As the above-mention'd print thus involved me in frequent disputes by explaining the qualities of the line, I was extremely glad to find it (which I had conceiv'd as only part of a system in my mind) so well supported by the above precept of Michael Angelo: which was first pointed out to me by Dr. Kennedy, a learned antiquarian and connoisseur, of whom I afterwards purchased the translation, from which I have taken several passages to my purpose. Let us now endeavour to discover what light antiquity throws upon the subject in question. Egypt first, and afterward Greece, have manifested by their works their great skill in arts and sciences, and among the rest painting, and sculpture, all which are thought to have issued from their great schools of philosophy. Pythagoras, Socrates, and Aristotle, seem to have pointed out the right road in nature for the study of the painters and sculptors of those times (which they in all probability afterwards followed through those nicer paths that their particular professions required them to pursue) as may be reasonably collected from the answers given by Socrates to Aristippus his disciple, and Parrhasius the painter, concerning FITNESS, the first fundamental law in nature with regard to beauty. I am in some measure saved the trouble of collecting an historical account of these arts among the ancients, by accidentally meeting with a preface to a tract, call'd the _Beau Ideal_: this treatise[3] was written by Lambert Hermanson Ten Kate, in French, and translated into English by James Christopher le Blon; who in that preface says, speaking of the Author, "His superior knowledge that I am now publishing, is the product of the Analogy of the ancient Greeks; or the true key for finding all harmonious proportions in painting, sculpture, architecture, musick, &c. brought home to Greece by Pythagoras. For after this great philosopher had travell'd into Phoenicia, Egypt and Chaldea, where he convers'd with the learned; he return'd into Greece about Anno Mundi 3484. Before the christian æra 520, and brought with him many excellent discoveries and improvements for the good of his countrymen, among which the Analogy was one of the most considerable and useful. [3] Publish'd in 1732, and sold by A. Millar. "After him the Grecians, by the help of this Analogy, began (and not before) to excel other nations in sciences and arts; for whereas before this time they represented their _Divinities_ in plain human figures, the Grecians now began to enter into the Beau Ideal; and Pamphilus, (who flourish'd A. M. 3641, before the christian æra 363, who taught, that no man could excel in painting without mathematicks) the scholar of Pausias and master of Apelles, was the first who artfully apply'd the said Analogy to the art of painting; as much about the same time the sculpturers, the architects, &c. began to apply it to their several arts, without which science, the Grecians had remain'd as ignorant as their forefathers.