38 HISTORY OF SCIENCE. 



preaches by increase in the number of its sides, without the possibility 

 of its absolutely reaching it. It is by the adoption of this principle 

 that Euclid is able to prove that the areas of circles are to each other 

 as the squares of their respective diameters. 



ARISTARCHUS OF SAMOS (c. third century B.C.) is famous for his 

 efforts in behalf of the Pythagorean doctrine of the earth's motion. He 

 taught that the sun was stationary, and that the earth revolved about 

 that luminary. He even explained away the objection which would be 

 brought forward against this doctrine, namely, that if the earth moved 

 as he alleged, the stars ought to present varying aspects : he said that 

 the reason this change in the apparent position of the stars did not 

 take place was because they were at so great a distance that the earth's 

 orbit was a mere point in comparison. A contemporary of the astrcP 

 nomer raised another kind of objection to the doctrine of the earth's 

 motion, by declaring that its author was leaving no space for the repose 

 of the gods ; but perhaps this objection was not urged in seriousness. 

 Had it been so, Aristarchus might have incurred no small risk in earn- 

 ing the title of the Greek Galileo. 



Aristarchus hit upon an ingenious method of forming an estimate 

 of the relative distances of the sun and moon from the earth. He 

 knew that the moon is a spherical opaque body illuminated by the 

 sun. He reasoned that when the moon is seen exactly divided into 

 a dark and a light semicircle, the straight line joining the moon and 

 the sun must be at right angles to the line between the moon and the 



observer. Thus, in Fig. u, let the obser- 

 ver's station on the earth be represented by 

 E ; when he sees the illumined side of the 

 moon at M as an exacT half-circle, it is ob- 

 vious that the line s M, between the sun and 

 moon, will be at right angles to the line E 

 FIG. it. M. Now, it frequently happens that the 



half-moon and the sun are simultaneously 



visible, and it is only necessary to measure the angle between them in 

 order to find the angle formed by the lines M E, E s. When this has 

 been ascertained, a triangle constructed on a line M E, with an angle at 

 E equal to the observed angle and with a right angle at M, would show 

 the relative distances from the earth to the sun and moon by the 

 lengths of the lines E s and E M. Aristarchus found that the angle 

 M E s was not less than 87, and that therefore the sun was at eighteen 

 or twenty times the distance of the moon ; and although this is vastly 

 below the reality, the estimate of Aristarchus greatly extended the 

 limits of the universe as they were accepted in his time. 



Another Alexandrian astronomer, ERATOSTHENES (B.C. 270 196), 

 attempted an exact measure of the magnitude of the earth, and the 

 method he adopted was in principle thefsame as astronomers have 

 used ever since. He had observed that at his native city of Syene, 



