The present work, a more or less textual reproduction of lectures given to candidates for the licence, is above all a teaching book. That is to say, it does not claim to exhaust the subjects of which it deals, and that it aims more for clarity than concision.
I have endeavoured, in the exposition of the principal theories, to employ concurrently geometry and analysis. The use of this latter method leads to a few longer expositions, but it is useful to resort to it, in the application of mathematics to natural phenomena, if the students are to retain the habits of generality and rigour that the teaching of our lycées has made possible for them.
It is not, I am sure, expected that I should quote all the works which I have made use of; I should not, however, fail to acknowledge the obligation of recognizing the work of MM Résal, Poincaré and, above all, the excellent lessons taught at the Sorbonne by M J Tannery in 1876. MM Le Barbier and Bourguignon are equally entitled to all my thanks for the care they have been pleased to give to the drafting and printing.
Paris, May 1890