Latin Works of Giordano Bruno

ON THE PROGRESS OF THE LOGICAL HUNT.

...[negative] original: "tivam," likely completing "negativam" from the previous page conclusion you intend, seek a middle term B, of which the subject is universally predicated, and which is universally denied by the predicate; thus you will have what you need to conclude according to the first figure; or seek a middle term B that is universally affirmed of A and universally denied of C, or universally denied
5 of A and universally affirmed of C; then you shall argue according to the second and first modes of the second figure. If you intend to conclude a particular affirmative A statement asserting something is true for some members of a group, e.g., "Some philosophers are Italians.", you can do so in the first figure, either with a middle term B that is entirely contained
10 by A and entirely contains C (because where we conclude a universal, we can also conclude its particular); or with a middle term B that is entirely contained by A and partially contains C. You can also do this in the third figure, either with a middle term that is entirely contained by both extremes, or
15 partially by one and entirely by the other—which occurs (as is evident there) in two ways. If you wish to infer a particular negative A statement like "Some animals are not mammals.", you can do so first by the same modes through which a universal negative is concluded, as is sufficiently clear
Folio 6 recto, P edition from what was just said; secondly, in the first figure, with a middle term
20 that is entirely excluded from A and partially affirmed of C; or with a middle term that is entirely contained by the subject A (or of which A is universally predicated) and contains nothing of C—that is, it is universally denied of the predicate of the problem—and thus the conclusion is reached indirectly; thirdly, in the second figure, if the middle term B
25 is universally denied of extreme A and partially affirmed of C, or universally affirmed of A and partially denied of C; fourthly, in the third figure, where A is universally denied of the middle term B and C is universally affirmed; or where A
Page 711, G edition is partially denied of it and C is universally affirmed; or where A is
30 universally denied of it and C is partially affirmed.