THE DUPLICATION OF THE CUBE 



HIS problem became famous because of the halo 

 of mythological romance with which it was sur- 

 rounded. The story is as follows : 



About the year 430 B.C. the Athenians were 

 afflicted by a terrible plague, and as no ordinary means 

 seemed to assuage its virulence, they sent a deputation of 

 the citizens to consult the oracle of Apollo at Delos, in the 

 hope that the god might show them how to get rid of it. 



The answer was that the plague would cease when they 

 had doubled the size of the altar of Apollo in the temple 

 at Athens. This seemed quite an easy task ; the altar was 

 a cube, and they placed beside it another cube of exactly 

 the same size. But this did not satisfy the conditions pre- 

 scribed by the oracle, and the people were told that the 

 altar must consist of one cube, the size of which must be 

 exactly twice the size of the original altar. They then 

 constructed a. cubic altar of which the side or edge was 

 twice that of the original, but they were told that the new 

 altar was eight times and not twice the size of the original, 

 and the god was so enraged that the plague became worse 

 than before. 



According to another legend, the reason given for the 

 affliction was that the people had devoted themselves to 

 pleasure and to sensual enjoyments and pursuits, and had 

 neglected the study of philosophy, of which geometry is 



