§ 8. "If then B and C are convertible, and the mean (B) does not extend further than extreme (C), it necessarily follows that every B is A.
§ 9. "For it was shown before, that, if any two things be true of the same, and if either of them be convertible with the extreme, the other of the things predicated is true of the convertible (extreme).
§ 10. "But we must conceive that C consists of a collection of all the particular cases; for Induction is applied to all the cases.
§ 11. "But such a syllogism is an inference of a first truth and immediate proposition.
§ 12. "For when there is a mean term, there is a demonstrative syllogism through the mean; but when there is not a mean, there is proof by Induction.
§ 13. "And in a certain way, Induction is contrary to Syllogism; for Syllogism proves, by the middle term, that the extreme is true of the third thing: but Induction proves, by means of the third thing, that the extreme is true of the mean.
§ 14. "And Syllogism concluding by means of a middle term is prior by nature and more usual to us; but the proof by Induction, is more luminous."
I think that the chapter, thus interpreted, is quite coherent and intelligible; although at first there seems to be some confusion, from the author sometimes saying that Induction is a kind of Syllogism, and at other times that it is not. The amount of the doctrine is this.
When we collect a general proposition by Induction from particular cases, as for instance, that all animals destitute of gall-bladder (acholous), are long-lived, (if this proposition were true, of which hereafter,) we may express the process in the form of a Syllogism, if we will agree to make a collection of particular cases our middle term, and assume that the proposition in which the second extreme term occurs is convertible. Thus the known propositions are
Elephant, horse, mule, &c., are long-lived.
Elephant, horse, mule, &c., are acholous.