mathematical school-books. In his Théorie générale des Équations Algébriques, 1779, he gave the method of elimination by
linear equations (invented also by Euler). This method was
first published by him in a memoir of 1764, in which he uses determinants, without, however, entering upon their theory. A beautiful theorem as to the degree of the resultant goes by his name.
Louis Arbogaste (1759–1803) of Alsace was professor of
mathematics at Strasburg. His chief work, the Calcul des Dérivations, 1800, gives the method known by his name, by which the successive coefficients of a development are derived from one another when the expression is complicated. De Morgan
has pointed out that the true nature of derivation is differentiation accompanied by integration. In this book for the first time are the symbols of operation separated from those of quantity. The notation for is due to him.
Maria Gaetana Agnesi (1718–1799) of Milan, distinguished as
a linguist, mathematician, and philosopher, filled the mathematical chair at the University of Bologna during her father's sickness. In 1748 she published her Instituzioni Analitiche, which was translated into English in 1801. The "witch of Agnesi" or "versiera" is a plane curve containing a straight line, , and a cubic .
Joseph Louis Lagrange (1736–1813), one of the greatest
mathematicians of all times, was born at Turin and died at Paris. He was of French extraction. His father, who had
charge of the Sardinian military chest, was once wealthy, but lost all he had in speculation. Lagrange considered this loss his good fortune, for otherwise he might not have made mathematics the pursuit of his life. While at the college in Turin his genius did not at once take its true bent. Cicero and Virgil at first attracted him more than Archimedes and Newton. He soon came to admire the geometry of the ancients, but the perusal of a tract of Halley roused his enthusiasm for the
analytical method, in the development of which he was destined to reap undying glory. He now applied himself to mathematics, and in his seventeenth year he became professor of mathematics in the royal military academy at Turin. Without assistance or guidance he entered upon a course of study which in two years placed him on a level with the greatest of his contemporaries. With aid of his pupils he established a society which subsequently developed into the Turin Academy. In the first five volumes of its transactions appear most of his earlier papers. At the age of nineteen he communicated to Euler a general method of dealing with
"isoperimetrical problems," known now as the Calculus of
Variations. This commanded Euler's lively admiration, and he courteously withheld for a time from publication some researches of his own on this subject, so that the youthful Lagrange might complete his