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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 3
# Folio 27r, page id 00068000:0053
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nvenire in integris
13X + 10 = Y.V
e
solutione comprehendantur
Fiat X = 13DD F 2B +2
vel X = 13V + 1a + 3
IL adsocare, unbicasus
 existente numero integio quocunque
solutio Methodus pro Generali problemate haec est
sit problema. bx + c = gu. Asuar  emn quam  ubi b et c sunt dati
X el y quaesiti. Sumatur Z minor quam b et quaeratur quot modis ibi succedat in integris Z
22 c,: b Exempli causa cum b est 13, pese Z esse  vet P quia
d6 et C est et C est 10, erit Z = 6 vel 7, nam 36-10 =26, qui numerus divisus
Nec vosaepius haberi potest 
et
per 13 eat 2; et 49 - 10 = 39 qui numerus divisus per 13 dat 3. Hoc modo igitur invento
jam yn - c :b qui est integer vocetur
et fiet X = pvD + AEV + F quae est problemais geperasis solutgo absolata
ba b012
numero  satis faciente, fiet X
ubi v surgi potest integer quiclangue. Atque haec est problematis generatis solutio absoluta
Et 3-
problema igitur indefinitum, reducitur ad tentandos numeros definitos dato
aliquo numero mipores.
Untatio caatem ipsac eariis modis e facilior
recdi erotesde veculi pe Cabjectionem
novenarim, undenariamve, hut aliis
 bx+ c = bbvv Y 2b1Z + fb +c sed fb =
etihae hi bphrosbilse
et fiet bx +C = bb vv + 2bvZ +7Z =c + C. Ergo bX + C = bbro + 2bv
L
demonstratio
= C
 +77 quod est quadr. a bP + 2
a
sed ut apporeat inson posse os alius solutiones dari, methodus ipsa
du ab y, adeobque bx+ C = gy.
oui
sed nethodus qua inventia solutio, haec est: 13X + 10 = gu ergo fic
i
melius
= yy -10,: 13. umatur y, = 13V + Z, ita erit Z residuum. quod relinquit y divrsum per 13
13. 13VV + 2. 13VZ+ 27 -10, : 13 = X  = 13VD + 2v7, + (22-16,: 13) = X. Ergo necesse
L ut ut detur 2Z - 10: 13 integer, et quoties datur, nec aliter, habetur quaesitum, in integris
fietque
est