5. Suppose there are two conclusions necessarily implicated with each other, and that it is your business to prove one of them: you may put as a question the other of the two. Thus, if you are seeking to prove that the diagonal is incommensurable with the side, you may put as a question, Is not the side incommensurable with the diagonal?[447]
[447] Topic. VIII. xiii. p. 163, a. 10.
There are also five distinct modes of Petitio Contrariorum:—
1. You may ask the respondent, in plain terms, to grant first the affirmative, next, the negative, of a given proposition.[448]
[448] Ibid. a. 14: πρῶτον μὲν γὰρ εἴ τις τὰς ἀντικειμένας αἰτήσαιτο φάσιν καὶ ἀντίφασιν.
2. You may ask him to grant, first, that a given subject is, e.g., good, next, that the same subject is bad.[449]
[449] Ibid. a. 16: δεύτερον δὲ τἀναντία κατὰ τὴν ἀντίθεσιν, οἷον ἀγαθὸν καὶ κακὸν ταὐτόν.
3. After he has granted to you the affirmative universally, you may ask him to grant the negative in some particular case under the universal: e.g., after he has granted that the knowledge of Contraries is one and the same, you ask him to grant that the knowledge of wholesome and unwholesome is not one and the same. Or you may proceed by the way of reversing this process.[450]
[450] Ibid. a. 17-21.
4. You may ask the contrary of that which follows necessarily from the premisses admitted.[451]