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 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