This entry draws largely on Philoponus, Commentary on Aristotle's de anima (28.7-18, 29.23-28, 20.12-13 and 20-26, 31.15-20 Hayduck), with a final sentence from Alexander of Aphrodisias, Commentaries on Aristotle's Topica 2.22-23.
cf. omicron 627.
[1] A demonstration is, in fact, a certain type of syllogism, for a deductive argument (or "syllogism") is a demonstration when the premises from which the deduction starts are true and primary, or are such that our knowledge of them has originally come through premises which are primary and true (see Topica 100a27-29). In more technical contexts Aristotle distinguishes o(/ros from o(rismo/s, the former meaning "term" and the latter "definition". In the present case both words are used indiscriminately, something more or less usual in Aristotle himself. For the Aristotelian definition by proximate genus and specific differentia, see Metaphysics 1037b25-1038a35 and Topica 103b14-19.
[2] As usual, the word ou)si/a is hard to render. In this context it probably means "essence", so the expression to\ kat' ou)si/an should be rendered "the essential". In the Suda example, animal belongs "by itself" (which, in accordance with the previous distinction, is the same as "essentially") to man.
[3] tekmh/rion and shmei=on are Aristotle's technical terms. A tekmh/rion is characterized as being "a necessary or always existing sign" or "a necessary sign" (Rhetoric 1357b4ff.). When people think it is impossible to refute an argument, they think they are offering a tekmh/rion, as though the matter at issue were shown and concluded (Rhetoric 1357b5-10). On the other hand, according to Aristotle, a shmei=on (sign) is meant to be a demonstrative proposition (pro/tasis a)podeiktikh/), either necessary or reputable; for anything such that when it is another thing is, or when it has come into being the other has come into being before or after, is a sign of the other's being or having coming into to being (An.Pr. 70a6-9; Oxford Translation). That is to say, given two propositions (p, q) indicating two events, p is said to be a sign of q if and only if p's verification implies q's verification. The fact that a sign is included within the domain of what "is reputable" or within the domain of "common beliefs" (e)/ndoca) shows that a sign, insofar as it is refutable, is fallible. For instance, if someone were to state that since Socrates was wise and just, it is a sign that the wise are just. Although this is a sign, it is refutable (the example is Aristotle's; Rhetoric 1357b12-14). So a sign differs from a tekmh/rion, because the former is a fallible type of demonstration while the latter is not. From the reasons offered above, a plausible translation of tekmh/rion is "conclusive proof". For further discussion on this issue see Mignucci 1969, 722.
[4] These lines are literally reproduced in tau 245, and the example is probably taken from Sextus Empiricus, Pyrrhoniae hypotyposes 2.100. The case of fire and smoke is an example of what Sextus calls "recollective sign", i.e. the one that "having been observed evidently together with the thing it signifies, at the same time as it makes an impression on us [...] it leads us to recall the thing which has been observed together with it and is not now making an evident impression on us, as in the case of smoke and fire" (Translation Barnes and Annas; see also Sextus, Adversis mathematicos 8.157). In the example, of course, smoke is the "recollective sign" of the presence of fire.
[5] This is, once more, Aristotle's position (see Rhetoric 1357b16-17, 1403a13-15.
[6] The example is taken from Aristotle, An.Pr. 70a13-16; 20-24; 35-38. The account offered by Aristotle is the following: the proof that a woman is pregnant because she is pale is meant to come through the middle figure. For since paleness follows pregnant women and is a concomitant of this woman, people suppose it has been proved that she is pregnant (An.Pr. 70a20-23).
[7] That is to say "syllogisms" (sullogismoi/; see here note 1). On the scholarly controversy with regard to the relation between demonstration and syllogistic, see Barnes (1994) xv-xviii.