336 A SHORT HISTORY OF SCIENCE 



Its curriculum included, in the first year, analytic geometry of 

 space and descriptive geometry, in the second, mechanics of 

 solids and liquids, in the third, theory of mechanics. 



Reviewing eighteenth century mathematics, a recent German 

 writer says : 



In the science itself there showed itself with the close of the 

 eighteenth century a certain exhaustion. 'The mine is, it seems to 

 me, too deep/ wrote Lagrange in the year 1781 to d'Alembert, 'and 

 unless new veins are discovered it must sooner or later be abandoned/ 

 In the nineteenth century men have dug deeper and struck noble 

 ores, but serious obstacles opposed the progress. It appeared that 

 the men of genius of the illustrious period had to some extent practised 

 bad building and the whole framework threatened to cave in unless 

 the passages were newly supported and the oncoming floods of doubt 

 conducted away. For two generations a considerable share of the 

 efforts of mathematics must be applied to the hard work of security 

 and safety, a labor from which even the greatest . . . have not held 

 back. 



NINETEENTH CENTURY MATHEMATICS. As in the century 

 following Newton France became the great centre of mathe- 

 matical activity, so in the nineteenth century the leadership 

 passed to Germany, under the inspiration of Gauss and Riemann 

 of Gottingen, Jacobi of Konigsberg, Weierstrass of Berlin, 

 to mention but a few of those no longer living. Outside of Ger- 

 many conspicuous names are Cauchy, Galois, Hermite, Legendre, 

 and Poincare in France, Cayley and Sylvester in England, Abel in 

 Sweden, and Lobatchewski in Russia. 



Characteristic of this period are: the development of a 

 general theory of functions based on unifying coordinating prin- 

 ciples, compensating the powerful specializing tendencies, and a 

 profound critical revision of the previously accepted axioms, 

 leading for example to the development of a non-Euclidean 

 geometry. In the science generally there is systematic devel- 

 opment of instruction and research, notably in the German 

 universities; of publication, by the establishment of mathemati- 

 cal journals, and the preparation of encyclopedias; numerous 



