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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 184v, page id 00068196:0364
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XX q. X3. Pationales integne
n aequ. x.
v aqu
v aequ
XX
X3
Y nyo ox
Veniamus ad irrationales simplices integras: 
v aequ. TX 
SXx
x
Ix
VEx
Ex
YX. eu.
Vxx iu
es
ete
y aequ. 2
2Y X
fYX
3 x
dix
X.
XX
V aequ
ti V aequ X Et y aequ. X
XI
esx
X
ye
s
eia
vaqu. B Ix
LYX
XHC
ad
3 Sx
2st
X
Yx
ri
Habemus Ergo. Q vadraturas omnium
simplices explicabilium.
Curra Figurarum per aequationes
deniamus ad compositas:
Et quidem incipiamus a rationalibus: sit;
ec Primum manifestum est b
x  s
V aequ
1- X revocari ad 
X
a+ bX
ponendo Zaequbx
Equidem manifestium est  vel 1 permissum enim est  mdicem indeterminatam
tox
A - XX
x argere vel minuere quantitate constante a, itemue
eam multiplicare per constantem, ut b. eadem manente figura quadrabili
1 -X
 manifestum est omnes rationales habentes numeratorem indeterminatum
racta
valores
reduci posse ad eas alios fractos habentes numeratorem constantem,
etoem primi frad
ex. g. sit s
ergo fiet:
x multiplicetur per b fiet a +bk
afbx a+bx
X
a+ bx q seu 1. Ergo
a + bx
seu bx aequ. 1- a
a + bx
de
a + bX
7b
similiter XX reducetur ad X et per hanc ad 
a+b
aequ. 1. seu P x aego  adtm
a + bX
 Ergo quant redacta est 6X ad _ a, quae habet
a + bX
numeratorem constantem.
a+ bx
a +bx
Nam
X a + bX
bb XX  + 2ab X + aa aequ a + bX
a + bx
a + bx
a + bX
a + bX
idem est etsi ad cubum assurgamus. Idem etiam ests
quicunque. Et si sit compositus numerator
etsi nominator sit alius
X X + Cx resolvetur in simplices
ea reduci potert ad proxime inferiorem gadum, faciendo Xaequ q + (R
a + bX + XX
het:
Z+_R equ. Ponendo ae R + b R + a aequ. 0.
+ WRZ + RR
 b Z + bd
x
a + bx. sed quid sit si sit:
qui singuli separatim resolventur modo dicto.