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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 1
# Folio 5r, page id 00067996:0009
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(mmmua quadratorumque aequalis numergo dato solvere problemata in integris
Nomiau sanna dicit se methodum habere aequandi cna quadrator
quantitatem etiam, qu in qua nulla sit quantitas quadratas
vy.
BX + b  d. Res huc redinitur, mmmetum invenirequadiat
s
a
qui ad eatem coditus facit quadratum vel vel a dutu ademtrs, vg. f AC  e
Eligend non est ut ad datum addatur seu f +C 7 e, seu f+( (D+ 2C9+90
seu f - qu
c
1d
 F
c. po videndum an hoc
35 + f 1 e
lifficile est eqare quad n et f ut nonnullis videtur impossibile, invenre
duo quadrata, quorum summa numerus datus.
it et
ex ipsis quadrati,
ba. seu X + X. ba. p0. Quaeramus alterius
X, quia eligere licet eaticem, utique aequatio ista
at habet rudicem  quam ponamus: X + d0. Hanc
aequationem duiamus in hanc, =X + f. fiet: ex + edX + fd ,0
sive X
es proplosite.
+ d X + fda
+
at.
Hinc aequatro collatitia prior:
d
ba
a
+ f
pnmus Quae aequatio conferenda
Ergo edas, vel ep af
de + af (70. sive f,
de.
a
at
Aena
in priore aequatione
X
+
paaa
Exy+ay
ajavi
+4
+d +y (+ba Unic patet redire
Aliter inquiramus: ponamus
4 +va
cumque valorem
X + y. B ba substituendo fier:
1 (~ +2XZ + Z +va meritque Xp γ - Z- va
Rationem video cur simplex ae quationum collatio nihil
praestiterit, quia ipsius y ad  X relationem dedit gullam
itaque sic faciamusq
ut continent
a
X,
e
E
d
eoque vatore
in po  posterior aequatio collaritia: fda   - b a +Y sive.
pro f subpituendo ejus valorem expriore, fiet.
eandem difficultatem
ba 
X
+
a explicanda est V, itaque ita
iaqu non tantum in numeratore sed et in nominatore
continere potest, dqs infinilis modis, ascendendo per quodrunque gradus
dummodo quantilas semper quadrata sit.
tius eratain
vag
per exempla ergo in