' 
Legendre’s Geometry. 295 
tering into long discussions. and giving numerous details, 
which must be imperfectly understood. without diagrams 
and without a minute comparison*ef the arrangement adopt- 
ed by the writers of whom we are speaking. This is a 
particular upon which a sound opinion cannot be formed 
without personal inspection. We think that the conclusion 
at which we have arrived, and which we have stated at the 
beginning of this paragraph will be inevitable in the mind 
of every one who will be at the pains of a comparison some- 
what extensive and elaborate. All that we ask of our read- 
ers on the point now under consideration, is, that they will - 
not conclude us to be entirely and. necessarily wrong, until 
they have given the subject an attentive examination. 
“In his judices desidero, qui tractarunt in sua amplitudine.* 
We trust that this will not be considered an unreasonable 
claim upon their candor 
On the geometry of solids or volumes, also, the elements 
than those of Euclid. On this point, it is impossible: to 
convey an adequate idea to those who are not, to a consid- 
erable extent, acquainted with the subject. At the time of 
Euclid, the geometry of solids appears to have been quite 
imperfectly investigated. It is true, that before this period, 
the five regular bodies had been studied 1 in the celebrated 
school of Plato; and A iscov- 
eries in relation to the properties of the sphere and cylinder. 
But the properties of Polyedrons in general, and their meas- 
ure, have not received, until within a short period, the at- 
tention” which their importance merited ; and | egendre 
in particular, has contributed heh to die elacidatian of the 
subject. M. Cauch , also, has done gaat towards 
etry. 
e are now sufficiently prepared to ate: with advan- 
definitions and axioms are laid down very much in the usual 
style. .The latter are nearly the same in substance with 
those of Euclid, and differ from them principally in the cir- 
cumstance, that the idea of equality is not drawn out into 
a They are but five in number. It is evident 
e does not attempt a complete enumeration of them, a 
thing which no geometer has accomplished. A. straight 
line is defined to be, “the shortest way from one point to 
* Valckenaer ad Herodotum, p. 585. 
