Among the philosophers were some noted as mathematicians whose leader was Pythagoras (c. 550 B.C.). He and at least one of the members of his school, Eudoxus (409?-356? B.C.), had visited Egypt, according to Diogenes Laërtius,[9] and had in all probability been much interested in and influenced by the astronomical observations made by the Egyptian priests. On the same authority, Pythagoras was the first to declare the earth was round and to discuss the antipodes. He too emphasized the beauty and perfection of the circle and of the sphere in geometry, forms which became fixed for 2000 years as the fittest representations of the perfection of the heavenly bodies. [Footnote 9: Diogenes Laërtius: _De Vitis_, Lib. VIII, c. 1, et 8 (205, 225).] There was some discussion in Diogenes' time as to the author of the theory of the earth's motion of axial rotation. Diogenes[10] gives the honor to Philolaus (5th cent. B.C.) one of the Pythagoreans, though he adds that others attribute it to Icetas of Syracuse (6th or 5th cent. B.C.). Cicero, however, states[11] the position of Hicetas of Syracuse as a belief in the absolute fixedness of all the heavenly bodies except the earth, which alone moves in the whole universe, and that its rapid revolutions upon its own axis cause the heavens apparently to move and the earth to stand still. [Footnote 10: Diogenes: _Op. cit._, Lib. VIII, c. 7 (225).] [Footnote 11: Cicero: _Academica_, Lib. II, c. 39 (322).] Other thinkers of Syracuse may also have felt the Egyptian influence; for one of the greatest of them, Archimedes (c. 287-212 B.C.), stated the theory of the earth's revolution around the sun as enunciated by Aristarchus of Samos. (Perhaps this is the "hearth-fire of the universe" around which Philolaus imagined the earth to whirl.[12]) In _Arenarius_, a curious study on the possibility of expressing infinite sums by numerical denominations as in counting the sands of the universe, Archimedes writes:[13] "For you have known that the universe is called a sphere by several astrologers, its center the center of the earth, and its radius equal to a line drawn from the center of the sun to the center of the earth. This was written for the unlearned, as you have known from the astrologers.... [Aristarchus of Samos][14] concludes that the world is many times greater than the estimate we have just given. He supposes that the fixed stars and the sun remain motionless, but that the earth following a circular course, revolves around the sun as a center, and that the sphere of the fixed stars having the same sun as a center, is so vast that the circle which he supposes the earth to follow in revolving holds the same ratio to the distance of the fixed stars as the center of a sphere holds to its circumference." [Footnote 12: Plutarch: _Op. cit._, Lib. II (V. 299-300).] [Footnote 13: Archimedes: _Arenarius_, c. 1. Delambre: _Astr. Anc._, I, 102.]