658 SCIENTIFIC THOUGHT. 



ducements is likely to prove fruitful for the progress of 

 science ; they look upon the first as an amusing pastime, 

 and upon the third as empty and not devoid of danger. 

 In recognition of the partial correctness of this view, I 

 will follow up the practical stimulus in its fruitful in- 

 fluence upon the development of the lines of mathe- 

 matical research. 



This stimulus came in the closing years of the pre- 

 ceding century through the lectures of Gaspard Monge 

 at the cole Nonnale, and has become popularly known 

 22. through his invention of Descriptive Geometry, the first 

 Geometry, modern systematic application of purely graphical methods 

 in the solution of mathematical problems. As Cauchy 

 was the founder of the modern school of analysts, so 

 Monge, together with Carnot, founded the modern school 

 of geometricians ; Dupin, Poncelet, and Chasles being 

 among his most illustrious pupils. The aim of this 

 school was to give to geometrical methods, such as 

 had been practised by the ancients, 1 the same generality 

 and systematic unity which characterised the analytical 

 methods introduced by Descartes. 



Not long after the introduction of the latter, Leibniz 



1 These methods had been parties. Carnot s'attacha a prouver 



largely used in this country by qu'une seule demonstration ap- 



Newton, Robert Simson, and pliquee a un e"tat assez ge'ne'ral 



Stewart. They were systematised de la figure devait suffire pour 



by L. N. M. Carnot. Chasles i tous les autres cas ; et il montre 



(" Discours d'iuauguration, &c.," , comment, par des changemenfcs 



1846, ' Geometric Superieure,' p. de signes de tennes, dans les 



Ixxvii) says : " Dans le siecle formules de'montrees par une 



dernier, R. Simson et Stewart ] figure, ces forinules s'appliquaient 



donnaient, a 1'instar des Anciens, a une autre figure ne different de 



autant de demonstrations d'une la premiere, commes nous 1'avons 



proposition, que la figure a laquelle dit, que par les positions relatives 



elle se rapportait presentait de j de certaines parties. C'est ce qu'il 



formes diSerentes, a raison des : appela le ' Principe de correlation 



positions relatives de ses diverses des figures.' " 



