animal or without feet, but that he is pedestrian is not necessary, but they assume it, and this again is what they ought to have proved. After this manner it always happens to those who divide, namely, that they assume an universal middle, and what they ought to show, and the differences as extremes. In the last place, they assert nothing clearly, as that it is necessary that this be a man, or that the question necessarily is whatever it may be, but they pursue every other way, not apprehending the available supplies. It is clear however, that by this method we can neither subvert nor syllogistically infer any thing of accident or property or genus, or of those things of which we are a priori ignorant as to how they subsist, as whether the diameter of a square be incommensurable, for if it assumes every length to be either commensurable or incommensurable, but the diameter of a square is a length, it will infer that the diameter is either incommensurable or commensurable, and if it assumes that it is incommensurate, it will assume what it ought to prove, wherefore that we cannot show, for this is the way, and by this we cannot do it; let however the incommensurable or commensurable be A, length B, and diameter C. It is clear then that this mode of inquiry does not suit every speculation, neither is useful in those to which it especially appears appropriate, wherefore from what sources, and how demonstrations arise, and what we must regard in every problem, appear from what has been said.
Chapter 32
How then we may reduce syllogisms to the above-named figures must next be told, for this is the remainder of the speculation, since if we have noticed the production of syllogisms, and have the power of inventing them, it moreover we analyze them when formed into the before-named figures,
