125. After reiterated efforts and pangs of thought(416) to apprehend the general idea of a triangle(417), I have found it altogether incomprehensible. And surely, if any one were able to let that idea into my mind, it must be the author(418) 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(419) describes the general or [which is the same thing, the(420)] abstract idea of a triangle. “It must be,” says he, “neither oblique nor rectangle, 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 Human Understanding_, B. iv. ch. 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. [Sure I am, if this be the case, it is impossible for me to attain to know even the first elements of geometry: since I have not the faculty to frame in my mind such an idea as is here described(421).] 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. ch. 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 [of such a clear understanding(422)], who thought so much and so well, and 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 [of abstract figures and extension (423)] 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 vast and comprehensive to be insisted on in this place(424). [I shall only observe that your metaphysicians and men of speculation seem to have faculties distinct from those of ordinary men, when they talk of general or abstracted triangles and circles, &c., and so peremptorily declare them to be the subject of all the eternal, immutable, universal truths in geometry(425).] And so much for extension in abstract. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐