if both there will be the same conclusion, when we need another. In those terms then which are not converted, a syllogism is produced from one undemonstrated proposition, for we cannot demonstrate by this term, that the third is with the middle, or the middle with the first, but in those which are converted we may demonstrate all by each other, as if A B and C reciprocate; for A C can be demonstrated by the middle, B; again, A B (the major) through the conclusion, and through the proposition B C, (the minor) being converted; likewise also B C the minor through the conclusion, and the proposition A B converted. We must however demonstrate the proposition C B, and B A, for we use these alone undemonstrated, if then B is taken as present with every C, and C with every A, there will be a syllogism of B in respect to A. Again, if C is assumed present with every A, and A with every B, it is necessary that C should be present with every B, in both syllogisms indeed, the proposition C A is taken undemonstrated, for the others were demonstrated. Wherefore if we should show this, they will all have been shown by each other. If then C is assumed present with every B, and B with every A, both propositions are taken demonstrated, and C is necessarily present with A, hence it is clear that in convertible propositions alone, demonstrations may be formed in a circle, and through each other, but in others as we have said before, it occurs also in these that
