[Footnote 30: Analyt. Post. II. xii. p. 95, a. 10, 36: [Greek: to\ ga\r me/son o(mo/gonon dei= ei)=nai], &c.] [Footnote 31: Ibid. a. 24 seq., b. 32; Julius Pacius, ad loc.; Biese, Die Philosophie des Aristot. pp. 302-303.] [Footnote 32: Analyt. Post. II. xii. p. 95, a. 39-b. 8; Themistius, p. 86.] [Footnote 33: Analyt. Post. II. xii. p. 95, b. 14-31: [Greek: a)rchê\ de\ kai\ e)n tou/tois a)/mesos lêpte/a].] [Footnote 34: Ibid. b. 38-p. 96, a**. 7.] [Footnote 35: Ibid. p. 96, a. 8-19.] How are we to proceed in hunting out those attributes that are predicated _in Quid_,[36] as belonging to the Essence of the subject? The subject being a lowest species, we must look out for such attributes as belong to all individuals thereof, but which belong also to individuals of other species under the same genus. We shall thus find one, two, three, or more, attributes, each of which, separately taken, belongs to various individuals lying out of the species; but the assemblage of which, collectively taken, does not belong to any individual lying out of the species. The Assemblage thus found is the Essence; and the enunciation thereof is the Definition of the species. Thus, the triad is included in the genus number; in searching for its definition, therefore, we must not go beyond that genus, nor include any attributes (such as _ens_, &c.) predicable of other subjects as well as numbers. Keeping within the limits of the genus, we find that every triad agrees in being an odd number. But this oddness belongs to other numbers also (pentad, heptad, &c.). We therefore look out for other attributes, and we find that every triad agrees in being a prime number, in two distinct senses; first, that it is not measured by any other number; secondly, that it is not compounded of any other numbers. This last attribute belongs to no other odd number except the triad. We have now an assemblage of attributes, which belong each of them to every triad, universally and necessarily, and which, taken all together, belong _exclusively_ to the triad, and therefore constitute its essence or definition. The triad is a number, odd, and prime in the two senses.[37] The _definitum_ and the definition are here exactly co-extensive. [Footnote 36: Ibid. xiii. p. 96, a. 22: [Greek: pô=s dei= _thêreu/ein_ ta\ e)n tô=| ti/ e)sti katêgorou/mena?]] [Footnote 37: Analyt. Post. II. xiii. p. 96, a. 24-b. 14. [Greek: ei) toi/nun mêdeni\ u(pa/rchei a)/llô| ê)\ tai=s a)to/mois tria/si, tou=t' a)\n ei)/ê to\ tria/di ei)=nai. u(pokei/sthô ga\r kai\ tou=to, ê( ou)si/a ê( e(ka/stou ei)=nai ê( e)pi\ tai=s a)to/mois e)/schatos toiau/tê katêgori/a. ô(/ste o(moi/ôs kai\ a)/llô| o(tô|ou=n tô=n ou(/tô deichthe/ntôn to\ _au)tô=| ei)=nai_ e)/stai.]]