32 THE SEVEN FOLLIES OF SCIENCE 



a circle whose diameter is twice that of another will each 

 have an area four times that of the original. And in the 

 case of solids : A ball of twice the diameter will weigh 

 eight times as much as the original, and a ball of three times 

 the diameter will weigh twenty-seven times as much as the 

 original. 



In attempting to calculate the side of a cube which shall 

 have twice the volume of a given cube, we meet the old 

 difficulty of incommensurability, and the solution cannot be 

 effected geometrically, as it requires the construction of 

 two mean proportionals between two given lines. 



