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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 39v, page id 00068200:0080
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ot sit quadratum illud a radice: ryn
or
vayr et dividendo:
Xy -Xy aequ. xy
e X = y aequ Xyy seu X - D equ. y.
D
Unde patet si impossibilis est area trianguli
au mupri
loiatr etia rectanguli aequalis quadrato
o in numens etiam impossilllem fore differentian
ne
p
efractionum reciprocaum quadinta aequalem
od
a
sed ut perganus; debet Xy -XG aequar
quadinto, ponatur  X aequ yco
41
a aequ. quadrato
ergo et co-co aequ. quadrato seu faccum
ex his quatuar: 1,Cd, co - 1, cod1
vel quod idem est ex his tribus: ed, co-t, co+
debet esse quadratus quod in numeris integr
praestari bnon potest, ut alibi demonstravi
seu posito eo esse integrum. ergo non
 sucledit omnibus multiplicalis et divisis
e2
E
per c mueri in p. Cd, Co, Cd C0 C0 + co
1)
i
C
esciet
Ce
-+, c0, Co- 1Co + 1
Ergo si haec quantitos in integiis no posito
eit esse inhegrum non est quadratus etiam
 saco vaco
trunat atate dicamet
X
co + Cogco non
erit quadratu e vel o co 1) i
a
a
celuriper ag podublum etiam non erit
a
maxmu
quadratus frevantem.
2
o
e
a
x+X
ut f co
1N X -I, X +1 non est quadrocus
LL L+
x
ergosi X integer. Ergo
3
e L..
etiam non est quadratu divisis scilicet omnibus per
X. vel prox onendo et sponerdo X divido posse
der y vel mulcipercando omnia per y. fit.
1, 1- L, 1+ L, non quadatus erigo
eo
qge zcomda
eo
equenti scheda rem melius
mulli do per zeo, fier
absolveuqus:
bu