Legendre’s Geometry. 285 
ests of science and humanity, had fallen a victim of the 
most sanguinary tyranny, before their eyes. The subse- 
quent organization of a system of public instruction, gave 
the French mathematicians an opportunity of rend 
eminent services to the government. The _— of the 
exact sciences to the views of the French nation, as con- 
stituting the basis of the science of war, salle 32 full ex- 
ercise all the mathematical talents in the kingdom. But 
above all, the establishment of the National Institute con- 
centrated the talents of the nation, and the pensions and 
high honors which were liberally bestowed, especially up- 
on those who successfully cultivated the exact sciences, 
gave an astonishing impulse to mathematical learning. To 
these circumstances we owe the geometry of Legendre, 
the numerous mislemobinry treatin of Lacroix, Laplace’s 
System-of the World, Lagrange’s Theory of Analytical 
pene aie Poisson’s Mechani bar “and an immense number 
other works of the highest inesit, which cannot now 
medidatohed The exact sciences are vastly indebted to the 
rench revolution and its long train of consequences, what- 
ever may be its ultimate effect upon the progress of knowl- 
edge ingeneral. The science of calculation is now invest- 
ed with such resources, that almost nothing is too compli- 
cated, or too stubborn to yield to its power. 
efore proceeding to a particular examination of the 
work before us, we feel called upon to say a few words up- 
on the enquiries,—what ought an elementary treatise of 
geometry to contain, in the present state of the pure and 
applied mathematics ?—and = we should adopt M. Le- 
gendre’s treatises, or that of any other modern writer, in 
preference to “ Euclid’s Danie’ which have been 
real os the most part, asa dextchsiebient in the American 
college 
With respect to the first enquiry, it is plain, that an . ele- 
mentary treatise cannot contain all the truths within the 
compass of elementary geometrical investigation. The 
each other, are innumerable. Some of these properties 
and relations have never been applied “a any practical ob- 
ject, others form links more or less important in a long 
chain of connected truths, others are truths important in 
