THE SQUARING OF THE CIRCLE. 99 



The allurements of the problem. — Attention must first be called to 

 the antiquity of the problem. A quadrature was attempted in Egypt 

 500 years before the exodus of the Israelites. Among the Greeks the 

 problem never ceased to play a part that greatly influenced the pro- 

 gress of mathematics. And in the middle agesalso the squaring of the 

 circle isporadically appears as the philosopher's stone of mathematics. 

 The problem has thus never ceased to be dealt with and considered. 

 But it is not by the antiquity of the problem that circle-squarers are 

 enticed, but by the allurement which everything exerts that is calcu- 

 lated to raise the individual out of the mass of ordinary humanity, and 

 to bind about his temples the laurel crown of celebrity. It is ambition 

 that spurred men on in ancient Greece and still spurs them on in mod- 

 ern times to crack this primeval mathematical nut. 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 to that of any other. They do not remember 

 that— 



Toil before houor is placed by sagacious decrees of Immortals, 



and that it requires years of continued studies to gain possession of the 

 mathematical weapons that are indispensably necessary to attack the 

 problem, but which even in the hands of the most distinguished math- 

 ematical strategists have not sufficed to take the stronghold. 



About the only problem hnown to the lay world. — But how 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 mathematical questions? The question is 

 answered by the fact that the squaring of the circle is about the only 

 mathematical problem that is known to the unprofessional world — at 

 least by name. P^ven among the Greeks the problem was very widely 

 known outside of mathematical 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 desig- 

 nate this species of activity, namely, nrpaywAZiiv, which means to 

 busy one's self with the quadrature. In modern times, also, every ed- 

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

 by name, and knows that it is insolvable, 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 used in the 

 sense of attempting the impossible. • 



Belief that rewards have been offered. — But in addition to the antiquity 

 of the problem, and the fact also that it is known to the lay world, we 

 have yet a third factor to point out that induces people to take up with 

 it. This is the report that has been spread abroad for a hundred years 

 now, that the Academies, the Queen of England, or some other influeu- 



