ALEXANDRIAN OR HELLENISTIC PERIOD 



it seem but the more wonderful. Yet the method of 

 Eratosthenes, like many another enigma, seems simple 

 enough once it is explained. It required but the appli- 

 cation of a very elementary knowledge of the geometry 

 of circles, combined with the use of a fact or two from 

 local geography which detracts nothing from the 

 genius of the man who could reason from such simple 

 premises to so wonderful a conclusion. 



Stated in a few words, the experiment of Eratos- 

 thenes was this. His geographical studies had taught 

 him that the town of Syene lay directly south of Alex- 

 andria, or, as we should say, on the same meridian of 

 latitude. He had learned, further, that Syene lay 

 directly under the tropic, since it was reported that 

 at noon on the day of the summer solstice the gnomon 

 there cast no shadow, while a deep well was illumined 

 to the bottom by the sun. A third item of knowledge, 

 supplied by the surveyors of Ptolemy, made the dis- 

 tance between Syene and Alexandria five thousand 

 stadia. These, then, were the preliminary data re- 

 quired by Eratosthenes. Their significance consists in 

 the fact that here is a measured bit of the earth's arc 

 five thousand stadia in length. If we could find out 

 what angle that bit of arc subtends, a mere matter of 

 multiplication would give us the size of the earth. But 

 how determine this all-important number? The an- 

 swer came through reflection on the relations of con- 

 centric circles. If you draw any number of circles, of 

 whatever size, about a given centre, a pair of radii 

 drawn from that centre will cut arcs of the same 

 relative size from all the circles. One circle may be so 

 small that the actual arc subtended by the radii in 



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