middle, but the middle is in no last, there is not a syllogism of the extremes, for nothing necessarily results from the existence of these, since the first happens to be present with every, and with no extreme; so that neither a particular nor universal (conclusion) necessarily results, and nothing necessary resulting, there will not be through these a syllogism. Let the terms of being present universally, be "animal," "man," "horse," and let the terms of being present with no one be "animal," "man," "stone." Since, then, neither the first term is present with the middle, nor the middle with any extreme, there will not thus be a syllogism. Let the terms of being present, be "science," "line," "medicine," but of not being present, "science," "line," "unity;" the terms then being universal, it is manifest in this figure, when there will and when there will not be a syllogism, also that when there is a syllogism, it is necessary that the terms should subsist, as we have said, and that if they do thus subsist there will evidently be a syllogism.
But if one of the terms be universal and the other particular, in relation to the other, when the universal is joined to the major extreme, whether affirmative or negative, but the particular to the minor affirmative, there must necessarily be a perfect syllogism, but when the (universal) is joined to the minor, or the terms are arranged in some other way, a (syllogism) is impossible. I call the major extreme that in which the middle is, and the minor that which is under the middle. For let A be present with every B, but B with some C, if then to be predicated "of every" is what has been asserted from the first, A must necessarily be present with some C, and if A is present with no B, but B with some C, A must necessarily not be present with some C, for what we mean by the being predicated of no one has been defined, so that there will be a perfect syllogism. In like manner, if B, C, being affirmative, be indefinite, for there will be the same syllogism, both of the indefinite, and of that which is assumed as a particular.
If indeed to the minor extreme an universal affirmative or negative be added, there will not be a syllogism, whether the indefinite, or particular, affirms or denies, e. g. if A is or is not present
