A HISTORY OF SCIENCE 



disks of the sun and the moon. This, of course, could 

 in itself give him no clew to the distance of these bod- 

 ies, and therefore no clew as to their relative size ; but 

 in attempting to obtain such a clew he hit upon a won- 

 derful yet altogether simple experiment. It occurred 

 to him that when the moon is precisely dichotomized 

 that is to say, precisely at the half the line of vision 

 from the earth to the moon must be precisely at right- 

 angles with the line of light passing from the sun to 

 the moon. At this moment, then, the imaginary lines 

 joining the sun, the moon, and the earth, make a right- 

 angle triangle. But the properties of the right-angle 

 triangle had long been studied and were well under- 

 stood. One acute angle of such a triangle determines 

 the figure of the triangle itself. We have already seen 

 that Thales, the very earliest of the Greek philosophers, 

 measured the distance of a ship at sea by the applica- 

 tion of this principle. Now Aristarchus sights the 

 sun in place of Thales' ship, and, sighting the moon at 

 the same time, measures the angle and establishes the 

 shape of his right-angle triangle. This does not tell 

 him the distance of the sun, to be sure, for he does not 

 know the length of his base-line that is to say, of the 

 line between the moon and the earth. But it does es- 

 tablish the relation of that base-line to the other lines 

 of the triangle ; in other words, it tells him the distance 

 of the sun in terms of the moon's distance. As Aris- 

 tarchus strikes the angle, it shows that the sun is 

 eighteen times as distant as the moon. Now, by com- 

 paring the apparent size of the sun with the apparent 

 size of the moon which, as we have seen, Aristarchus 

 has already measured he is able to tell us that the 



218 



