92 THE WORLD MACHINE 



of the earth's shadow, G I H J, and the lines, a B a C, until 

 the two meet as at D and F, to have the figure we have drawn. 

 Knowing the distance from the earth to the moon, one could 

 measure the distance to the sun with a foot-rule. 



Did Aristarchus do it ? Possibly not. The device is not 

 in his treatise " On the Distance and Size of the Sun and Moon." 

 It is likely that it was a development of the next generation or so. 



Living in that same wonderful day was another giant, 

 Apollonius of Perga, styled " the great geometer." His was 

 the glory, 'twas said, to have applied geometry to the problem 

 of the heavens. Evidently by this was meant the higher 

 geometry, for, as we have seen, Bion and Aristarchus and 

 Eratosthenes and many another had already given good account 

 of themselves in the use of geometrical methods. Apollonius 

 developed the theory of conic sections, and introduced the idea 

 of epicycles as an explanation of the motion of the planets. 

 This latter idea was borrowed by Hipparchus, " greatest ob- 

 serving astronomer of antiquity," and it was doubtless the 

 example of Apollonius which led him to the discovery of the 

 idea of parallax usually attributed to him. It was doubtful, 

 though, if he was the actual discoverer. The observation that 

 the stars, like other objects, change in their apparent position 

 under different points of view, must have been almost as old 

 as astronomy, and a geometrical method for taking advantage 

 of this must have been found very early. Be this as it may, 

 the problem of the shadow cone, as is clear from the pages of 

 Ptolemy, 1 had been worked out by Hipparchus, apparently 

 with great precision, but with the strange result of confirming 

 the calculations of Aristarchus. He, too, found the distance of 

 the sun about twenty times that of the moon, or from 1379 to 

 1472 half diameters of our globe. Ptolemy, a couple of centu- 

 ries later, tries his hand at the matter, but with no better success 

 indeed, he reduces the distance to 1210 such half diameters. 



But with three distinct methods leading identically to the 

 same result, there could now be little question of their truth. 

 There seems indeed to have been no question for another 

 seventeen centuries, and until Galileo and the telescope had 

 come. Hipparchus' method it is generally so styled is re- 

 produced, with new proofs, but similar estimates, in the De 

 Revolutionibus of Coppernicus, A.D. 1543. 



1 Almagest, Lib. V. chap. xiv. xv. 



