The number of solutions of $ax^4 - by^4 \equiv 1$ (mod $p$) for a prime of the form $p = 4n + 1$

Question

Weil writes in his paper "The number of solutions of equations in finite fields" that Gauss finds the number of solutions of $ax^4 - by^4 \equiv 1$ (mod $p$) for a prime of the form $p = 4n + 1$ in his first paper on biquadratic residues. I would like to know how the Gauss derives the number of solutions of that equation. I cannot read Latin, but I have a Japanese translation of the paper. However, I couldn't find the part because the paper is difficult to decipher even in Japanese. Weil does not write the exact page number of the Gauss's paper in his Werke vol. II pp. 67-92. If the page number is clear, it would be of help. Any help would be appreciated.