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ound all the other spheres, and the sphere next in order, which has its motion in the circle which bisects the zodiac, is common to all the planets); the third sphere of all the planets has its poles in the circle which bisects the zodiac; and the fourth sphere moves in the circle inclined to the equator of the third. In the case of the third sphere, while the other planets have their own peculiar poles, those of Venus and Mercury are the same. Callippusof Cyzicus (fl. 380 B.C.). Simplicius says (Simplicius 493.5-8) that he corrected and elaborated Eudoxus's theory with Aristotle's help while on a visit to him at Athens. assumed the same arrangement of the spheres as did Eudoxus (that is, with respect to the order of their intervals), but as regards their number, whereas he assigned to Jupiter and Saturn the same number of spheres as Eudoxus, he considered that two further spheres should be added both for the sun
are we shall now, to give some idea of the subject, quote what some of the mathematicians say, in order that there may be some definite number for the mind to grasp; but for the rest we must partly investigate for ourselves and partly learn from other investigators, and if those who apply themselves to these matters come to some conclusion which clashes with what we have just stated, we must appreciate both views, but follow the more accurate. EudoxusOf Cnidus (circa 408 -355 B.C.). He was a pupil of Plato, and a distinguished mathematician. held that the motion of the sun and moon involves in either case three spheres,For a full discussion of the theories of Eudoxus and Callipus see Dreyer, Planetary Systems 87-114; Heath,Aristarchus of Samos190-224. of which the outermost is that of the fixed stars,Not identical with that of the fixed stars, but having the same motion. the second revolves in the
ird sphere of all the planets has its poles in the circle which bisects the zodiac; and the fourth sphere moves in the circle inclined to the equator of the third. In the case of the third sphere, while the other planets have their own peculiar poles, those of Venus and Mercury are the same. Callippusof Cyzicus (fl. 380 B.C.). Simplicius says (Simplicius 493.5-8) that he corrected and elaborated Eudoxus's theory with Aristotle's help while on a visit to him at Athens. assumed the same arrangement of the spheres as did Eudoxus (that is, with respect to the order of their intervals), but as regards their number, whereas he assigned to Jupiter and Saturn the same number of spheres as Eudoxus, he considered that two further spheres should be added both for the sun and for the moon, if the phenomena are to be accounted for, and one for each of the other planets. But if all the spheres in combination are to account for t
e other spheres, and the sphere next in order, which has its motion in the circle which bisects the zodiac, is common to all the planets); the third sphere of all the planets has its poles in the circle which bisects the zodiac; and the fourth sphere moves in the circle inclined to the equator of the third. In the case of the third sphere, while the other planets have their own peculiar poles, those of Venus and Mercury are the same. Callippusof Cyzicus (fl. 380 B.C.). Simplicius says (Simplicius 493.5-8) that he corrected and elaborated Eudoxus's theory with Aristotle's help while on a visit to him at Athens. assumed the same arrangement of the spheres as did Eudoxus (that is, with respect to the order of their intervals), but as regards their number, whereas he assigned to Jupiter and Saturn the same number of spheres as Eudoxus, he considered that two further spheres should be added both for the sun and for the
all now, to give some idea of the subject, quote what some of the mathematicians say, in order that there may be some definite number for the mind to grasp; but for the rest we must partly investigate for ourselves and partly learn from other investigators, and if those who apply themselves to these matters come to some conclusion which clashes with what we have just stated, we must appreciate both views, but follow the more accurate. EudoxusOf Cnidus (circa 408 -355 B.C.). He was a pupil of Plato, and a distinguished mathematician. held that the motion of the sun and moon involves in either case three spheres,For a full discussion of the theories of Eudoxus and Callipus see Dreyer, Planetary Systems 87-114; Heath,Aristarchus of Samos190-224. of which the outermost is that of the fixed stars,Not identical with that of the fixed stars, but having the same motion. the second revolves in the circle