urfaces, 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.

155. Farther, he cannot comprehend the manner wherein geometers describe
a right line or circle; the rule and compass with their use being things
of which it is impossible he should have any notion: nor is it an easier
matter for him to conceive the placing of one plane or angle on another,
in order to prove their equality: since that supposeth some idea of
distance or external space. All which makes it evident our pure
intelligence could never attain to know so much as the first elements of
plane geometry. And perhaps upon a nice inquiry it will be found he
cannot even have an idea of plane figures any more than he can of solids;
since some idea of distance is necessary to form the idea of a
geometrical plane, as will appear to whoever shall reflect a little on
it.

156. All that is properly perceived by the visive faculty amounts to no
more than colours, with their variations and different proportions of
light and shade. But the perpetual mutability and fleetingness of those
immediate objects of sight render them incapable of being managed after
the manner of geometrical figures; nor is it in any degree useful that
they should. It is true there are divers of them perceived at once, and
more of some and less of others: but accurately to compute their
magnitude and assign precise determinate proportions between things so
variable and inconstant, if we suppose it possible to be done, must yet
be a very trifling and insignificant labour.

157. I must confess men are tempted to think that flat or plane figures
are immediate objects of sight, though they acknowledge solids are not.
And this opinion is grounded on what is observed in painting, wherein (it
seems) the ideas immediately imprinted on the mind are only of planes
variously coloured, which by a sudden act of the judgment are changed
into solids. But with a little attention we shall find the planes here
mentioned as the immediate objects of sight are not visible but tangible
planes. For when we say that pictures are planes, we mean thereby that
they appear to the touch smooth and uniform. But then this smoothness and
uniformity, or, in other words, this planeness of the picture, is not
perceived immediately by vision: for it appeareth to the eye various and
multiform.

158. From all which we may conclude