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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 10v, page id 00068229:0020
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Tres Numeros reperire quorum summa
quadratus, et aelatere dato; et summa
quadratorum; qua drato quadratus ab eodem
latere dato.
sinto
(1 Numerus L.
2) Num. II.
6) Num. IIL
(1) summa Numerorm
(5) Quadratum Numeri UHi
(6) Summa oium Quadratorum. per, 1. 2. 3
(7) summa omnium quadratorum
per 4.
(8) Ergo
(9) sive
50Lu
(10. Num. 7.
(11) Num. 2L
(12) Num TIL
JN INE
(13) Num. L
(14)..
(15) ....
DEURmiA
ab
ac
X = ab - dc
X - 2abX - _ 2aCX + b 2abc + ac
X - 2abX - 2ac X + 2a b +2a bc + 28
Xy Xa b + fac + paebe
Xpb 474C
a  Xb L XrC
+c+ bc
Xb + X Cb
b +C + bc
X bc + XC
b+ c + bc
Xxd cb   b C XbC  bc- 2 xbeZ b CX
b  bc bc+ be
b4 Xbc
XC + X bC
xcb broro
Hinc sequitur aliquem ex
numeris quaerendis esse
nihilo minorem. Nempe
tertium si b et c. habent idem
signum verum, seve id sit +, sive
e c
b sit affectum signo
vel contra,
tunc si est HiC erit signus
nimerus
 nihilo minor sin
b est  qua
nunerus primus.
a
N 1. Quadratus, et quadrato quad ratus datus.
15
+ bc
ide e
2. Quadratus datus.
10d. Quadratus
36+ 9 4 4 _. Quodrato quadratusdatus.
qundo in interis
sive = X bc
abc
49. Quadratus a 7.
X= ab -ac
seu negativum
quadrato-quadratus postulantur
ab eodem latere du;
nempe tertium.
N. puncta significant quod deletum erat, restituendum (1t) suindi
Ne
A quandocunque quadratus et
Exemplum.
161) m
n
.(16) Ponatur
(15) ...
5)
.
(10) Num. 1.
(20) ...- 21
(21) .n. . II
(32) Summa Numerorum:
(23) summa quadratorum.
Exemplum in integris sed func non potest effici, ut quadratus
et quadrato quadratus sint ab eodem latere dato
Retenta eadem explicatione, ipsarum X. b. c. vide 16. 17.18.
(24) Num. Z
(25) .. 11
(6)
-- 1II
27) summa Numerorum:
28) summa quadratorum
2401. Quadrato quadratus a 1.
In integris ergo problema sic proponi
Tres Numeros integros reperire, quorum summa
potest:
quadratus, et summa quad ratorum quadrato- quadratus;
ae ita ut quadratum et quadrato-quadratus sint
ab eodem latere omnium possibilium minimo
14
semp
d non utao eodem catere dato
55