In the survey prescribed, nothing is gained by looking out for predicates (of A and E) which are different or opposite: we must collect such as are identical, since our purpose is to obtain from them a suitable middle term, which must be the same in both premisses. It is true that if the list B (containing the predicates universally belonging to A) and the list F (containing the predicates universally belonging to E) are incompatible or contrary to each other, you will arrive at a syllogism proving that no A can belong to E. But this syllogism will proceed, not so much from the fact that B and F are incompatible, as from the other fact, distinct though correlative, that B will to a certain extent coincide with H (the list of predicates which cannot belong to E). The middle term and the syllogism constituted thereby, is derived from the coincidence between B and H, not from the opposition between B and F. Those who derive it from the latter, overlook or disregard the real source, and adopt a point of view merely incidental and irrelevant.[58] [Footnote 58: Ibid. p. 44, b. 38-p. 45, a. 22. [Greek: sumbai/nei dê\ toi=s ou(/tôs e)piskopou=si prosepible/pein a)/llên o(do\n tê=s a)nagkai/as, dia\ to\ lantha/nein tê\n tau)to/têta tô=n B kai\ tô=n Th.]] The precept here delivered--That in order to obtain middle terms and good syllogisms, you must study and collect both the predicates and the subjects of the two terms of your thesis--Aristotle declares to be equally applicable to all demonstration, whether direct or by way of _Reductio ad Impossibile_. In both the process of demonstration is the same--involving two premisses, three terms, and one of the three a suitable middle term. The only difference is, that in the direct demonstration, both premisses are propounded as true, while in the _Reductio ad Impossibile_, one of the premisses is assumed as true though known to be false, and the conclusion also.[59] In the other cases of hypothetical syllogism your attention must be directed, not to the original _quæsitum_, but to the condition annexed thereto; yet the search for predicates, subjects, and a middle term, must be conducted in the same manner.[60] Sometimes, by the help of a condition extraneous to the premisses, you may demonstrate an universal from a particular: _e.g._, Suppose C (the list of subjects to which A belongs as predicate) and G (the list of subjects to which E belongs as predicate) to be identical; and suppose farther that the subjects in G are the _only_ ones to which E belongs as predicate (this seems to be the _extraneous_ or _extra-syllogistic_ condition assumed, on which Aristotle's argument turns); then, A will be applicable to all E. Or if D (the list of predicates which cannot belong to A) and G (the list of subjects to which E belongs as predicate) are identical; then, assuming the like extraneous condition, A will not be applicable to any E.[61] In both these