analysis by attempting to imagine the world first dawning upon the eye of
the infant or of a person newly restored to sight. Yet even with them the
mind as well as the eye opens or enlarges. For all three are inseparably
bound together--the object would be nowhere and nothing, if not perceived
by the sense, and the sense would have no power of distinguishing without
the mind.

But prior to objects of sense there is a third nature in which they are
contained--that is to say, space, which may be explained in various ways.
It is the element which surrounds them; it is the vacuum or void which they
leave or occupy when passing from one portion of space to another. It
might be described in the language of ancient philosophy, as 'the Not-
being' of objects. It is a negative idea which in the course of ages has
become positive. It is originally derived from the contemplation of the
world without us--the boundless earth or sea, the vacant heaven, and is
therefore acquired chiefly through the sense of sight: to the blind the
conception of space is feeble and inadequate, derived for the most part
from touch or from the descriptions of others. At first it appears to be
continuous; afterwards we perceive it to be capable of division by lines or
points, real or imaginary. By the help of mathematics we form another idea
of space, which is altogether independent of experience. Geometry teaches
us that the innumerable lines and figures by which space is or may be
intersected are absolutely true in all their combinations and consequences.
New and unchangeable properties of space are thus developed, which are
proved to us in a thousand ways by mathematical reasoning as well as by
common experience. Through quantity and measure we are conducted to our
simplest and purest notion of matter, which is to the cube or solid what
space is to the square or surface. And all our applications of mathematics
are applications of our ideas of space to matter. No wonder then that they
seem to have a necessary existence to us. Being the simplest of our ideas,