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
demonstrations in geometry might be universal, though they who make them
never think of abstract general ideas of triangles or circles.

125. After reiterated endeavours to apprehend the general idea a
triangle, I have found it altogether incomprehensible. And surely if
anyone were able to introduce that idea into my mind, it must be the
author of the ESSAY CONCERNING HUMAN UNDERSTANDING; he who has so far
distinguished himself from the generality of writers by the clearness
and significancy of what he says. Let us therefore see how this
celebrated author describes the general or abstract idea of a triangle.
'It must be (says he) neither oblique nor rectangular, neither
equilateral, equicrural, nor scalenum; but all and none of these at once.
In effect, it is somewhat imperfect that cannot exist; an idea, wherein