THE SQUARING OF THE CIRCLE. 



AN HISTORICAL SKETCH OF THE PROBLEM FROM 'THE RE- 

 MOTEST TIMES. 



i. 

 UNIVERSAL INTEREST IN THE PROBLEM. 



T7O R two and a half thousand years, both competent and incom- 

 * petent minds have striven in vain to solve the problem known 

 as the squaring of the circle. Now that geometers have at last suc- 

 ceeded in giving a rigorous demonstration of the impossibility of 

 solving the problem with straight edge and compasses, it seems 

 fitting and opportune to cast a glance into the nature and history 

 of this very ancient problem. And this will be found the more jus- 

 tifiable in view of the fact that the squaring of the circle, at least 

 in name, is very widely known outside of the narrow circle of pro- 

 fessional mathematicians. 



The Proceedings of the French Academy for the year 1775 con- 

 tain at page 61 a resolution of the Academy not to examine from 

 that time on, any so-called solutions of the quadrature of the circle. 

 The Academy was driven to this determination by the overwhelm- 

 ing multitude of professed solutions of the famous problem which 

 were sent to it every month in the year, solutions which of course 

 were an invariable attestation of the ignorance and self-conceit of 

 their authors, but which suffered collectively from the very impor- 

 tant drawback in mathematics of being wrong. Since that time all 

 professed solutions of the problem received by the Academy find a 

 sure and permanent resting-place in the waste-basket, and remain 

 unanswered for all time. The circle-squarer, however, sees in this 



