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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 5
# Folio 3r, page id 00068218:0005
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X + a 
Si a radix quadralica 
X teu si a radix enbica
c
ex+a
X +1aX + 12a
+iaX + 124
trax +.aX
+ax
Pone a b. trrationales quadvaticas
X +12a
ponende l aego un et
ponendo. 1a + a aequ.o. et F124+14 aequ. 0.
ergo 1 aequ. - Unit. et 12 aequ - 1. seu 1eaqu + unit
adeue X + a divisibi per aeta
uti 2∞ = a divisib. per X- a
X + a divisib. per X + a
+ a k
Uende ponendo ab quantitatem
rationalem, seu duas irrationales ,
b
inde teqgritur in impanidus etiam x-a  Stales esse, ut factum ex ipsis sit rationat
15= a. etc. dividi puse
a
ponendoque praeterea  10b + b aequ. 0. sive
10 aequ = unit. et 1a + a aequ. 0. seu laequ -unit
Ergo prodibit:
a. b. radices
quadratice
X +1a + 10b
Fetgenentibr ita
potest per X-a
a dindi Et ita porro in infinitum
1obX 4roab + 10b2
1a, riax +b ab
bX
Hic ut omnes formas  ipsarum a. et b. Follamus
praeter ab. quam pono esse rationalem,
erit 1aqu (1)  Eaequ - 1. seu 249 +(1)
et 11 aequ - 2 seu 1 aequ. 2 seu 11 aequ. - (1)
N X - 3 ab X + q
X+ _ abiradicas
X +, aX +24
+1aX +24X
+nab X
4 1ae X
+(2) 1abX
+ vab
+24
+2ab a
=naba
Eodem modo res semper procedet etiamsi a. b. sint radices quadrato-
quadraticae, sundesolidae, aliaeve altiores, quemadmodum jam alias
ostendi.) si a+b vituissemus esse ponendo semper ab rationalem
secissemus atb  esse rationalem aequatio vel etiam apso
alius prodisset calculus
Y +VyAC. Ergo 5aby Ab e bu X +1 a X+ 24X + 34
A aequ. b+ s
fiat 1. aequ - 1) - raequ  +11
2 + V 16 ab
ta (sib. (etab qu
suspectus calculus novae enim
Baequ. 3  () 2 + β aequ. 0.
3aequ. 3.
eit
arbitrariae (vitentu esse debere.
inutiles
Zu quo  ) )
2
V’agys.  + 3b C -31- 2bC + Y erc
(9)B aequ. Ergo 3 agus el2 aequ
21 - (2) B. V aqu. 0.. Ergo Y aequ 21 - (2) + (2)2
2) ab + 1 ab +) ab + 9 uqu. 0. Engu ()ab radr na s sad (abra luus (17 ab X
un
en
+(2) 21 - (2)) ag +( aequ. 0. Ergo (X(2) 21- (2) 21 (2)Y- (4) 2 a gu Vabae
denique E 1 rap cus suqus
b
et cum duae tantum restent
aplssunt solum itenent ab. 2. 21
X X a (2) ab
+X +ax
cubisae
+ 11 ab X +21ab4
tX +q
+24 X +34
+ aX HaX
+(24bX
trabax +21ab
+14 x
tnabax 32a6
+24X + 343 X
Lβab4
6at
v
dia
+nab X
cul suptronmelarier et habemm omnta per u adeoque qispcabiaa