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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 59r, page id 00068207:0117
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puis
aotata per B valet, priora non prosuns
problemata sumerica in
eries
at +txx
dulectris
solvenda
lesto pro verbi gratia problima bx +a = 7y ubi
b et a data, quaeruntur X et y. Ponamus seriem sumi ipsarum
 progressionis Arithmeticae, quibus aptemquse b et a
1
C
b dx = 2ydyue + dIdu, et posito ay = 1= fiet  bdx = 2yl + l,
Itaque re reducta ad solam b, oportet (ryt +l, impares ordine sumtis
solos eosquadra
om b ompolles ordine
e
t
1
s
fure isos ax poso, sex datis imparibus 2 ri ad 2yl es dantur y
posse qui divisitiies sint per b
nempe ab imparibus sublinhendo renitatem  Il, et esidum samendo dimidium
Habemus ergo quadratom
vu aquisudctraris a opotetio qui quadrares
.
qui tenglandi a quibus ili sol
Esto
succedent qui detracto 10 relinquime divisibilem
dX +10 = yy
bx + _ = 1 2= bdx. Ergo eligendi
ex +a 
bx + a = 9
Ergo fb
impares sunt divisibiles per
bdx +da = 29+1
si impar sit 13. eut X =6 et quadat
= 36c
bdre = dZ
bx +a = Z
bda + dda = 2 Ergo dax
x progressionis prithmetrcae
sumamus potius
oet
t
az+ a22
= d
 et
bdd de + da
sed bddx= Elgd fiet  ada = ada
+Se a=
impares divitibiles per b. sit b = 13. Ei impares ernul 13, 39, 65
3 horum primus est cy fiet bdx  = 2y4
per b.
ia
- 1
e
0, sed ddp =0
et faciamus bx + a = 2
bdee
d
Cae
 IdasL +2(7d + 2d2cl 7
 + 2ddzauz