  For each of the thirty-four premise combinations that allow no conclusion Aristotle proves by counterexample that they allow no conclusion. As his overall result, he acknowledges four first figure syllogisms (later named Barbara, Celarent, Darii, Ferio), four second figure syllogisms (Camestres, Cesare, Festino, Baroco) and six third figure syllogisms (Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison); these were later called the modes or moods of the figures. (The names are mnemonics: e.g. each vowel, or the first three in cases where the name has more than three, indicates in order whether the first and second premises and the conclusion were sentences of type a, e, i or o.) Aristotle implicitly recognized that by using the conversion rules on the conclusions we obtain eight further syllogisms (An. Pr. 53a3–14), and that of the premise combinations rejected as non-syllogistic, some (five, in fact) will yield a conclusion in which the minor term is predicated of the major (An. Pr. 29a19–27). Moreover, in the Topics Aristotle accepted the rules ‘from AaB infer AiB’ and ‘from AeB infer AoB’. By using these on the conclusions five further syllogisms could be proved, though Aristotle did not mention this.