658 



SCIENTIFIC THOUGHT. 



22. 

 Descriptive 



Geometry. 



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 I^cole Normale, and has become popularly known 

 through his invention of Descriptive Geometry, the first 

 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,^ the same generality 

 and systematic unity which characterised the analytical 

 methods introduced by Descartes. 



Not long after the introduction of the latter, Leibniz 



^ These methods had been 

 largely used in this country by 

 Newton, Robert Simson, and 

 Stewart. They were systematised 

 by L. N. M. Cai-not. Chasles 

 (" Discours d'inauguration, &c.," 

 1846, 'G(?om^trie Superieure,' p. 

 Ixxvii) says : " Dans le siecle 

 dernier, R. Simson et Stewart 

 donnaient, li I'instar des Anciens, 

 autant de demonstrations d'une 

 proposition, que la figure h. laquelle 

 elle se rapportait presentait de 

 formes differentes, h, raison des 

 positions relatives de ses diverses 



parties. Carnot s'attacha a prouver 

 qu'une seule demonstration ap- 

 pliquee h. un ^tat as.sez general 

 de la figure devait suftire pour 

 tous les autres cas ; et il montre 

 comment, par des changements 

 de signes de ternies, dans les 

 formules d^montrees par une 

 figure, ces foruiules s'appliquaient 

 il une autre figure ne ditteraut de 

 la premiere, commes nous I'avons 

 dit, que par les positions relatives 

 de certaines parties. C'est ce qu'il 

 a()pela le ' Principe de correlation 

 des figures.' " 



