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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 121v, page id 00068200:0244
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Invemri tres numeros, quorum differentiae quadrati, e differentiae quadra
torum, etiam
quadrati.
Inveniamus primum tres numeros quorum differentiae quadrati
a
b. C..
aub.
a -b a - c, b- c  X + dX +
Inveniamus primum tres numeros quorum different quadrati
Ergo primum a  e X +, dX + d. Ergo a A X + 2dx + d  + bl
Ergo X + 2dX + d + bl Y = el N Z + 2eZ + C, poneudoque ZX ef
fiet _X + f s
1et
+2e  +ref
+Vor
comparanda cum X + 2d X + d
ideo d sut
bl et d  f 2fl + 
ideoque nes i fl + C +bl + cl sive e + bl + et   seu
2
HI
ntmerus quadiatus
bl- cl. tartumque Ergo et, pro arbiteae sumatur, et duo quilibe
alii numeri, negati, ipsi quadrato aequales,
vim
cuio non comparanda sed ot ascribenda, non enum sunt duaeaequationes, sed
una, fiet
ilem
2dX x + WX +s
Rursus bl- el 57 X + 2gX + g
vel mntatus siguis
v
n
+X
n
tec eno + ref
uid.
-2f X ++ 2ef. 2d sy s
-re
+2d
+29
+C -20d- 2 + +ef
+ +d +2dq + e
(9 = d2
+C
+ et
c
v
qu
+f2 es - 2df - 2gf
S
+ et-red - 2 eg
 + d +2gd.
Rectius numerum literarum contrahemus, omisso df, fietque uno non est omittendu
X +2dx +d +bl - cl 5, X + ref + e
Ergo X a- f - e + d rgF 2f + 4 ef +2C, +29 = adf - 2gf a2gd
=2d0 - 2ge
ponendoque e af h, fiet X - h + 2d +g5) S2h + 29 - 2dh - 2gh + 29d
nde t sufficere ab initio dici: X
sive X + 2d X + d
sive
+29
-2C
+ qu
et
1
+2dX + de+ bl - cl BX + 2CX + e
0
+X +29X +g
sive X +2d X + d f2d9F2de (  +d rdgrude
+29
ne
+92 - 2ge
gv 4922ge
+fer dc +
sive X + fd rg sive X + fd H. fe B S 3d + a Ygd + 2de - 2cg + 2gr
+2dX + d
+ 29
+gu 5 x + e.
erus Ergo d d +9 1 d +g. sive
12
+ 29.. + qu 1I X2 + 2ex + e  9 B d + g + 2d9. Ergo 2d95
vel X + 2dX + 3V
+ 2d9
X + d + g 1
+ 2d9: fiet X + d +g( SX +2ex+
poncudoque idg  B2h x + rehrt h, fiet:
tione arbitraria, fiet d +gF, 2dg + 2hX +-h
ac proinde
vel e ad + sg + B9 + G. Unesi, d cedut adgh
item X ( e - bl + cl - d
2d - 2 e
+2d9
X + C + h. et pro e substituto ejus valore ex aequa
X Y, 2dh + 2gh - 2d9 + h
2h
2 h
= c + d + g
Unde C3 - ble + de - de + de  - bl d + cld + d + Cg- blg +clg - dg 5
( = 2d e + 2d9 + 2d g