More generally, the Parmenides is concerned throughout with the metaphysics of the one and the many, of unity and plurality and the Republic 7.521C–531D outlines a mathematics curriculum in five parts beginning with arithmetic and ratio theory and thence proceeding to plane and solid geometry, and ending with astronomy and music. For these and other references, see Paul-Henri Michel, De Pythagore à Euclide:Ĭontribution à l'histoire des mathématiques préeuclidiennes (Paris, 1950), pp. de Vogel, Pythagoras and Early Pythagoreanism (Assen, 1966), pp. For Plato's relationship to the Pythagoreans, see Cornelia J. Waszink, Timaeus a Calcidio Translatus Commentarioque Instructus (London and Leiden, 1962 2d ed., 1975)-volume 4 in the series Corpus Platonicum Medii Aevi but see also that by Johannes Wrobel, Platonis Timaeus Interprete Chalcidio cum Eiusdem Commentario (Leipzig, 1876). The authoritative modern edition is by J. The Timaeus was known to the Latin West principally by way of Calcidius's Commentary. Michael Hayduck, Commentaria in Aristotelem Graeca, vol. The inscription was familiar to Ficino, however, from a number of later sources, including perhaps Philoponus's commentary on Aristotle's De Anima ( Ioannis Philoponi in Aristotelis de Anima Libros Commentaria 1.3.406b25 ff., ed. Fowler, The Mathematics of Plato's Academy: A New Reconstruction (Oxford, 1987), pp. Saffrey, " Ageômetrêtos mêdeis eisitô: Une inscription légendaire," Revue des études grecques 81 (1968), 67–87, traces the evidence for the inscription (which is possibly apocryphal) back to a reference in an oration by the emperor Julian and to another in a scholion on Aelius Aristides, both from the mid fourth century A.D. Other dialogues contain mathematical references or observations: for instance, the Euthyphro at 12D, the Hippias Major at 303BC, the Philebus at 56D, the Charmides at 166A, the Statesman at 266AB, the Phaedrus at 274C, and the Laws 7 at 817E–820C. Apart from the Timaeus with its exceptionally important sections on means and proportions at 34B–36D and on the five regular polyhedra at 53C–56C, the Meno has two well-known passages on the duplication of the square at 82B–85B and on the measurement of areas at 86E–87B, the Theaetetus raises the issue of irrational or incommensurable roots at 147D–148B, and the Epinomis (which the Renaissance considered authentic) has an arresting section at 990C–991A on astronomy, geometry, progressions, the mean proportions, and the formation of numbers. Although none of Plato's dialogues focus primarily on mathematics, several do contain significant loci mathematici. Scholars were also aware that in the Timaeus, the dialogue on the Demiurge and his creation and the one most familiar to and most treasured by the medieval and the Renaissance West, Plato had advanced various Pythagorean notions-with what degree of seriousness it is now virtually impossible to say-on the harmonies governing the soul, and on the structure of the elements and the geometrical figures that constituted them. and 7.531D–534E, it was subordinate, like all its "sister" mathematical arts, to the "comprehensive" power of dialectic, "the coping stone" of the intellectual skills. For geometry was a marvelous art that the Epinomis 990D had claimed was of divine not human origin, even though, as the Republic had argued at 6.511B ff. Tion in the vestibule of the Academy had forbidden anyone unskilled in geometry to cross the threshold and seek initiation into the sacred mysteries. Renaissance scholars were familiar with the report that the inscrip. The supreme ancient authority of this mathematical view of man as mathematician was Plato, spokesman for what was preeminently the Pythagorean tradition in which his own scientific studies had been nurtured. And man in the divine image of God the Creator had been designed with a body of geometrical proportions, with a harmoniously balanced temperament, with a mathematical mind. For the influential book of the Apocrypha known as the Wisdom of Solomon had proclaimed in a much-quoted text that God had made all things "in number, weight, and measure" (11.20) as the architect of the world, as the heavenly geometer, as the musical master of a divine harmonics. Necessarily the mathematical structures in the world were part of the divine figuration, and a sense of this figuration provided the foundation for both the methods and the goals of such learned disciplines as arithmology and numerology, astrology, iatromathematics, and musical therapy, the mathematical or at least computational arts that the age regarded as legitimate branches of learning and of proven utility. In the notable nineteenth expostulation in his Devotions, John Donne refers to God as a metaphorical God and the Renaissance in general was enthusiastically attuned to the assumption that the world was itself a figure, a cipher. Ficino's Commentary on the Eighth Book of the Republic
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