and have an existence distinct and separate
from them: so that the question is not now concerning the same numerical
ideas, but whether there be any one and the same sort of species of ideas
equally perceivable to both senses; or, in other words, whether
extension, figure, and motion perceived by sight are not specifically
distinct from extension, figure, and motion perceived by touch.

122. But before I come more particularly to discuss this matter, I find
it proper to consider extension in abstract: for of this there is much
talk, and I am apt to think that when men speak of extension as being an
idea common to two senses, it is with a secret supposition that we can
single out extension from all other tangible and visible qualities, and
form thereof an abstract idea, which idea they will have common both to
sight and touch. We are therefore to understand by extension in abstract
an idea of extension, for instance, a line or surface entirely stripped
of all other sensible qualities and circumstances that might determine it
to any particular existence; it is neither black nor white, nor red, nor
hath it any colour at all, or any tangible quality whatsoever and
consequently it is of no finite determinate magnitude: for that which
bounds or distinguishes one extension from another is some quality or
circumstance wherein they disagree.

123. Now I do not find that I can perceive, imagine, or any wise frame in
my mind such an abstract idea as is here spoken of. A line or surface
which is neither black, nor white, nor blue, nor yellow, etc., nor long,
nor short, nor rough, nor smooth, nor square, nor round, etc., is
perfectly incomprehensible. This I am sure of as to myself: how far the
faculties of other men may reach they best can tell.

124. It is commonly said that the object of geometry is abstract
extension: but geometry contemplates figures: now, figure is the
termination of magnitude: but we have shown that extension in abstract
hath no finite determinate magnitude. Whence it clearly follows that it
can have no figure, and consequently is not the object of geometry. It is
indeed a tenet as well of the modern as of the ancient philosophers that
all general truths are concerning universal abstract ideas; without
which, we are told, there could be no science, no demonstration of any
general proposition in geometry. But it were no hard matter, did I think
it necessary to my present purpose, to show that propositions and