GEOMETRY OF POSITION. 83 



high. I wish I could say, with the same truth, that the 

 views of our member had more or less filtered into tliat 

 multitude of elementary treatises which appears every 

 year, and that they had contributed towards perfecting 

 instruction ; but on this point I can only express my re- 

 gret. In the present day the philosophical part of science 

 is very much neglected ; the means of shining in an ex- 

 amination, or an assembly, hold the first place ; with 

 some rare exceptions, professors think much more of 

 familiarizing their pupils with the mechanism of the cal- 

 culus, than of causing them to penetrate to its principles. 

 In fact, I almost think we might say of certain persons, 

 that they employ analysis in the same manner as most 

 manufacturers do the steam-engine, without reflecting on ' 

 its mode of action. And let it not be supposed that this 

 faulty style of instruction is a necessary sacrifice to the 

 reigning passion of our age, the rage for going fast in 

 every thing, Have not illustrious members of this Acad- 

 emy shown, in justly celebrated works on geometry and 

 statics, that extreme exactness does not exclude concise- 

 ness ? 



Carnot's Geometry of Position would not have the high 

 merit which I have attributed to it, with regard to the 

 metaphysics of science, if it were not also the origin and 

 base of the progress which geometry, cultivated after the 

 manner of the ancients, has made in tlie last thirty years 

 in France and Germany. The numerous properties of 

 space which our member has discovered, show to all eyes 

 the power and fecundity of the new methods with which 

 he has endowed science. Permit me to justify by some 

 quotations the favourable opinion which I have formed of 

 the methods of investigation discovered by Carnot. 



"If at a given point there be imagined three planes 



