BEGINNINGS IN GREECE 55 



the earth in the opposite direction. This latter motion, however, 

 was thought of, not as a rotation, but as an orbital motion about a 

 so-called "central fire." Just as the moon revolved about the 

 earth, always turning the same face towards the latter, so the 

 earth might revolve about the central fire which would be forever 

 invisible to the inhabitants of the other side of the earth. While 

 we say that the moon rotates about its axis in the same time in 

 which it revolves about the earth, to the ancients such a motion 

 was not considered to include rotation at all. A further essen- 

 tially arbitrary assumption introduced between the earth and 

 the central fire a counter-earth (antichthori) , which was required to 

 make up the supposed number of the heavenly bodies, and which 

 would hide the central fire from dwellers in the antipodes. 

 Aristotle, criticising this theory, says of the Pythagoreans : 



They do not with regard to the phenomena seek for their reasons 

 and causes, but forcibly make the phenomena fit their opinions and 

 preconceived notions. . . . When they anywhere find a gap in the 

 numerical ratios of things, they fill it up in order to complete the sys- 

 tem. As ten is a perfect number and is supposed to comprise the 

 whole nature of numbers, they maintain that there must be ten bodies 

 moving in the universe, and as only nine are visible, they make the 

 antichthon the tenth. 



All the other heavenly bodies describe orbits, each in its own 

 hollow sphere about the central fire, the generally adopted order, 

 based on the apparent rate of motion among the stars, being 

 Moon, Sun, Venus, Mercury, Mars, Jupiter, Saturn. Pythagorean 

 speculations as to relative distances of the different planets were 

 naturally mystical notions merely. The sun was said to move 

 around the central fire in an "oblique circle," i.e. the ecliptic. 

 The moon was believed to be inhabited by plants and animals. 

 The moon might be eclipsed either by the earth or by the 

 counter-earth. This remarkable system, admitting the earth to 

 move and not to be the centre of the universe, was not generally 

 or long accepted, but had a share in securing the acceptance of 

 the theories of Copernicus nearly 2000 years later. One at least 



