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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 22
# Folio 13v, page id 00068235:0026
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mio nonduu exhis Demonstratio resolutionis omnium
radicum aequationum, peu
inventio radicum analytica gegeralis
sit X aequ  p + 4+ r a 
et Zaequ par + 1p95 etc.
a
20
Et dag p9 + Spr etc. et  Zagd p
erunt quatuor
tunc erunt p. q. r. saC. Cradices aequationis
15
(10
quadraticae sit l’aeqo Sp. erit l +0. l +. l + = l +.. aequ.0 quantitas
aequatio rationalis
a
en
M
+l. M
seul aequ. v.
jam X- y x + Z XD_ ∞Xx + (B X = C0 aequ. 0
raeeunt exky
et si nsr, eut n = n en
et
O aequ Y5, eut 920, etc
jam sit X yX + ZX - ∞ x+ B aequ. 0, quae compretur cum data quinti gradus habebitur
roi vigesium gravus, si pro indicibus
quaeratur aequatio in qua radicibus radices suit  radicum, ea erit
0
15
25
10
201
d ex sae etc
equatio austem data resolvenda attollatur ad a X et nova multiplicatione
5
per X4 e attalletur ad X X
0
M
eu
de
X 9 x aequi 0.
C  LX + l’m’no aequ. op
15 1Sue
tum X (5 X ume
a Aut
P
10 e 145
Cnib
eu Si bene memini
et f
Sed haec coincidere alibi demonstrarum est, quo facto
An hace procedit, seu coincidet
e.  cum l+mere. et
et fl cum l’n+ l’neeu.
Imo an sic.
Imo sic e est summa omnium  quatuor X Quae haberi potest ex praecedente
necesse enim est cum sublatie sint irrationales iut non aliae ingrediantur aequationem  quam
m  (15. po 5 155
11o
1
100
5 1
lin Imn eic. Sed tolei possunt
omnes lem aliae praeter solas 1 1 ou et l m. eo ipso artificio
+m.
quia jem habemus 1 colletur l in altero gradu et habitis l. Cm tollee
5
1a
nec. it etro gradu et ita porro, et si voca restabunt
Habentur autem strimum
 cum data exaltata. de qua post.
l’m
comparando aequatione
Habetur autem neces
Pano
. Quia habetur aequ. . ubi pro y sbsto vi rund revera
poincidunt, nam y est nam in aequ. O sublatae sunt omnes irratiinales
aqu
ergo si loco r. 7. as exprimeretur per l. m. nn eliam sublatae forent
superest ut agursvideamus quomodo habeatur com
naratio cum data exaltata. Nempe data aequatio C vel
irrationales.
L
a
mullipliciter per xt e vel per XE, N 1 et habebitur aequatio
ergo
e
5+
mo
o
15
am aequ
fiet X + s4
X
A
s
7V
m
sequatio nns reducatur ad solas ln
noc
 l’ M + Pn’eco
+XX + 3AXD +15
a
X
+ an
2
ar
et jem es lnin, quiq per
aqu. M.
.. 5
oe
2
s
l’mn equ. V. et
aequ.0
sed iba
Cinventio ipsi
A accedeglo
ad gradum
ptum
derte
X IX
a
aequ.d