The proposition _No X is Y_ (E.) cannot be said in any sense to equate X and Y; though, if we obvert it into _All X is some not-Y_, we have (in the same sense, of course, as in the above affirmative forms) X equated with part at least of 'not-Y.' But what is that sense?
Clearly not the same as that in which mathematical terms are equated, namely, in respect of some mode of quantity.

For if we may say _Some X is some Y_, these Xs that are also Ys are not merely the same in number, or mass, or figure; they are the same in every respect, both quantitative and qualitative, have the same positions in time and place, are in fact identical.

The proposition 2+2=4 means that any two things added to any other two are, _in respect of number_, equal to any three things added to one other thing; and this is true of all things that can be counted, however much they may differ in other ways.

But _All X is all Y_ means that Xs and Ys are the same things, although they have different names when viewed in different aspects or relations.

Thus all equilateral triangles are equiangular triangles; but in one case they are named from the equality of their angles, and in the other from the equality of their sides.