Aristotle remarks that there is great liability to error about these _Universalia Prima_. We sometimes demonstrate a predicate to be true, universally and _per se_, of a lower species, without being aware that it might also be demonstrated to be true, universally and _per se_, of the higher genus to which that species belongs; perhaps, indeed, that higher genus may not yet have obtained a current name. That proportions hold by permutation, was demonstrated severally for numbers, lines, solids, and intervals of time; but this belongs to each of them, not from any separate property of each, but from what is common to all: that, however, which is common to all had received no name, so that it was not known that one demonstration might comprise all the four.[18] In like manner, a man may know that an equilateral and an isosceles triangle have their three angles equal to two right angles, and also that a scalene triangle has its three angles equal to two right angles; yet he may not know (except sophistically and by accident[19]) that a triangle _in genere_ has its three angles equal to two right angles, though there be no other triangles except equilateral, isosceles, and scalene. He does not know that this may be demonstrated of every triangle _quatenus_ triangle. The only way to obtain a certain recognition of _Primum Universale_, is, to abstract successively from the several conditions of a demonstration respecting the concrete and particular, until the proposition ceases to be true. Thus, you have before you a brazen isosceles triangle, the three angles whereof are equal to two right angles. You may eliminate the condition brazen, and the proposition will still remain true. You may also eliminate the condition isosceles; still the proposition is true. But you cannot eliminate the condition triangle, so as to retain only the higher genus, geometrical figure; for the proposition then ceases to be always true. Triangle is in this case the _Primum Universale_.[20] [Footnote 18: Aristot. Analyt. Post I. v. p. 74, a. 4-23. [Greek: a)lla\ dia\ to\ mê\ ei)=nai ô)nomasme/non ti pa/nta tau=ta e(/n, a)rithmoi/, mê/kê, chro/nos, sterea/, kai\ ei)/dei diaphe/rein a)llê/lôn, chôri\s e)lamba/neto.] What these four have in common is that which he himself expresses by [Greek: Poso/n]--_Quantum_--in the Categoriæ and elsewhere. (Categor. p. 4, b. 20, seq.; Metaph. [Greek: D]. p. 1020, a. 7, seq.)]