also possible, that passing to other things which are naturally adapted to be demonstrated by that (which was to be investigated), to demonstrate by these the original proposition; as if a person should demonstrate A through B, and B through C, while C was naturally adapted to be proved through A, for it happens that those who thus syllogize, prove A by itself. This they do, who fancy that they describe parallel lines, for they deceive themselves by assuming such things as they cannot demonstrate unless they are parallel. Hence it occurs to those who thus syllogize to say that each thing is, if it is, and thus every thing will be known through itself, which is impossible.
If then a man, when it is not proved that A is with C, and likewise with B, begs that A may be admitted present with B, it is not yet evident whether he begs the original proposition, but that he does not prove it is clear, for what is similarly doubtful is not the principle of demonstration. If however B so subsists in reference to C as to be the same, or that they are evidently convertible, or that one is present with the other, then he begs the original question. For that A is with B, may be shown through them, if they are converted, but now this prevents it, yet not the mode; if however it should do this, it would produce what has been mentioned before, and a conversion would be made through three terms. In like manner if any one should take B to be present with C, whilst it is equally doubtful if he assumes A also (present with C), he
