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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 314r, page id 00068194:0627
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Deux nombres quelquaques, divise par le donsile it leur somme, sont tels
que la difference de leur quarez, estant adjontée au plus petit; et estant
ostee du plus graud; Il vient un même
leur sommee
A
1
2a+ 2b 2a + 2b
o
quarie, qui est le quare de
du
ea
Ia +8ab + 4b 4a+8ab +4V
 ux a) +a + 2ab
4a F8 ab 4 4b 
2a + 2b
va
l ab - a
a = 2ab 
+a + 8ab + 4b
4a + 8 ab r 46 2ab. +0b  l)+
36
13
1061, 3.
100
+ a +6ab + 4b  va (570
cut Hugemus
as
tr a 193
4a +5ab + 4b
a
deator suma quadralus ut
AErIACF, E PF
Ben CF
GHK E ABEPFCA.
vaeritur AB ratio AB ad GH.
a
a2 +6avga,
s
2
+ 2ab
ar +8ab + 46
F2
2a + ib
dcubus
nuo latere non potest esse quadratus. lt unna
AY
DBlongens
AABC. maximum
inscripturus.
methodo utitur dosanna.
quad. parab
80
circa C L. frat semicirenlus aMt. Secans. 1140
HK prodactum in M.
gungatur lik
friat GN ~ 1M
Sit 1O parallela L. K.
Recta C00 lateri Hexagoni cujus
area vareae proposit AE HK
36
duat1 c02a +1.
b. ~3a +1
a2
a2 16a 1.
a a in. (+9)7 34, a
a a x+
sa
1
tba ru
Methodus qua D. Osania
acit  vaniant aliquando ut
aequentur quadrato formulae cu
quibus quadratis nullus. Sailicet
quadratus, ut in praecedenti exemplo
2 +. + 5 i M mea methodo
si sit 2a 4 5 b  C reducitur ad hoc
sione est
2 bH
2+5BC vel ad hoc:
5+2a  er vel 2+5l= d
s
vel 5 +2a 2 8  c2
20
BIBLIOTHKOR
SC
ALAABOVESIAHA
producatur perp. C.N in L, ita at 1L. ∞ IX
a2 4 26d + 5b2
d~. 
si summa omnum unitatum
Lb 53