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Aristotle, Prior Analytics. Book I, Chapter 09

1. It also sometimes happens that one of the propositions being necessary, a necessary syllogism will be produced, yet not of either proposition casually, but of that which contains the greater extreme.

2. For instance, if A is assumed to be present or not present with B from necessity; but B is assumed to be alone present with C; for the propositions being thus assumed, A will be present or will not be present from necessity with C. For since A is present or is not present with every B from necessity, but C is something belonging to B, it is evident, that C will be from necessity one of these.

3. If, however, the proposition AB is not necessary, but BC is necessary, there will not be a necessary conclusion. For if there will be, it will happen that A is necessarily present with a certain B, as may be demonstrated as well in the first as in the third figure. But this is false; for it may happen that B may be a thing of that kind that A may not be present with anything belonging to it. Farther still, from the terms also it is evident, that there will not be a necessary conclusion; as, for instance, if A is motion, B animal, and C man. For man is necessarily an animal; but neither animal, nor man, is necessarily moved.

4. The like will also take place if AB is privative; for there is the same demonstration.

5. But in particular syllogisms, if the universal assertion is necessary, the conclusion also will be necessary; but if the particular is necessary the conclusion will not be necessary; whether the universal proposition is primitive, or categoric.

6. In the first place, therefore, let the universal be necessary, and let A be necessarily present with every B, but let B be only present with a certain C. It is necessary, therefore, that A should be necessarily present with a certain C; for C is under B, and A was present from necessity with every B.

7. The like will also take place, if the syllogism is privative; for there will be the same demonstration.

8. But if the particular is necessary; the conclusion will not be necessary; for nothing absurd will happen, as neither in universal syllogisms.

9. A similar consequence also will be the result in particular privative syllogisms. Let the terms be, motion, animal, white.

Every animal is moved:
It is necessary that something white should be an animal:
Therefore, something white is moved.
But not necessarily, because it is possible that it might not be moved.

No animal is moved:
It is necessary that something white should not be an animal:
Therefore, something white is not moved.
But this is not necessary, because it may be moved.

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