[Footnote 8: Analyt. Post. II. iii. p. 90, b. 13: [Greek: i(kanê\ de\ pi/stis kai\ e)k tê=s e)pagôgê=s; ou)de\n ga\r pô/pote o(risa/menoi e)/gnômen, ou)/te tô=n kath' au(to\ u(parcho/ntôn ou)/te tô=n sumbebêko/tôn. e)/ti ei) o( o(rismo\s ou)si/as tis gnôrismo/s, ta\ ge toiau=ta phanero\n o(/ti ou)k ou)si/ai.]] Again, let us ask, _vice versâ_, Can everything that is declared by Definition, or indeed anything that is declared by Definition, be known also by Demonstration? Neither is this possible. One and the same _cognitum_ can be known only by one process of cognition. Definitions are the _principia_ from which Demonstration departs; and we have already shown that in going back upon demonstrations, we must stop somewhere, and must recognize some _principia_ undemonstrable.[9] The Definition can never be demonstrated, for it declares only the essence of the subject, and does not predicate anything concerning the subject; whereas Demonstration assumes the essence to be known, and deduces from such assumption an attribute distinct from the essence.[10] [Footnote 9: Ibid. b. 18-27.] [Footnote 10: Ibid. b. 33, seq.: [Greek: e)/ti pa=sa a)po/deixis ti\ kata/ tinos dei/knusin, oi(=on o(/ti e)/stin ê)\ ou)k e)/stin; e)n de\ tô=| o(rismô=| ou)de\n e(/teron e(te/rou katêgorei=tai, oi(=on ou)/te to\ zô=|on kata\ tou= di/podos ou)de\ tou=to kata\ tou= zô=|ou--o( me\n ou)=n o(rismo\s ti/ e)sti dêloi=, ê( de\ a)po/deixis o(/ti ê)\ e)/sti to/de kata\ tou=de ê)\ ou)k e)/stin.] Themistius (p. 71, Speng.) distinguishes the [Greek: o(rismo/s] itself from [Greek: ê( pro/tasis ê( to\n o(rismo\n katêgorou/menon e)/chousa].] Prosecuting still farther the dialectical and dubitative treatment,[11] Aristotle now proceeds to suggest, that the Essence (that is, the entire Essence or Quiddity), which is declared by Definition, can never be known by Demonstration. To suppose that it could be so known, would be inconsistent with the conditions of the syllogistic proof used in demonstrating. You prove by syllogism, through a middle term, some predicate or attribute; _e.g._ because A is predicable of all B, and B is predicable of all C, therefore A is predicable of all C. But you cannot prove, through the middle term B, that A is the essence or quiddity of C, unless by assuming in the premisses that B is the essence of C, and that A is the essence of B; accordingly, that the three propositions, AB, BC, AC, are all co-extensive and reciprocate with each other. Here, then, you have assumed as your premisses two essential propositions, AB, BC, in order to prove as an essential proposition the conclusion AC. But this is inadmissible; for your premisses require demonstration as much as your conclusion. You have committed a _Petitio Principii_;[12] you have assumed in your minor premiss the very point to be demonstrated.