Aristotle - The Organon ANALYTICA POSTERIORA Book 1 Part 29

One can have several demonstrations of the same connexion

1. One can have several demonstrations of the same connexion not only by taking from the same series of predication middles which are other than the immediately cohering term e.g. by taking C, D, and F severally to prove A-B - but also by taking a middle from another series. Thus let A be change, D alteration of a property, B feeling pleasure, and G relaxation. We can then without falsehood predicate D of B and A of D, for he who is pleased suffers alteration of a property, and that which alters a property changes. Again, we can predicate A of G without falsehood, and G of B; for to feel pleasure is to relax, and to relax is to change. So the conclusion can be drawn through middles which are different, i.e. not in the same series - yet not so that neither of these middles is predicable of the other, for they must both be attributable to some one subject.

2. A further point worth investigating is how many ways of proving the same conclusion can be obtained by varying the figure.

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