In this paper Euler considers the Diophantine equation A^4+B^4=C^4+D^4. He
gives a method for finding solutions of it, and gives two particular solutions
of A=2219449, B=-555617, C=1584749, D=2061283 and A=477069, B=8497, C=310319,
D=428397; the first four satisfy this but the second four do not. Euler also
states the ``Euler quartic conjecture'' in this paper, that there is no
biquadratic which is the sum of three other biquadratics. However, this may be
because of typographical errors or a bad digital copy of the original, and I
will try to get a cleaner copy to double check.