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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 3
# Folio 1v, page id 00068216:0002
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# After the first blank line: the recognised lines in reading order, one per line.

mde. Amul +
 -n + = n m = K m + m
314
rugo 2 + 3  + In- Imo + 1t = 2 nene + 3  (1- Inq +1- m
m
17
mu
+ 4
X A PX + gX +r nqu. 0. X equ. a + b + c; composita ex radicibus aequationis
a  +V a d aequ. 0 cujus cndices a. b. ct. Est t
Est autem a + b++c aego β  et ab + aC +bC aequ) et a aequ d
 X aequ si Xrgo a +b+ C. et sint a. b. c. radices quadratoquatuaticae patet
id quod in ipsis est ratione quod est in X latere non in a. sed in ab eodem modo
quia X aequ a id est quia pr aego a + 2y.  rationale ipsius X erit intry.
item X aequ. a + 39X = 3Z, patet in ae nihil esse ntionalitatis. ipsa autem  intantu
est quantitus irrutionalis ex parte
nimirum in quantuma in se continet Z seu abc.
non curducitur xin y ducitur a + b +C in ab + ac + bC. Juri ain ab, dut
ab quod necessario maned int irrationale si a et b. inationali Hinit videtur dn quantum
eodem modo ac. sed abc. dat aliquio rationale ipivora non nnsi in quantam
partibus constant rationalibus. ita ergo delepminari polerit quid si
sit in Z rntionale, et ita porro. sed haec paulo laborioseta quam
par sit
X + bx +c
+Cx3 AcpX Cq)
+bX alex +bq
X + p X + 9
(1)
X + pX + q aequ. 0.
Xaequ. a + b
Ducatur aequ. 1. in formulam: X +BX +
Ponatur in aequ. 3. baegu. p et cpagubu.
fire Tex sp Cagu. 9. per 4. et luo aequ. 3. fiet:
Quaeritur aeqquatiotalis:
fiat. X-
.......
X + aX ta X+ 1ax
+10 ab +21 8b..
X + AX + q. ex sitt : X + nX + n aequ n - 9.. sei Xaego Yn. 9 - n
2
a ta b + ab
X _ + PX +g. fin: X aequ 14 + Y4. P + V. 4-4  aqu. +
Nm sit Xago a +b. erit X equ a + 2 ab X, seu X - 3abX - a rego
fiet pago ab. seu abaequB et  aequo  4. Ergo a aequ B. et fiet
P
B aqu. 4s
2763
i
aadeous 62 ago 4
n
b+ 4b3 = P seu b+ qu + 4 ago P+ qt
+n Y + m  + l. aqu. 0.  fiat  aequ X- _ fier
Y aequ   = X - 3RX + 32 y - n
n’y aequo.
+my
+
y
27
nX - 2n X + n. 
+ m X = m 
=Etx + 213 equ. 0.
+ m.
=ma
27 4
+X. pX + 9 XapXrgH-r
ppiin
A - pA = qXL AXHA
X +AX + A2 PXDpA
1X + pR + q++Y
A3 - pA = 9A = Y
p
saequ. o
+p. .. +9.
H X +
Gaxq
114
(5
+a b aepu. 0
9X X X +29X. pX X +9. aequ. 0
e
16) a
a + ab + b
1= b
-ab - ab - b
fiet
Y aequ .n +
un
XD +AK AX A
pX +pA
mu