116 A SHORT HISTORY OF SCIENCE 



tury was due to Hipparchus, a great astronomer, and Hero, an 

 engineer. 



ORBITAL MOTION OF THE EARTH. ARISTARCHUS. Before 

 dealing with Hipparchus and Hero, however, we have to consider 

 the highly interesting and significant astronomical theories of 

 Aristarchus of Samos (270 B.C.-?), who was the author of a 

 treatise On the Dimensions and Distances of the Sun and Moon. 

 He endeavored to determine these distances relatively by ascer- 

 taining or estimating the angular distance between the two bodies 

 when the moon is just half illuminated, that is, when the lines 

 joining sun, earth, and moon form a right angle at the moon a 

 method which may have been due to Eudoxus. The difficulties of 

 this determination are so serious, however, that no high degree 

 of accuracy could be attained, the actual result of Aristarchus 

 !- of a right angle against the true fr corresponding to a 

 ratio of about 1 to 19 of the two distances. Aristarchus had no 

 trigonometry, and no other method of attacking this problem seems 

 to have been known to the Greeks. 



In his Sand Counting already mentioned, Archimedes says of 

 Aristarchus, 



He supposes that the fixed stars and the sun are immovable, but 

 that the earth is carried round the sun in a circle which is in the middle 

 of the course ; but the sphere of the fixed stars, lying with the sun round 

 the same centre, is of such a size that the circle, in which he supposes 

 the earth to move, has the same ratio to the distance of the fixed stars 

 as the centre of the sphere has to the surface. But this is evidently 

 impossible, for as the centre of the sphere has no magnitude, it follows 

 that it has no ratio to the surface. It is therefore to be supposed that 

 Aristarchus meant that as we consider the earth as the centre of the 

 world, then the earth has the same ratio to that which we call the world, 

 as the sphere in which is the circle, described by the earth according 

 to him, has to the sphere of the fixed stars. 



Aristarchus thus meets the objection that motion of the earth 

 would cause changes in the apparent positions of the stars by as- 

 suming that their distances are so great as to render the motion of 



