to the particular, because evidently the aggregates can not be regarded as more particular than their elements.
Great importance, and justly, has been attached to this procedure of 'construction,' and some have tried to see in it the necessary and sufficient condition for the progress of the exact sciences.
Necessary, without doubt; but sufficient, no.
For a construction to be useful and not a vain toil for the mind, that it may serve as stepping-stone to one wishing to mount, it must first of all possess a sort of unity enabling us to see in it something besides the juxtaposition of its elements.
Or, more exactly, there must be some advantage in considering the construction rather than its elements themselves.
What can this advantage be?
Why reason on a polygon, for instance, which is always decomposable into triangles, and not on the elementary triangles?
It is because there are properties appertaining to polygons of any number of sides and that may be immediately applied to any particular polygon.
Usually, on the contrary, it is only at the cost of the most prolonged exertions that they could be found by studying directly the relations of the elementary triangles. The knowledge of the general theorem spares us these efforts.
A construction, therefore, becomes interesting only when it can be ranged beside other analogous constructions, forming species of the same genus.
If the quadrilateral is something besides the juxtaposition of two triangles, this