On the resolution of irrationals by continued fractions, where a certain minor new and singular type is set forth
This paper begins with a review of Pell’s equation and continued fractions. It includes the following problems: (1) Given that the formula Ax2–2Bxy+Cy2 produces the value c when x=a and y=b, find an infinity of other values for x and y that produce that same value c, assuming that the quantity B2–AC is a positive non-square number; (2) Given a formula Ax2–Bxy+Cy2 in which B2–AC is a positive non-square number, find values for x and y that produce the minimum value in this formula.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 18, pp. 218-244.
Opera Omnia Citation
Series 1, Volume 3, pp.310-334.