11. The third indirect or inverted figure, is made by the conversion of both the premises. For example, this direct syllogism, _Every man is a living creature_, _Every living creature is not a stone_, Therefore, _Every man is not a stone_, being inverted, will stand thus, _Every stone is not a living creature_, _Whatsoever is not a living creature, is not a man_, Therefore, _Every stone is not a man_; which conclusion is the converse of the direct conclusion, and equipollent to the same. The figures, therefore, of syllogisms, if they be numbered by the diverse situation of the middle term only, are but three; in the first whereof, the middle term has the middle place; in the second, the last; and in the third, the first place. But if they be numbered according to the situation of the terms simply, they are four; for the first may be distinguished again into two, namely, into direct and inverted. From whence it is evident, that the controversy among logicians concerning the fourth figure, is a mere λογόμαχια, or contention about the name thereof; for, as for the thing itself, it is plain that the situation of the terms (not considering the quantity or quality by which the moods are distinguished) makes four differences of syllogisms, which may be called figures, or have any other name at pleasure. [Sidenote: There are many moods in every figure, but most of them useless in philosophy.] 12. In every one of these figures there are many moods, which are made by varying the premises according to all the differences they are capable of, by quantity and quality; as namely, in the direct figure there are six moods; in the first indirect figure, four; in the second, fourteen; and in the third, eighteen. But because from the direct figure I rejected as superfluous all moods besides that which consists of universal propositions, and whose minor proposition is affirmative, I do, together with it, reject the moods of the rest of the figures which are made by conversion of the premises in the direct figure. [Sidenote: An hypothetical syllogism when equipollent to a categorical.] 13. As it was showed before, that in necessary propositions a categorical and hypothetical proposition are equipollent; so likewise it is manifest that a categorical and hypothetical syllogism are equivalent. For every categorical syllogism, as this, _Every man is a living creature_, _Every living creature is a body_, Therefore, _Every man is a body_, is of equal force with this hypothetical syllogism: _If any thing be a man, the same is also a living creature_, _If any thing be a living creature, the same is a body_, Therefore, _If any thing be a man, the same is a body_. In like manner, this categorical syllogism in an indirect figure,