The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is...

The genius of Laplace was a perfect sledge hammer in bursting purely mathematical obstacles; but, like that useful instrument, it gave neither finish nor beauty to the results. In truth, in truism if the reader...

There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, … the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its...

It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler...

Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty (of the parallel axiom). He went so far as to write a paper, which he took with him...

When one day Lagrange took out of his pocket a paper which he read at the Académe, and which contained a demonstration of the famous Postulatum of Euclid, relative to the theory of parallels. This...