confuted _quâ_ geometer, and must correct or modify his answer. But he is not bound, _quâ_ geometer, to undergo scrutiny as to the geometrical _principia_ themselves; this would carry the dialogue out of the province of Geometry into that of First Philosophy and Dialectic. Care, indeed, must be taken to keep both questions and answers within the limits of the science. Now there can be no security for this restriction, except in the scientific competence of the auditors. Refrain, accordingly, from all geometrical discussions among men ignorant of geometry and confine yourself to geometrical auditors, who alone can distinguish what questions and answers are really appropriate. And what is here said about geometry, is equally true about the other special sciences.[37] Answers may be improper either as foreign to the science under debate, or as appertaining to the science, yet false as to the matter, or as equivocal in middle term; though this last is less likely to occur in Geometry, since the demonstrations are accompanied by diagrams, which help to render conspicuous any such ambiguity.[38] To an inductive proposition, bringing forward a single case as contributory to an ultimate generalization, no general objection should be offered; the objection should be reserved until the generalization itself is tendered.[39] Sometimes the mistake is made of drawing an affirmative conclusion from premisses in the Second figure; this is formally wrong, but the conclusion may in some cases be true, if the major premiss happens to be a reciprocating proposition, having its predicate co-extensive with its subject. This, however, cannot be presumed; nor can a conclusion be made to yield up its principles by necessary reciprocation; for we have already observed that, though the truth of the premisses certifies the truth of the conclusion, we cannot say _vice versâ_ that the truth of the conclusion certifies the truth of the premisses. Yet propositions are more frequently found to reciprocate in scientific discussion than in Dialectic; because, in the former, we take no account of accidental properties, but only of definitions and what follows from them.[40] [Footnote 34: Ibid. a. 10, seq.] [Footnote 35: Ibid. a. 26-30: [Greek: kai\ ei)/ tis katho/lou peirô=|to deiknu/nai ta\ koina/, oi(=on o(/ti a(/pan pha/nai ê)\ a)popha/nai, ê)\ o(/ti i)/sa a)po\ i)/sôn, ê)\ tô=n toiou/tôn a)/tta.] Compare Metaph. K. p. 1061**, b. 18.] [Footnote 36: Aristot. Analyt. Post. I. xii, p. 77, a. 36-40; Themistius, p. 40. The text is here very obscure. He proceeds to distinguish Geometry especially (also other sciences, though less emphatically) from [Greek: ta\ e)n toi=s dialo/gois] (I. xii. p. 78, a. 12).