But it is impossible to divide a cube into two cubes, or a fourth power into fourth powers, or generally any power beyond the square into like powers; of this I have found a remarkable demonstration. This margin is too narrow to contain it.

In particular he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines which is analogous to that of the differential calculus then unknown and his research into number theory. He made notable contributions to analytic geometry probability and optics.