b. Rejection of the Opinion

143. On the contrary:

That is per se the subject of any accident of which the accident is predicated per se in the second mode [n.73 footnote]; but of some accident is some accident predicated per se in the second mode, as the proper attribute of it;     therefore etc     .

Proof of the major: that of which an accident is predicated per se in the second mode falls in the definition of that accident as something added to it, and only added as subject, because the defined thing has on such a defining subject no other dependence.

The minor is plain because universally all the properties demonstrated in the whole of mathematical science are demonstrated of accidents, and are said of them per se in the second mode. The point is plain by beginning from the first conclusion to the last of arithmetic or geometry, to such an extent that, if there were no incorporeal substance in the universe, any knowable property would be as equally known of that of which it is known; for a triangle no less has three angles [sc. equal to two right angles] even if triangularity were not in any substance; and three lines would no less be able to be the sides of an equilateral triangle even if no substance were the subject for them.

144. Again, Avicenna Metaphysics 2.1 manifestly maintains that some accident is the subject of another accident, and he gives an example, as motion for instance is the subject of fast speed and slow speed.

145. And third the fact appears in the issue at hand, in the argument given for the opposite [n.114], because it is manifest here that there are many relations by which things are related, as equality, likeness, passive circumscription [sc. being circumscribed by place]; but these relations would not be able to be posited, nor able to be so in a subject, since absolutes cannot be related by these relations were these relations not formally in them.