Now, although the principles were universally acted upon, yet they were more particularly attended to in the construction of temples and sacred edifices, the beauties or defects of which were destined to remain as a perpetual testimony of their skill or of their inability.” Vitruvius, however, gives no explanation of this ancient principle of proportion, as derived from the human form; but plainly shews his uncertainty upon the subject, by concluding this part of his essay in the following words: “If it be true, therefore, that the decenary notation was suggested by the members of man, and that the laws of proportion arose from the relative measures existing between certain parts of each member and the whole body, it will follow, that those are entitled to our commendation who, in building temples to their deities, proportioned the edifices, so that the several parts of them might be commensurate with the whole.” It thus appears certain that the Grecians, at the period of their highest excellence, had arrived at a knowledge of some definite mathematical law of proportion, which formed a standard of perfectly symmetrical beauty, not only in the representation of the human figure in sculpture and painting, but in architectural design, and indeed in all works where beauty of form and harmony of proportion constituted excellence. That this law was not deduced from the proportions of the human figure, as supposed by Vitruvius, but had its origin in mathematical science, seems equally certain; for in no other way can we satisfactorily account for the proportions of the beau ideal forms of the ancient Greek deities, or of those of their architectural structures, such as the Parthenon, the temple of Theseus, &c., or for the beauty that pervades all the other formative art of the period. This system of geometrical harmony, founded, as I have shewn it to be, upon numerical relations, must consequently have formed part of the Greek philosophy of the period, by means of which the arts began to progress towards that great excellence which they soon after attained. A little further investigation will shew, that immediately after this period a theory connected with art was acknowledged and taught, and also that there existed a Science of Proportion. Pamphilus, the celebrated painter, who flourished about four hundred years before the Christian era, from whom Apelles received the rudiments of his art, and whose school was distinguished for scientific cultivation, artistic knowledge, and the greatest accuracy in drawing, would admit no pupil unacquainted with geometry.[30] The terms upon which he engaged with his students were, that each should pay him one talent (£225 sterling) previous to receiving his instructions; for this he engaged “to give them, _for ten years_, lessons founded on an excellent theory.”[31]