Excerpt from Lectures on Elementary Mathematics

The present work, which is a translation of the Lecons elementaires sur les mathematiques of Joseph Louis Lagrange, the greatest of modern analysts, and which is to be found in Volume VII. of the new edition of his collected works, consists of a series of lectures delivered in the year 1795 at the Ecole Normale, - an institution which was the direct outcome of the French Revolution and which gave the first impulse to modern practical ideals of education. With Lagrange, at this institution, were associated, as professors of mathematics, Monge and Laplace, and we owe to the same historical event the final form of the famous Geometrie descriptive, as well as a second course of lectures on arithmetic and algebra, introductory to these of Lagrange, by Laplace.

With the exception of a German translation by Niedermuller (Leipsic, 1880), the lectures of Lagrange have never been published in separate form; originally they appeared in a fragmentary shape in the Seances des Ecoles Normales, as they had been reported by the stenographers, and were subsequently reprinted in the journal of the Polytechnic School. From references in them to subjects afterwards to be treated it is to be inferred that a fuller development of higher algebra was intended, - an intention which the brief existence of the Ecole Normale defeated. With very few exceptions, we have left the expositions in their historical form, having only referred in an Appendix to a point in the early history of algebra.

The originality, elegance, and symmetrical character of these lectures have been pointed out by DeMorgan, and notably by Duhring, who places them in the front rank of elementary expositions, as an exemplar of their kind.

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