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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 3r, page id 00068229:0005
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invenires tres quadratos quorum et sum differentiae singulorum
st qudor sint quadrati et differentiae quadrato quadratorum sint
quadrati.
_ X ∞ y aequ. LI.
X - y aequ e
X2Z.  aequ. B.
X-Z4. cego L.
Hinc sequitur etiam fore;
X + y aequ A.
X + Z aequ 11.
3= Z aequ 1
32Z1 aego E
y + Z aequ. L1
Quono quia X + y x - y aequ X - y. hinc f ad hibeamus aequationes
Sequentes:
X - y aequ.  a b. X+ y aequ. ab. X+y aequ 
Ergo 2x aequ. ae b + ab. et 2y aequ ab - aeb
Et eodem modo 2X aequ d’ex de et  et 2Z aequde- d’e e. X + Z aequ f
Et denique 2y aequ. gh + 9h et 7Z aequ gh - gh et y +Z aequ N
Ergo ab + at aequ det de. ab - a b. aequ. 9 h + gti de-de aqug gh.
seu ab aqu d +e ab  eth de aequ. h - 9
e- d
de a +b
ot Y p- D gh
Poro al aesmbtb, + gk, 29 righese aequ.
a+b
+ si
b-a
ba.
Sthigh.
X L y aequ aV) Erg. Ergo 2X aqu. ab + c. 29 aequ. c- a
similiter. X qu aequ d2. Ergo 2X aqu a d c + f. 1q uaequ f - d et
Xa it aequ. C
fic
renique _ y- Z0 aequ gh. Ergo 27 aqu gh + K et 2Z aequ R -9h
X +22
y +Z aequ K
pro ab ponumus X4 l. et pro c. fiat Xm. et erit
(2 aequ. (∞ IX +  + (X 4- 2m X + m. Ergo X aqo l’ +m
ruih.
ultum
XQY+Z aequ se2
X+ F X t est aeque. X + Qu aequ.
X aequ C - s. aequ  f ZV. Ergo, y - Z5 aequ c =f. Ergo rest aequ c- f.  k
et2ZV aequ. f +K = C. et  aequ c+ Kf et 2X aqu c + fV - K ~
sut 8. c. f K. Ergo siat E (Baequ. AX + 2, 3 X + 3 +  y 4 2   y +  + 2, _ xy
2
X13 EXit
3+4
rt
28 _X112
s’aqu q
Paist aequ xt 2X et8
ergo raequ  C sit eaqui hu, per X aq V. ny
X +Z aequ X + 2X9+9
ergo. X aequi Z. -9. sit gugo pZ fei vaego 22
ergo  3, 1-ln, 2p. aequ 2, 1- p, 2n
X + 27X +7
Ergo ex f+Z fit qZu + ZV aequ R aequ pZ 
ubipomendo  aqu K Z aeyusR fiet 945 aequs
+2, 8X
+2.2,8
+2 , f1 X
2F26ZF=4Z
+27
K aeq Y +2,1y + 1 + Z +2, 1Z +29Z
seu Y aequ. L- p . 2n seu y aequ 4Z. Ergo _Z
1- nV, 2 p 
12 (4 X
+274
+2 1y +127
+2112
+2, 11 Z
s aequ