 3d-2pd - ag.
as 3du +pu - in  - d - p d - aqd - ar
3d + p - in
Sed si abinitio posuissemus X +G Y3.... + Y6)...
habuissemus aequationem X 4 2g X + s  f. sive: X + 2gX + g ppo.
si a Ergo aequatio inter duos ipsius af valores,
Notanda haec
comprehensio
forma:
(343 ut 43
d
+
malliplicetur per X +m
= pd XE + eg N +g X
- aqd (
er
Am..
fa.
 id - 3d 3d = 2 pd 3d - aq 3d, + 9d 6 pu p (n 3d +. d 
n)
Lin
-2n
in
sed ita ascenditur ad aequationem Culicam
in 9
+4
non minus difficilem quam est datu olsi mas habeat in specrem
abitrarias:
videndum quid fiat si radix superior culetur: tiet: Quad retur potus X - 3g X . L Y +96. fet
12F
+ r
+ 29
+13
14fr
-39
compre
X = 6gX + 9g X2 - p Y Corparetur cum X 4. 3n X 4 + 3u V X - 3
-Eg data
= p . + 2p - pn2
fiet. q 7 3nat pa. et 27+ Epa 2n + 2pn +aq et fer n + : pn + Ap e taque agu
et fiet n et n  - 
post 5.4 uta q _ na  Pa + npae n
dug
216
+ et
+ 33
H
+ C- ag
21.
e
73a.
=ar
72 - 2pa (7a) (2p a) + L pa
+9a +ga aq
16
14
ai gueltis qudi sa raa guanus 5. si ete pe s. e age us pui  a e , ver 1 n i1 
scilicet: , + 3d  2 - 3d
d
+ag. +aqd
3d
4bc H 4
6dp
-12 dn,
C2n) ragd
en
-Fu