ANNIVERSARY ADDRESS. 17 



Contemporary with these giant mathematicians may be men- 

 tioned Alexis Claude Clairaut [1713 - 1765] whose researches in 

 'curves of double curvature,' theory of the figure of the earth 

 and theory of the moon, will keep his memory green : Jean-le-ftond 

 D'Alembert [1717 - 1783] notable for the discovery of the principle 

 in mechanics which bears his name, and for his complete solution 

 of the problem of the precession of the equinoxes : and Johann 

 Heinrich Lambert [1728 - 1777] who introduced into trigonometry 

 the hyperbolic functions. A little later Adrieri Marie Legendre 

 [1752 - 1833] devoted his genius to the study of elliptic functions 

 — the starting point of which is to be found in the earlier work 

 of the Count de Fagnano [1682 - 1766] — and to the theory of 

 numbers. Legendre moreover calculated extensive tables of 

 elliptic functions, which I believe will yet be greatly utilized : he 

 also preceded Laplace in developing the theory of spherical 

 harmonics, to which however the latter made splendid contribu- 

 tions. 



Jean B. Fourier [1768 — 1830] in his 'La Theorie Analytique de 

 la Chaleur ' set at rest a long controversy as to the possibility of 

 representing any arbitrary function by means of a trigonometric 

 series. 



The wealth of mathematical discovery and development is now 

 so great that only the briefest reference can be made to even part 

 of it. Synthetic geometry had, through the influence of Lagrange 

 been contemned. The efforts of Mydorge [1585 - 1647], Desargues 

 [1593 - 1662], Pascal, De Lahire [1640 - 1718], and even those of 

 Newton and Maclaurin to revive synthetic methods seemed to be 

 doomed to failure; when they reached their object through thegenius; 

 of Gaspard Monge [1746 - 1818], who raised descriptive geometry 

 to the rank of a distinct branch of mathematical science. It was 

 further developed by the labours of Carnot [1753 - 1823] and 

 Poncelet [1788-1867], still more by Mobius [1790-1868]— 

 author of the ' barycentric calculus ' and generaliser of spherical 

 trigonometry, and abundantly enriched by the " greatest geo- 

 metrician since the time of Euclid," Jakob Steiner of Utzendorf 



B— May 3, 1899. 



