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 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.