Page:O. F. Owen's Organon of Aristotle Vol. 1 (1853).djvu/157

 commendable, if then any one should require it to be granted that pleasure is commendable, and did not add all pleasure, there would not be a syllogism, but if that a certain pleasure is so, if indeed it is a different pleasure, it is nothing to the purpose, but if it is the same it is a petitio principii, this will however be more evident in diagrams, for instance, let it be required to show that the angles at the base of an isosceles triangle are equal. Let the lines A B be drawn to the centre of a circle, if then he assumes the angle A C to be equal to the angle B D, not in short requiring it to be granted that the angles of semicircles are equal, and again that C is equal to D, not assuming the whole (angle) of the section, if besides he assumes that equal parts being taken from equal whole angles, the remaining angles E F are equal, he will beg the original (question), unless he assume that if equals are taken from equals the remainders are equal. Wherefore in all syllogism we must have an universal; universal is also shown from all universal terms, but the particular in this or that way, so that if the conclusion be universal, the terms must of necessity be universal, but if the terms be universal, the conclusion may happen not to be universal. It appears also that in every syllogism either both premises or one of them must be similar to the conclusion, I mean not only in its being affirmative or negative, but in that it is either necessary, or absolute, or contingent; we must also have regard to other modes of predication.

In a word then it is shown when there will and will not be a syllogism, also when it is possible, and when perfect, and that when there is a syllogism it must have its terms according to some one of the above modes.