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
some parts of several different and inconsistent ideas are put together'
ESSAY ON HUM. UNDERSTAND. B. iv. C. 7. S.9. This is the idea which he
thinks needful for the enlargement of knowledge, which is the subject of
mathematical demonstration, and without which we could never come to know
any general proposition concerning triangles. That author acknowledges it
doth 'require some pains and skill to form this general idea of a
triangle.' IBID. But had he called to mind what he says in another place,
to wit, 'That ideas of mixed modes wherein any inconsistent ideas are put
together cannot so much as exist in the mind, i.e. be conceived.' VID. B.
iii. C. 10. S. 33. IBID. I say, had this occurred to his thoughts, it is
not improbable he would have owned it above all the pains and skill he
was master of to form the above-mentioned idea of a triangle, which is
made up of manifest, staring contradictions. That a man who laid so great
a stress on clear and determinate ideas should nevertheless talk at this
rate seems very surprising. But the wonder will lessen if it be
considered that the source whence this opinion flows is the prolific womb
which has brought forth innumerable errors and difficulties in all parts
of philosophy and in all the sciences: but this matter, taken in its full
extent, were a subject too comprehensive to be insisted on in this place.
And so much for extension in abstract.

126. Some, perhaps, may think pure space, VACUUM, or trine dimension to
be equally the object of sight and touch: but though we have a very great
propension to think the ideas of outness and space to be the immediate
object