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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 27
# Folio 7v, page id 00068240:0014
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Ut ex his vel aliquam saltem novam
consideremus ab  A + 2od  eaco
u
co +a
determinationem traham
 a
. 4
et 2a  l. p B debetesse ponendo d  1.
1d2+ aY
aqua debet esse  L - 1. aequalis quadrato, ponendoque
deber esse fier:
1 
NpEAd
non quadratus et
Ata
C
 H m
e uedu
UD ergo numerus datus nuos quadratos dividi possit, non esst necesse ut
jum habeantur duo numeri quadrati in quos dividi possit; ad alios inveniendo,
sed sufficit eum dividi posse nis atres quantitates quarum numeros ex
quibus duo suit quadrati, vertius vero sit one u numerus rectanguli
Tub duobus quadratorum lateribus multiplem peranierum quotiens per numerum
cnus quadratum unitate diminutum relinquit quadracum
Hideamus anseliceat facere 
fiet
e2 + rest +ucf 1p7 ab.
et + re R + A2 
+2e f
+24f0
+
2
1I abat A2 +2Af ef
ma um.
et e + A + f Y) V ab + A
a + 2Af + fr
+ 21f
t
V
e
HI H. . A +  n
12An + n2 et A A
11
v 1
n-
e
2
f :
sed quoniam haec ipserenda un aequ 3. hiniccusu non sunt
+ V 1
c - Z2 b 0.ponendo e
X. y aZ. v. b. c esse integros
2
2
Ergo X vC divisibile per 2 seu et H Z ad ergo B1G. ergo C ∞to
et yrgec H v a e. ergo  quadrato est autem c. datus
t
porro ponatur  Cr b + f frecti 
.
v
2
+27coV b + 27cov
corv b + corvt
e X1Z+ co, fiei
e
b
quod si jam vf + SC +yf posset fieri pro. seu exd
seu   8 v
mus quaesitum
s
vesi 1
∞+ I
solvi posse generaliter  si f4 F posset sumi pro aibitrio
sit X
2
e
 integro si c non sit quadratis poterit nec d esse quadratus Resolvatur 3.
a
in suosi pro e none SZ pro v, pone multiplo poters
mempe Z1 Ysf. ert X F (~S ) m vH (Y5+) n.
a, i ouins anter un triperes e, st nti, ves et
si c ponatur esse numerus primus, reliaquemus:
aneoque
um