Il6 THE SQUARING OF THE CIRCLE. 



problem. As a matter of fact, the hope of obtaining this large 

 prize of money is with many circle-squarers the principal incitement 

 to action. And the author of the book above referred to begs his 

 readers to lend him their assistance in obtaining the prizes offered. 



Although the opinion is widely current in the unprofessional 

 world, that professional mathematicians are still busied with the 

 solution of the problem, this is by no means the case. On the con- 

 trary, for some two hundred years, the endeavors of many great 

 mathematicians have been directed solely towards demonstrating 

 with exactness that the problem is insoluble. It is, as a rule, 

 and naturally, more difficult to prove that a thing is impossible 

 than to prove that it is possible. And thus it has happened, that 

 up to within a few years ago, despite the employment of the most 

 varied and the most comprehensive methods of modern mathemat- 

 ics, no one succeeded in supplying the wished^for demonstration of 

 the problem's impossibility. At last, Professor Lindemann, now 

 of Munich, in June, 1882, succeeded in furnishing a demonstra- 

 tion, and the first demonstration, that it is impossible by em- 

 ploying only straight edge and compasses to construct a square 

 that is mathematically exactly equal in area to a given circle. The 

 demonstration, naturally, was not effected with the help of the old 

 elementary methods; for if it were, it would have been accom- 

 plished centuries ago ; but methods were requisite that were first 

 furnished by the theory of definite integrals and departments of 

 higher algebra developed in the last few decades ; in other words, 

 it required the direct and indirect preparatory labor of many cen- 

 turies to make finally possible a demonstration of the insolubility 

 of this historic problem. 



Of course, this demonstration will have no more effect than 

 the resolution of the Paris Academy of 1775, in causing the fecund 

 race of circle-squarers to vanish from the face of the earth. In the 

 future as in the past, there will be people who know nothing of 

 this demonstration and will not care to know anything, and who 

 believe that they cannot help succeeding in a matter in which oth- 

 ers have failed, and that just they have been appointed by Provi- 

 dence to solve the famous puzzle. But unfortunately the inerad- 



