[Footnote 74: Ibid. I. xxxiii. p. 47, b. 16-40: [Greek: au(/tê me\n ou)=n ê( a)pa/tê gi/netai e)n tô=| para\ mikro/n; ôs ga\r ou)de\n diaphe/ron ei)pei=n _to/de tô=|de u(pa/rchein, ê)\ to/de tô=|de panti\ u(pa/rchein_, sugchôrou=men.] M. B. St. Hilaire observes in his note (p. 155): "L'erreur vient uniquement de ce qu'on confond l'universel et l'indeterminé séparés par une nuance très faible d'expression, qu'on ne doit pas cependant negliger." Julius Pacius (p. 264) gives the same explanation at greater length; but the example chosen by Aristotle ([Greek: o( A)ristome/nês e)sti\ dianoêto\s A)ristome/nês]) appears open to other objections besides.] [Footnote 75: Analyt. Prior. I. xxxiv. p. 48, a. 1-28.] [Footnote 76: Ibid. a. 2-23. See the Scholion of Alexander, p. 181, b. 16-27, Brandis.] Again, we must not suppose that we can always find one distinct and separate name belonging to each term. Sometimes one or all of the three terms can only be expressed by an entire phrase or proposition. In such cases it is very difficult to reduce the reasoning into regular syllogism. We may even be deceived into fancying that there are syllogisms without any middle term at all, because there is no single word to express it. For example, let A represent equal to two right angles; B, triangle; C, isosceles. Then we have a regular syllogism, with an explicit and single-worded middle term; A belongs first to B, and then to C through B as middle term (triangle). But how do we know that A belongs to B? We know it by demonstration; for it is a demonstrable truth that every triangle has its three angles equal to two right angles. Yet there is no other more general truth about triangles from which it is a deduction; it belongs to the triangle _per se_, and follows from the fundamental properties of the figure.[77] There is, however, a middle term in the demonstration, though it is not single-worded and explicit; it is a declaratory proposition or a fact. We must not suppose that there can be any demonstration without a middle term, either single-worded or many-worded. [Footnote 77: Ibid. I. xxxv. p. 48, a. 30-39: [Greek: phanero\n o(/ti to\ me/son ou)ch ou(/tôs a)ei\ lêpte/on ô(s to/de ti, a)ll' e)ni/ote lo/gon, o(/per sumbai/nei ka)pi\ tou= lechthe/ntos.] A good Scholion of Philoponus is given, p. 181, b. 28-45, Brand.]