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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 27
# Folio 7r, page id 00068240:0013
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Aey. 1.
X + p ab. Ponatur X F. A + c. et y p e + d. fiet:
scid
+ d
t
a da 
a n0. quia eo non indigenus solutum erit
problema, et hinc jam patet, quomodo
sin vero ab non sit quadratus possit tamen plividi in duos quadratos seu si possit
fieriferi C+ dp ab. tunc infinitis aliis modis potest ab. dividi in duos
alios quadratos. Et huc usque progressus est diophantus, et qui cum secuti
Ac
excess
sunt omnes. Jam ipsam literam C explicemus porro. ponendo CH etf.
V
et
ret:
 ect + 2 eotas
t + + 2. 1 ab.
+ 2f1) reref
in  2h.
fr
N
+Egh
l+ F2
dr gFh
mni ia sdffex Ex his jam variae
rursus aperiuntur viae, quarum prineps
a
a
istaest: si diff ponatur c+ d
numerus major quam ab. et excessus ejus
Dminor
uper datum  smmae duorum quadratum  e+d, super numerum datum
tumpesexer dati  su ab. super summam duorum
quorundam quadratorum, C +d. quos pro arbitrio jumere licet induos quadratos
dividi possit 
sed jam ex aq. 2. nova mihi videtur aperiri via, pone enim:
N + 2C + d_ ab. seu pone a divide ab in duos quadratos et entum
et rectangutum sub latere unius quadrati latere, A, et alia quantitace
2c. contentum; restabit: c+  +2dn 1 0. Quod ut fieri possit
d
pone c  . et fier:
sive et H 
da
Erta er C FI
qu
N +  +2dp p0. sive 2  + n +2d p0.
b
- 4 oda + d  ab. F)
N
noda adeoque
cr+a
ve
A - 2 d A  2aW + d
a 6
W + a
videndum jam tantum an 2a possit aequari numero datop l.
W+a
fiet enim: 2atoY ∞l + ael. sed hoc fanle fori non potest. Ergonec sic
1 +a
a
quaerendum fiet 
a
ga gr.
ergo Fco  a e  M et   Y a- a . Jam sit qua = 1
n
12
seu a=  H): seu (4I esinta.
12,Y.
an
+2 m + a,
+ 1 H. et ∞,, ec m+a. unde = - 2 am - m  H
unde ca) me
et ponendo Y , mn fier. = 2a - m  mn seu m  20 a- n.
l
ei
a3- an +a
alug II a- n7
Iu B 1a-n unde la-In taan, seu n- a- la. Ergo si l. talis
on
la ppesitum
ea
sumi possit, ut sucedat hoec extractio haletin