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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 11v, page id 00068229:0022
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Dres Numeros reperire, quorum summa quadratus, et summa quadratorum
() Qua dratum L.
(2) quad. II.
(3) quad. 1IL
(4) summa Ltorum: 2 - - -
(5) summa Ctorum . . - -
(6) Pone
D Equlx 4. 5. 6.
(9t sone
(Fab X H
N 2XC
Quadrato. quadratus.
x- xequla 2a sive 3
yr 94
=2
X2 + 2 1C d
ayr 94
I ZG. senquadrato quadcatus a Z
Cn (1) 5(+ 2Z erit CnS Z 
axhC
BX  p6 
Jam  ZaC X
+2X C
ponendo aC B e
destinitur ois X,
utc restat niso X
vel b. sumitex
x - X 2. , a l.f  15 XZ + X 2. n 210
sive destructis destruendis:
+4 + 1.f  lf 1Z
M d
IX
at
0.
L, et ZH If2X
 (t) S (4) X4 + 17 X +  (X
fk
-----
..-
dut  _ b, 145 p.sd  X1 s2 F 125 d (F 7d  125x
+XxF......
WX
(H
0
d
d.  +d n d
 Sed facilius se o supenoris paginae methoro exitus habebitur
() 2abX - 2ac X + a b  2abc ac  vt  (X) 4IX9C+6X C+ Xe
unde incipe a nund num. 6.
sive ab  ta bc + aC  y X + 2 abX t ( a b a b +2 abC
2ac
sii ab adc p Fy4 =  pbXCL ab C
+ 2ac 1
fiet ( X 28 2acX + 2X X raC H3
= + se . id est quaerasuo nuncrus balie, ut si a dimidio quadiato anferas
 unidatem residuum sit numerus ipse,
55 at 4 l) =l Quod est absurdum, ergu talis numerus est in possi
tilis, etiam crrationalis si semper est imaginarius. sit enim s  l21
o
1S
sive Xb + a bc + a   y = X  + ab X + rabc
+ Zac
sive ab + aC + Vt- x 2ab X abC
12ac.
Pouc ab + aC  (8) ap7d A n () a 33587 ato a PA
erit b  b ....... . . . ..... ............ . - a
Et ay25  n  () a B d 8A E F )aSN, + a 307
+4X ep 2 ab X + 2aCX, + (1C0) 2a259 v v + _ B
ca
pd, 444
et 2∞+ + (477 + 2Xd ( 2 145 d + d+ (2
X +413 fa
2ab p 
seu dep b riive- Hac
Ergo 2a b2
2
orgo
I y2 - X + 2aCX  + (8) a βYS dn X (Y) a βdBEX (0) a614 X act
2
232549  aar. BR GX + a
per Ne = BXCaC + 2aC + 2X eaC (24c +2 ac  (6X C) = 4X C3 + e+
 130
aC C. ac 1. gc
Y Sed matum in
videamus an 2X e 2 - 8 Xeac + 2a + 2ea cY destrni possint ideo pone cp  X + t, fiet:
2X  eReas X 8 Xca b + 2a
pone ar B X. fiet + LXC- BnX + XN NC f Ergo X Be. Unde posuendo C⊓) .
En e fiet X p, 6 on).
Et o rasedit LMXC +C, fiet XH Z. Ergo C
12- 6+ be ecnpo
365nB
no
Auc on n fC 11. lu 4e 145. 3 et 1t 5 e - hcet 1t. a  4 B E
Ln 52+
fea et + Quer t)  spse. Sx te, 1 fict et c = 2579e- 35 ∞t e = set + r e  1qute svte
50
Ex
75 videnmus an licent pontre 1 - 3579 - 35t + 9. V 770, si = 35l = 1 50 en 5 - 5l + L3 ⊓+ 
(8) Num L.
(9) ... II.
(1..... 11I.
(11) Summa Numerorum:
12) Ponatur
3) x
(2 sonc
() fier. per b. 7.
(9) sione
(2