cut should die, and through the wound, because he will die in consequence of his throat being cut, but it did not accidentally happen that he whose throat was cut died. Those therefore which are predicated in things which are simply objects of science per se, so as to be inherent in the things predicated, or which are themselves inherent in subjects, are on account of themselves, and from necessity, for it does not happen that they are not inherent either simply or as opposites, as the straight and the curved in a line, and the even or odd in number. For a contrary is either privation or contradiction in the same genus, as that is even which is not odd in numbers, so far as it follows: hence if it is requisite to affirm or deny, it is also necessary that those which are per se should be inherent.
Let then the expressions "of every" and "per se" be thus defined: I call that universal, however, which is both predicated "of every" and "per se," and so far as the thing is. Now it is evident that whatever are universal are inherent in things necessarily, but the expressions "per se," "and so far as it is," are the same; as a point and straightness are per se present in a line, for they are in it, in as far as it is a line, and two right angles in a triangle, so far as it is a triangle, for a triangle is per se equal to two right angles. But universal is then present, when it is demonstrated of any casual and primary thing, as to possess two right angles is not universally inherent in figure, yet it is possible to demonstrate of a figure that it has two right angles, but not of any casual figure, nor does a demonstrator use any casual figure, for a square is indeed a figure, yet it has not angles equal to two right. But
