[9] An adept in the philosophy of Plato will at once be convinced of the truth of this assertion, by comparing what Hierocles has said about prayer in his Commentary On the Golden Verses of the Pythagoreans, with what is said respecting it by Iamblichus, in his Treatise on the Mysteries; and by Proclus, at the beginning of the second book of his Commentary On the Timæus of Plato. See the Introduction to the second Alcibiades, in Vol. 4. of my translation of Plato, and the Notes to my translation of Maximus Tyrius; in which the reader will find what Iamblichus, Proclus, and Hierocles have said on this subject. And that he was not consummately accurate in his knowledge, will be evident by comparing what he says in his above mentioned Commentary, about that middle order of beings denominated _the illustrious heroes_, with what Iamblichus and Proclus have most admirably unfolded concerning them. And this will still more plainly appear from what he says about the celebrated _tetrad_, or _tetractys_ of the Pythagoreans, in p. 166, and 170, of the same Commentary. For in both these places, he clearly asserts, that this tetrad is the same with the _Demiurgus_, or _maker_ of _the universe_. Thus, in the former of these places και την τετραδα πηγην της αιδιου διακοσμησεως, αποφαινεται την αυτην ουσαν τῳ δημιουργῳ θεῳ. i.e. “And the author of these verses shows that the tetrad, which is the fountain of the perpetual orderly distribution of things, is the same with the God who is the Demiurgus.” And in the latter passage, εστι γαρ ως εφαμεν, δημιουργος των ολων και αιτια η τετρας, θεος νοητος, αιτιος του ουρανιου και αισθητου θεου. i.e. “For as we have said, the tetrad is the Demiurgus and cause of the wholes of the universe, being an intelligible God, the source of the celestial and sensible God.” The tetrad, however, or the _animal itself_, (το αυτωζωον) of Plato; who, as Syrianus justly observes, was the best of the Pythagoreans; subsists at the extremity of the _intelligible_ triad, as is most satisfactorily shown by Proclus in the third book of his Treatise On the Theology, and in the fourth book of his Commentary On the Timæus of Plato. But the Demiurgus, as it is demonstrated by the same incomparable man, in the fifth book of the former of these works, subsists at the extremity of the _intellectual_ triad. And between these two triads another order of Gods exists, which is denominated _intelligible, and at the same time intellectual_, as partaking of both the extremes. The English reader who has a genius for such speculations, will be convinced of this by diligently perusing my translations of the above mentioned works. Notwithstanding, however, the knowledge of Hierocles was not so consummately accurate on certain most abstruse theological dogmas as that of Iamblichus, Proclus, and Damascius, yet where ethics are concerned, his notions are most correct, most admirable, and sublime.