THE SQUARING OF THE CIRCLE. 



AN HISTORICAL SKETCH OF THE PROBLEM FROM THE EARLIEST TIMES 

 TO THE PRESENT DAY.* 



By Hermann Schubert. 



I.— UNIVERSAL INTEREST IN THE PROBLEM. 



For two and a half thousand years both trained and nntrained minds 

 have striven in vain to solve the problem known as the squaring of the 

 circle. Now that geometers have at last succeeded in giving a rigid 

 demonstration of the impossibility of solving the problem with ruler 

 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 all the more justifiable in view of the fact that the squaring of 

 the circle, at least in name, is very widely known outside of the narrow 

 limits of professional mathematicians. 



The resolution of the French Academy. — The Proceedings of the French 

 Academy for the year 1775 contain, at page 61, the resolution of the 

 Academy not to examine, from that time on, any so-called solutions of 

 the quadrature of the circle that might be handed in. The Academy 

 was driven to this determination by the overwhelming multitude of pro- 

 fessed solutions of the famous problem, which were sent to it every 

 month in the year — solutions which, of course, were an invariable attes- 

 tation of the ignorance and self-consciousness of their authors, but 

 which suffered collectively from a very important error in mathematics : 

 they were tcrony. Since that time all professed solutions of the problem 

 received by the Academy find a sure haven in the waste-basket, and re- 

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

 this high-handed manner of rejection only the envy of the great towards 

 his grand intellectual discovery. He is determined to meet with recog- 

 nition, and appeals, therefore, to the public. The newspapers must 

 obtain for him the appreciation that scientitic societies have denied. 

 And every year the old mathematical sea serpent more than once dis- 

 ports itself in the columns of our papers, that a Mr. N. N., of P. P., has 

 at last solved the problem of the quadrature of the circle. 



* From Holtzendorflf and Vircbow's Samvilung gemeinversiandlicher tvisstnurhafllidier 

 Vorirufje, Hcift 67. Hamburg : Verlagsanstalt, etc. Ro-priiited from The Moiiisl, Jau- 

 uary, 18'Jl, vol. i, No. 2. pp. 197-228. 



H. Mis. 129 7 w 



