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§§ 23, 24] Greek thought, and was in later times an established part of Greek systems, whence it has been handed down, almost unchanged, to modern times. This belief is thus 2,000 years older than the belief in the rotation of the earth and its revolution round the sun (chapter ), doctrines which we are sometimes inclined to couple with it as the foundations of modern astronomy.

In Pythagoras occurs also, perhaps for the first time, an idea which had an extremely important influence on ancient and mediaeval astronomy. Not only were the stars supposed to be attached to a crystal sphere, which revolved daily on an axis through the earth, but each of the seven planets (the sun and moon being included) moved on a sphere of its own. The distances of these spheres from the earth were fixed in accordance with certain speculative notions of Pythagoras as to numbers and music; hence the spheres as they revolved produced harmonious sounds which specially gifted persons might at times hear: this is the origin of the idea of the music of the spheres which recurs continually in mediaeval speculation and is found occasionally in modern literature. At a later stage these spheres of Pythagoras were developed into a scientific representation of the motions of the celestial bodies, which remained the basis of astronomy till the time of Kepler (chapter ).

24. The Pythagorean Philolaus, who lived about a century later than his master, introduced for the first time the idea of the motion of the earth: he appears to have regarded the earth, as well as the sun, moon, and five planets, as revolving round some central fire, the earth rotating on its own axis as it revolved, apparently in order to ensure that the central fire should always remain invisible to the inhabitants of the known parts of the earth. That the scheme was a purely fanciful one, and entirely different from the modern doctrine of the motion of the earth, with which later writers confused it, is sufficiently shewn by the invention as part of the scheme of a purely imaginary body, the counter-earth (ἁντιχθών), which brought the number of moving bodies up to ten, a sacred Pythagorean number. The suggestion of such an important idea as that of the motion of the earth, an idea so