M. Barthélemy St. Hilaire (in the note to his translation, p. 14) does not lend any additional clearness, when he talks of the "_conclusion_" from the propositions A and E in the First figure. Julius Pacius says (p. 134): "Si tamen _conclusio_ dici debet, quæ non colligitur ex propositionibus," &c. Moreover, M. St. Hilaire (p. 19) slurs over the legitimate foundation, the appeal to experience, much as Aristotle himself does: "Puis prenant des exemples où la _conclusion est de toute évidence_, Aristote les applique successivement à chacune de ces combinaisons; celles qui donnent la _conclusion fournie d'ailleurs par le bon sens_, sont concluantes ou syllogistiques, les autres sont asyllogistiques."] We are now introduced to the Second figure, in which each of the two premisses has the middle term as Predicate.[29] To give a legitimate conclusion in this figure, one or other of the premisses must be negative, and the major premiss must be universal; moreover no affirmative conclusions can ever be obtained in it--none but negative conclusions, universal or particular. In this Second figure too, Aristotle recognizes four valid modes; setting aside the other possible modes as invalid[30] (in the same way as he had done in the First figure), because the third proposition or conjunction of the major term with the minor, might in some cases be a true universal affirmative, in other cases a true universal negative. As to the third and fourth of the valid modes, he demonstrates them by assuming the contradictory of the conclusion, together with the major premiss, and then showing that these two premisses form a new syllogism, which leads to a conclusion contradicting the minor premiss. This method, called _Reductio ad Impossibile_, is here employed for the first time; and employed without being ushered in or defined, as if it were familiarly known.[31] [Footnote 29: Analyt. Prior. I. v. p. 26, b. 34. As Aristotle enunciates a proposition by putting the predicate before the subject, he says that in this Second figure the middle term comes [Greek: prô=ton tê=| the/sei]. In the Third figure, for the same reason, he calls it [Greek: e)/schaton tê=| the/sei], vi. p. 28, a. 15.] [Footnote 30: Analyt. Prior. I. v. p. 27, a. 18. In these invalid modes, Aristotle says there is no _syllogism_; therefore we cannot properly speak of a _conclusion_, but only of a third proposition, conjoining the major with the minor.] [Footnote 31: Ibid. p. 27, a. 15, 26, seq. It is said to involve [Greek: u(po/thesis], p. 28, a. 7; to be [Greek: e)x u(pothe/seôs] xxiii. p. 41, a. 25; to be [Greek: tou= e)x u(pothe/seôs], as opposed to [Greek: deiktiko/s], xxiii. p. 40, b. 25. M. B. St. Hilaire remarks justly, that Aristotle might be expected to define or explain what it is, on first mentioning it (note, p. 22).]