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 upon this idea. Landen showed how the algebraic expression for the roots of a cubic equation could be derived by application of the differential and integral calculus. Most of the time of this suggestive writer was spent in the pursuits of active life.

Étienne Bézout (1730–1783) was a French writer of popular mathematical school-books. In his Théorie générale des Équations Algébrique, 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 $$\scriptstyle{D_xy}$$ for $$\scriptstyle{\frac{dy}{dx}}$$ 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, $\scriptstyle{x=0}$, and a cubic $\scriptstyle{\left(\frac{y}{c}\right)^2+1=\frac{c}{x}}$.|undefined

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