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 that 
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 the 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 
