THE ALEXANDRIAN PERIOD 



83 



the length of 5,000 stadia, calculated by the day's 

 march accomplished by caravans, is necessarily only 

 approximate. The measurement found by Eratos- 

 thenes is nevertheless an interesting datum. Had 

 Newton been acquainted with it, he would have been 

 able to verify his hypothesis of gravitation, without 

 being obliged to shelve it for years * until Picard 

 succeeded in measuring the radius of the earth more 

 exactly. In other realms of knowledge, Eratosthenes 

 showed himself to be an erudite and remarkable 

 savant, whom Archimedes held in high esteem, and with 

 whom he wished to collaborate in his own researches. 

 We do not know very much of his work, except the 



Sj/eue 



Fig. 8. 



Sieve, which bears his name, which is a method of 

 finding the sequence of prime numbers. He also 

 invented, for finding the value of two mean propor- 

 tionals, an ingenious mesolabe, which he placed in a 

 temple of Alexandria with a dedication in honour of 

 Ptolemy II. Finally, he devised the Calendar after- 

 wards known as the Julian Calendar. 



Astronomy, like geography, developed in a remark- 

 able manner during this period, owing to the combined 

 progress of mathematics, mechanics and technique. 

 The surveying instruments with their screws and 

 toothed wheels were of great assistance to astronomers, 

 for instance the apparatus invented by Archimedes for 

 measuring the diameter of the sun. 



1 23 Rouse Ball, History of Mathematics, II, p. 16. 



