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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 131r, page id 00068200:0263
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duorum quorumlibet
Tres numeros invenore, ata ut eorum summae differentiaeque sint quadrati.
tertius
al. secudus al- X sus al -X = Z tertie Cyss. differentia primi 3 secundi erit  perua
et tertii Z2. Ut vero et differentia primi et quandi sit quadrata
seu aequalis C + 2cZ + Z et X  C = 2CZ. (srvC Z  +x+
lam summa primi et secundi ral - X. 5 _. Ed
N +X secund, d- X fertius d x  ergo ap d + x. Fiet ergo primus denmus
summa et primi et tertis eut (d - Z BC  d co + co
summa secundi et tertus est d = Xt - 72. side e
sive de vel cot + 2c038, y+
4∞2
vel Ponamus cd HZ. fiet:
sive 47 eFf2 +c2.
fiet primus terminus: 
Secundus:
Tertius:
pone 5r1. er c+A
secundus s
f2, 2fV +
a c +2c4
Co + 2C0 + V 
5)+
f= + 2fC2 4c4 + f
fiet:
vim tennirus
L4
209 +  4) 353
1 18-
128
Tertius sad inde sequeretur nihilo minor.
igtur lemendus f talis ut f sit major quam s
sed dem debet esse major per teminum primum. Ergo
quod est impossibile ideo mutanda suppositio
co + 2co G~ + Z
2c
sed resurmta aequatione
cor
y4 + L
porum ad A e 2. feo  t
= = - 2.
2 C
sive: 8 9u 4 F Z + la TK
4(2
12C
, sive Z,
qu
ciec licet ponere conL
F
Mc
L AS
+Z+ 1
44
e D- c Z 2  225 2
q + nequ ( ) Eit e et s d 
pro tf ct Z sume Z.  pro A + c + +Z sume co +Z a g, sive
+  + E4 1
(4) 200
4l2 4l
Fe + g.
explicando  per E Z fiet = Z + 2 + d sive erit +fc + +Z H E
e. - 9 1 f2. Et cut DEZ e F + 4. Ponanus  ess-
fiet ergo:  CqZ + ldZ.
e+
F2CZ
e  2 et (+) ese . fiet Z e S + g.
et C C Z 1I  L,g. ponendo + f ese t er t F esse, ergo C p g
pn   1 + EZ Z
Explicatis jam terminis fiet prumus: ex +      He
Explicemus terminos, ponendoque f H1. et 95 1. fiet Z et 2 Est autem  et l71. ++
CH = + F Z CF) ++ GZ+ EZ 4fg siue cy  f + + 2( 14 1f fil + x13. 2t +9
 Et fier Danius prings. o e 1c + + Z d E 4  +C f a F C  2 G 1 a1 4
Pone Cr 10. fit et + p et   crc +. fiet.
Ergo c 
substitui ejus valorem
Z potius eliminanda erat
2 5 2. etc r +2 4 2 +
10g04e 144 eo 10) 10o =1 sive 37 - 102. et X H 484 8-
. Ergo d e
Jam ergo Terminus priaus:
al primiatsccndio al - X
10000
ogeoH invod
et Video in eo a ne erralum quod pro X
qui tanen non centenebat characterem formamque quadraticum grtiu
rebus de integro sic assumtis:
al - X - 22
urgo X (2) ∞, C 4 2Z  Z. Ego Z 
Jam summa (2 al = X H d. Ergo _  a r d +X. Fient ergo: prinus terminus d’+X Secundus d
tertus. d -  - Z seu 4 X -X2+ 2XC - e pum et terti smmma: (NC - Ct  a  reod ( 
Ergo d pu co2 X+ +2X C- c+
tra
nc
 secndi et terti summa; d X ZV siui ;. cot - 2c X 3, 2XC - C+ X 1X8. XC
1aEC. Ex C+ C. X.  L 6  HI H
c 6c2
7c0.
Ponatur primus
fir sal - ad x + Z. quadata
co +Z s(4) Z
(+ 2C0
sive W 2cZ 
eritue des
+03
10404
non
256
289
rona
1 + 16 Hgit
sive