was a matter of dogma that certain proportions of the human body were perfect and obligatory. There was also a prevalent belief that certain shapes and proportions were in themselves perfect. Plato felt that the perfect proportion was the ratio of the side to the diagonal of a square. His authority was so great that architects and other artists continued using this proportion, even when ignorant of its source, as late as the Middle Ages. Another early idea — one that was to be espoused by many illustrious writers and artists of various periods — found perfection in the circle and the sphere. Aristotle wrote in the Physica that the circle was "the perfect, first, most beautiful form". Cicero wrote in De Natura Deorum (On the Nature of the Gods): "Two forms are the most distinctive: of solids, the sphere... and of plane figures, the circle... There is nothing more commensurate than these forms." In a commentary to Aristotle's De coelo et mundo (On the Heavens and Earth), the medieval Pole, Jan of Słupcza, wrote: "The most perfect body ought to have the most perfect form, and such [a body] is heaven, while the most perfect form is the round form, for nothing can be added to it." In the famous illustrated Les très riches heures du duc de Berry, paradise is depicted as contained within an ideal sphere. The Renaissance architect Sebastiano Serlio (1475–1554) stated: "the round form is the most perfect of all." The most excellent of 16th-century architects, Andrea Palladio, held that "the most perfect and most excellent" form was "the round form, since of all forms it is the simplest, the most uniform, the strongest, the most capacious" and "is the most suitable for rendering the unity, infinity, uniformity and righteousness of God". This was the same thought as in Jan of Słupcza and in Serlio, and it was one of uncommon durability. The Middle Ages — Romanesque and Gothic alike — had been quite taken with the idea of perfection. But a true explosion of the imperative for perfection came with the Renaissance. Renaissance aesthetics placed less emphasis than had classical aesthetics on the unity of things perfect. Baldassare Castiglione, in his Courtier, wrote, of Leonardo, Andrea Mantegna, Raphael, Michelangelo and Giorgione, that "each of them is unlike the others, but each is the most perfect [perfectissimus] in his style." The great architect and polymath