Elements of the philosophy of the human mind. By Dugald Stewart. Rev. and abridged, with critical and explanatory notes, for the use of colleges and schools. By Francis Bowen ...

258 MeMORY.
(4.) In the last place, the knowledge of the philosopher is
more extensive than that of other men, in consequence of the
attention which he gives, not merely to objects and events, but
to the relations which different objects and different events bear
to each other.
The observations and the experience of the vulgar are almost
wholly limited to things perceived by the senses. A similarity
between different objects, or between dif-erent events, rouses
their curiosity, and leads them to classification and to general
rules. But a similarity between different relations is seldom to
be traced without previous habits of philosophical inquiry.
Many such similarities or connections, however, are to be found
in nature; and when once they are ascertained, they frequently
lead to important discoveries; not only with respect to other
relations, but with respect to the objects or to the events which
are related. These remarks it will be necessary to illustrate
more particularly.
Aid derived fronz a study of the relactions of things. - The
great object of geometry is to ascertain the relations which
exist between different quantities, and the connections which
exist between different relations. When we demonstrate, that
the angle at the centre of a circle is double of the angle at the
circumference on the same base, we ascertain a relation between
two quantities. When we demonstrate, that triangles of the
same altitude are to each other as their bases, we ascertain a
connection between two relations. It is obvious, how much the
mathematical sciences must contribute to enlarge our knowledge
of the universe, in consequence of such discoveries. In that
simplest of all processes of practical geometry, which teaches
us to measure the height of an accessible tower, by comparing
the length of its shadow with that of a staff fixed vertically in
the ground, we proceed on the principle, that the relation
between the shadow of the staff and the heiht of the staff is
the same with the relation between the shadow of the tower
and the height of the tower. But the former relation we can
ascertain by actual measurement; and, of consequence, we not
only obtain the other relation, but, as we can measure one of