that hath no use of speech at all, such as is born and remains perfectly deaf and dumb, if he set before his eyes a triangle, and by it two right angles, (such as are the corners of a square figure) he may by meditation compare and find that the three angles of that triangle are equal to those two right angles that stand by it. But if another triangle be shewn him different in shape from the former, he cannot know without a new labour, whether the three angles of that also be equal to the same. But he that hath the use of words, when he observes that such equality was consequent not to the length of the sides, nor to any other particular thing in his triangle, but only to this, that the sides were straight and the angles three, and that that was all for which he named it a triangle, will boldly conclude universally, that such equality of angles is in all triangles whatsoever; and register his invention in these general terms: _Every triangle hath its three angles equal to two right ones_. And thus the consequence found in one particular, comes to be registered and remembered as an universal rule; and discharges our mental reckoning of time and place, and delivers us from all labour of the mind saving the first, and makes that which was found true _here_ and _now_ to be true _in all times_ and _places_.’—_Leviathan_, p. 14. Bishop Berkeley gives the same view of the nature of abstract reasoning in the introduction to his ‘Principles of Human Knowledge.’ ‘But here,’ he says, ‘it will be demanded how we can know any proposition to be true of all particular triangles, except we have first seen it demonstrated of the abstract idea of a triangle, which agrees equally to all. To which I answer, that though the idea I have in view, whilst I make the demonstration be, for instance, that of an isosceles rectangular triangle, whose sides are of a determinate length, I may nevertheless be certain it extends to all other rectilinear triangles of what sort or bigness soever. And that because neither the right angle nor the equality nor the determinate length of the sides are at all concerned in the demonstration. ’Tis true, the diagram I have in view includes all these particulars, but then there’s not the least mention made of them in the proof of the proposition. It is not said the three angles are equal to two right ones, because one of them is a right angle, or because the sides comprehending it are of the same length; which sufficiently shows that the right angle might have been oblique and the sides unequal, and for all that the demonstration have held good. And for this reason it is that I conclude that to be true of any oblique angular or scalenon, which I had demonstrated of a particular right angled equicrural triangle, and not because I demonstrated the proposition of the abstract idea of a triangle.’—Page 34.