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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 57r, page id 00068207:0113
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5
20), 1
15 531
165
16
hh = XX+gy
1b M 256 615 1296 2401
2 3
s
4 9 16 25 36 49
30 1 1c
50 1 4
6)0 1 4 3 4
5)0 1 4 2 2 4 1
8)014 10
01) a
1
4 9
d S
11)0 1495
170 1 49 4
ol 3)
2
es
149
1
3
3 12
a
C
4 9 16 25 81
s
10
4096 6561 10000
8 y 10
II
64 81 100 121
si
12
10
16
13
20 Nonts
16
a
4-4 = 0 etc
6-6=0 9-9 =0 etc
5-025 6-1 = 5 g- 4 = 5
 bcX+ r = 0 = b7 + EbZ +5 = b 145
169+2
58
139
O
216
10e
24, kB 8 11, 12, 2
1290
potest dividi in duos quadratas
quia duo residui ex divisione fondia
iea
alituius horum numerorum
ntea
PH
quam componunt desem
9-920
130
XRD.
64
5u
e
13
se
25C Eug poto
284f.
129099, 469b
8. 0
F.
tia
s
st5
B
q imu sufficil min
e
quam componere divsotem
nam multiplum divisctis
in emparibus crescit diffe- componere non possunt
rentia, in paribus
manet eadem
si numerus divisibilis per
nam. cum sint singuli,
minores divisore simul
quadrabum periovus residrio
Tum none numa dcanore ad duptumpius
mneru et ieminorum de ego multo minus ad al–
deminorem
idorem multiplum
Porro quotientes sunt hic divisoreminores. sit divisor t, quolens a
C fiet reseduus Y, sit o+ +V = et (q) E + (Y)
. unde fit
dividundus
e)  ee = () t +(Y) 9+ - Y si jam Y = (Y) fiet
ita (CC) ec = () 9, t = (() +e, ()
 =gC +r
cix + (9) +1 = th
 f6.
aut mahiplum divisoris 6415 49
36
144 169 196 225 2563
28
37
re pum numeri quorum nullus
(51
ytrfipt o+ +r = ee  (4) t + (Y) = (C) (C)
3+59)2
b+ c
a
(51 13 ut MS137 1ta2
Ge
a
pers 
10 -0 =10. 12.-1 = 11 Cp 8+ 1-4 =12 9413-9 = 12
B- 0=0 1- 1 =0
2- e diris. per b
sf
6+ Cg)
ee
+ Y+ (V) = ee + (() (C). Quod si
quili Ergo Y + (Y) = F fiet. ee + (ese
141 per t
divisitia
Integre miibta radice quae sit
Ergo _ si non datur dantur duo quadrati dato cumen
s dato numem ininores, quorum summa sit divisibilis per numem
Cex iat.) itir
shaix
non xi
datum non a possibile est non est numerum datum dividi 
in duos quadratos
quodsi tales duo reperiantur
habebimque duos resinuos
digui divisi per te
9+ 9(4
tabemus et 4. + (4) et fiet fyt +F=pX X
(HFXI)
dellent dam generalite
et 1X
yyh
1ofag
ged
 et et fq+ +r + g9) ++Y)
datos n qua praguH
ud quadratur B Jam
deveat par
Y+(Y) =C. Ergo fiet
eo tauhiles
Resolvatur (4) in q. et seu in quotientem et residnum ecunu
57
r
e
1
e
13)