As to the NUMERICAL METHOD, it is evidently that of which Vitruvius has preserved some notions, and which is at present practised by artists. "As it is the painter's business," says Bossi, "to imitate a great variety of human bodies, and as the difference of parts in beautiful bodies is generally slight, and becomes, as it were, imperceptible, in the most usual imitations less than life, Leonardo perceived it was necessary for the artist to use a general measure, for the purpose of preparing historical compositions quickly. He required that the figure to be employed should be carefully selected on the model of some natural body, the proportions of which were generally considered beautiful.--This measure, he required, should be employed solely for _length_, and not for width, which requires more evident variety." "It has been observed," says Flaxman, "that Vitruvius, from the writings of the most eminent Greek painters and sculptors, informs us that they made their figures eight heads high, or ten faces, and he instances different parts of the figure measured according to that rule, which the great Michael Angelo adopted, as we see by a print from a drawing of his." Winckelmann, however, shows that the foot served the Greeks as a measure for all their larger dimensions, and that their sculptors regulated their proportions by it, in giving six times its length, as the model of the human figure. Vitruvius says, "_Pes vero altitudinis corporis sextæ_." "The foot," says Winckelmann, "which among the ancients was used as the standard of measures of every magnitude (for a given measure of fluids was also called by this name), was very useful to sculptors in fixing the proportions of the body, and with reason; for the foot was a more determinate measure than that of the head or face, of which the moderns generally make use. The ancient artists regulated the size of their statues by the length of the foot, making them, according to Vitruvius, six times the length of the foot. Upon this principle, Pythagoras determined the height of Hercules, by the length of the feet with which he measured the Olympic stadium at Elis. "This proportion of six to one between the foot and the body, is founded upon experience of nature, even in slender figures: it is found correct, not only in the Egyptian statues, but also in the Grecian; and it will be discovered in the greater part of the ancient figures where the feet are preserved." "We would not omit mentioning," says Bossi, "the erroneous opinion of those, who esteem the feet of females beautiful in proportion to their smallness. The beauty of the feet consists in the handsomeness and neatness of their shape, not in their being short, or extremely small: were it otherwise, the feet of the Chinese and Japanese women would be beautiful, and those of the Venus de Medici frightful." Such, then, is evidently the numerical method of the ancients.--Of the GEOMETRICAL METHOD, we have many illustrations.