Kitap 9
4
Geometrical constructions, too, are discovered by an actualization, because it is by dividing that we discover them. If the division were already done, they would be obvious; but as it is the division is only there potentially. Why is the sum of the interior angles of a triangle equal to two right angles? Because the angles about one point 〈in a straight line〉 are equal to two right angles. If the line parallel to the side had been already drawn, the answer would have been obvious at sight.The figure, construction and proof are as follows: ***
5
Why is the angle in a semicircle always a right angle? If three lines are equal, the two forming the base, and the one set upright from the middle of the base, the answer is obvious to one who knows the former proposition.Aristotle implies a proof something after this fashion: FIGURE BAC is an angle in a semicircle. From D, the mid-point of the diameter BC, draw a perpendicular DE to meet the circumference at E. Join EB, EC.*** Thus it is evident that the potential constructions are discovered by being actualized. The reason for this is that the actualization is an act of thinking. Thus potentiality comes from actuality (and therefore it is by constructive action that we acquire knowledge). 〈But this is true only in the abstract〉, for the individual actuality is posterior in generation to its potentiality.This whole passage (sects. 4, 5) should be compared with Aristot. Met. 9.8.3-7, where it logically belongs.
