SQUARING THE CIRCLE II 



their Transactions. Attempts to "square the circle," 

 when made intelligently, were not only commendable but 

 have been productive of the most valuable results. At the 

 same time there is no problem, with the possible exception 

 of that of perpetual motion, that has caused more waste of 

 time and effort on the part of those who have attempted 

 its solution, and who have in almost all cases been ignorant 

 both of the nature of the problem and of the results which 

 have been already attained. From Archimedes down 

 to the present time some of the ablest mathemati- 

 cians have occupied themselves with the quadrature, or, 

 as it is called in common language, "the squaring of the 

 circle " ; but these men are not to be placed in the same 

 class with those to whom the term " circle-squarers " is 

 generally applied. 



As already noted, the great difficulty with most circle- 

 squarers is that they are ignorant both of the nature of 

 the problem to be solved and of the results which have 

 been already attained. Sometimes we see it explained as 

 the drawing of a square inside a circle and at other times 

 as the drawing of a square around a circle, but both these 

 problems are amongst the very simplest in practical geo- 

 metry, the solutions being given in the sixth and seventh 

 propositions of the Fourth Book of Euclid. Other defini- 

 tions have been given, some of them quite absurd. Thus 

 in France, in 1753, M. de Causans, of the Guards, cut a 

 circular piece of turf, squared it, and from the result de- 

 duced original sin and the Trinity. He found out that the 

 circle was equal to the square in which it is inscribed, and 

 he offered a reward for the detection of any error, and ac- 

 tually deposited 10,000 francs as earnest of 300,000. But 

 the courts would not allow any one to recover. 



