170 SCIENCE IN GRECO-ROMAN ANTIQUITY 



regular and uniform, for a body which turns freely 

 about another ; it is the circular movement. For, 

 if the revolving body begins to approach or recede 

 from the central body, it will end either by falling on 

 it or by going away from it altogether. 



3. THE MATHEMATICAL HYPOTHESES 



The mathematical hypotheses were on the whole 

 much more varied than the physical ones. In order 

 to grasp their significance, it must be remembered 

 that they do not pretend to explain the movements 

 of the heavenly bodies in regard to one another by 

 any physical cause such as Newton's law of attraction, 

 for instance. 1 They only attempt to give a geometrical 

 representation of these movements. This representa- 

 tion may be imaginary like the mechanical means for 

 going from the earth to the moon imagined by modern 

 novelists. The novelist must doubtless take into 

 account the known laws of physics and not contradict 

 these : but nevertheless it matters little to him that 

 the engineer has not the necessary funds for the con- 

 struction of the cannon which will send a bullet to the 

 moon. In the same way Greek astronomy was obliged 

 to take into consideration the four physical facts 

 mentioned above, but for the rest it was entirely free 

 to invent whatever geometrical representation appeared 

 to be most appropriate. Plato and his Pythagorean 



1 " We must, however, except a curious opinion reported 

 by Plutarch {De facie in orbe lunae, Ch. VI) which seems to 

 foreshadow the mechanics of Newton, and which may be 

 summarized as follows : What keeps the moon from falling 

 is its own movement and the rapidity of its rotation ; similarly, 

 for a projectile put in a sling, the force which prevents it from 

 falling comes from circular rotation. In fact, natural motion 

 only carries along a given body if nothing else opposes it. 

 The moon is not carried along by its weight, for this weight 

 is repelled and destroyed by the force of its rotation." Quoted 

 from Doublet, Histoire de I'Astronomie, p. 119. 



