$ si, aa] Aristarchus 35 



known ; its shape is therefore completely determined, and 

 the ratio of its sides EM, E s can be calculated without 

 much difficulty. In fact, it being known (by a well-known 

 result in elementary geometry) that the angles at E and s 

 are together equal to a right angle, the angle at s is 

 obtained by subtracting the angle s E M from a right angle. 

 Aristarchus made the angle at s about 3, and hence 

 calculated that the distance of the sun was from 1 8 to 20 

 times that of the moon, whereas, in fact, the sun is about 400 

 times as distant as the moon. The enormous error is due 

 to the difficulty of determining with sufficient accuracy the 

 moment when the moon is half full : the boundary separating 

 the bright and dark parts of the moon's face is in reality 

 (owing to the irregularities on the surface of the moon) an ill- 

 defined and broken line (cf. fig. 53 and the frontispiece), so that 

 the observation on which Aristarchus based his work could 

 not have been made with any accuracy even with our modern 

 instruments, much less with those available in his time. 

 Aristarchus further estimated the apparent sizes of the sun 

 and moon to be about equal (as is shewn, for example, at 

 an eclipse of the sun, when the moon sometimes rather more 

 than hides the surface of the sun and sometimes does not 

 quite cover it), and inferred correctly that the real diameters 

 of the sun and moon were in proportion to their distances. 

 By a method based on eclipse observations which was 

 afterwards developed by Hipparchus ( 41), he also found 

 that the diameter of the moon was about -3- that of the 

 earth, a result very near to the truth ; and the same 

 method supplied data from which the distance of the moon 

 could at once have been expressed in terms of the radius 

 of the earth, but his work was spoilt at this point by a 

 grossly inaccurate estimate of the apparent size of the moon 

 (2 instead of |), and his conclusions seem to contradict 

 one another. He appears also to have believed the dis- 

 tance of the fixed stars to be immeasurably great as 

 compared with that of the sun. Both his speculative 

 opinions and his actual results mark therefore a decided 

 -^advance in astronomy. 



Timocharis and Aristyllus were the first to ascertain and 

 to record the positions of the chief stars, by means of 

 numerical measurements of their distances from fixed 



