strange and unaccountable as prophesy doth to others. Even they who are
blessed with the visive faculty may (though familiarity make it less
observed) find therein sufficient cause of admiration. The wonderful art
and contrivance wherewith it is adjusted to those ends and purposes for
which it was apparently designed, the vast extent, number, and variety of
objects that are at once with so much ease and quickness and pleasure
suggested by it: all these afford subject for much and pleasing
speculation, and may, if anything, give us some glimmering analogous
prenotion of things which are placed beyond the certain discovery and
comprehension of our present state.

149. I do not design to trouble myself with drawing corollaries from the
doctrine I have hitherto laid down. If it bears the test others may, so
far as they shall think convenient, employ their thoughts in extending it
farther, and applying it to whatever purposes it may be subservient to:
only, I cannot forbear making some inquiry concerning the object of
geometry, which the subject we have been upon doth naturally lead one to.
We have shown there is no such idea as that of extension in abstract, and
that there are two kinds of sensible extension and figures which are
entirely distinct and heterogeneous from each other. Now, it is natural
to inquire which of these is the object of geometry.

150. Some things there are which at first sight incline one to think
geometry conversant about visible extension. The constant use of the
eyes, both in the practical and speculative parts of that science, doth
very much induce us thereto. It would, without doubt, seem odd to a
mathematician to go about to convince him the diagrams he saw upon paper
were not the figures, or even the likeness of the figures, which make the
subject of the demonstration. The contrary being held an unquestionable
truth, not only by mathematicians, but also by those who apply themselves