THE SQUARING OF THE CIRCLE. . 115 



Whether they are competent thereto is a secondary consideration. 

 They look upon the squaring of the circle as. the grand prize of a 

 lottery that can just as well fall to their lot as that of any other 

 man. They do not remember that 



"Toil before honor is placed by sagacious decrees of Immortals." 



and that it requires years of consecutive study to gain possession of 

 the mathematical weapons that are indispensably necessary to at- 

 tack the problem, but which even in the hands of the most distin- 

 guished mathematical strategists did not suffice to take the strong- 

 hold. 



But why is it, we must further ask, that it happens to be the 

 squaring of the circle and not some other unsolved mathematical 

 problem upon which the efforts of people are bestowed who have 

 no knowledge of mathematics yet busy themselves with mathemati" 

 cal questions? The question is answered by the fact that the squar- 

 ing of the circle is about the only mathematical problem that is 

 known to the unprofessional world, at least by name. Even among 

 the Greeks the problem was very widely known outside of mathe- 

 matical circles. In the eyes of the Grecian layman, as at present 

 among many of his modern brethren, occupation with this problem 

 was regarded as the most important and essential business of 

 mathematicians. In fact, they had a special word to designate this 

 species of activity, namely, TeTpayoweev, which means to busy one's 

 self with the quadrature. In modern times, also, every educated 

 person, though he be not a mathematician, knows the problem by 

 name, and knows that it is insoluble, or at least, that despite the 

 efforts of the most famous mathematicians it has not yet been 

 solved. For this reason the phrase "to square the circle," is now 

 generally used in the sense of attempting the impossible. 



But in addition to the antiquity of the problem, and the fact 

 also that it is known to the lay world, there is an important third 

 factor that induces people to occupy themselves with it. This is the 

 report that has been current for more than a century now, that the 

 Academies, the Queen of England, or some other influential person 

 has offered a large prize to be given to the one that first solves the 



