153. Though what has been said may suffice to show what ought to be
determined with relation to the object of geometry, I shall nevertheless,
for the fuller illustration thereof, consider the case of an
intelligence, or unbodied spirit, which is supposed to see perfectly
well, i.e. to have a clear perception of the proper and immediate objects
of sight, but to have no sense of touch. Whether there be any such being
in Nature or no is beside my purpose to inquire. It sufficeth that the
supposition contains no contradiction in it. Let us now examine what
proficiency such a one may be able to make in geometry. Which speculation
will lead us more clearly to see whether the ideas of sight can possibly
be the object of that science.

154. FIRST, then, it is certain the aforesaid intelligence could have no
idea of a solid, or quantity of three dimensions, which followeth from
its not having any idea of distance. We indeed are prone to think that we
have by sight the ideas of space and solids, which ariseth from our
imagining that we do, strictly speaking, see distance and some parts of
an object at a greater distance than others; which hath been demonstrated
to be the effect of the experience we have had, what ideas of touch are
connected with such and such ideas attending vision: but the intelligence
here spoken of is supposed to have no experience of touch. He would not,
therefore, judge as we do, nor have any idea of distance, outness, or
profundity, nor consequently of space or body, either immediately or by
suggestion. Whence it is plain he can have no notion of those parts of
geometry which relate to the mensuration of solids and their convex or
concave surfaces, and contemplate the properties of lines generated by
the section of a solid. The conceiving of any part whereof is beyond the
reach of his faculties.