136 THE SQUARING OF THE CIRCLE. 



First to be mentioned is the celebrated English philosopher 

 Hobbes. In his book De Problematis Physids, in which he pro- 

 poses to explain the phenomena of gravity and of ocean tides, he 

 also takes up the quadrature of the circle and gives a very trivial 

 construction, which in his opinion definitively solved the problem. 

 It made TT = ^. In view of Hobbes's importance as a philosopher, 

 two mathematicians, Huygens and Wallis, thought it proper to 

 ^refute him at length. But Hobbes defended his position in a spe- 

 cial treatise, where to sustain at least the appearance of being right, 

 he disputed the fundamental principles of geometry and the the- 

 orem of Pythagoras. 



In the last century France especially was rich in circle-squarers. 

 We will mention : Oliver de Serres, who by means of a pair of 

 scales determined that a circle weighed as much as the square upon 

 the side of the equilateral triangle inscribed in it, that therefore 

 they must have the same area, an experiment in which 7T=3; 

 Mathulon, who offered in legal form a reward of a thousand dol- 

 lars to the person who would point out an error in his solution of 

 the problem, and who -was actually compelled by the courts to pay 

 the money ; Basselin, who believed that his quadrature must be 

 right because it agreed with the approximate value of Archimedes, 

 and who anathematised his ungrateful contemporaries, in the con- 

 fidence that he would be recognised by posterity ; Liger, who 

 proved that a part is greater than the whole and to whom therefore 

 the quadrature of the circle was child's play ; Clerget, who based 

 his solution upon the principle that a circle is a polygon of a defi- 

 nite number of sides, and who calculated, also, among other things, 

 how large the point is at which two circles touch. 



Germany and Poland also furnish their contingent to the army 

 of circle-squarers. Lieutenant-Colonel Gorsonich produced a quad- 

 rature in which 7t equalled 3^, and promised fifty ducats to the per- 

 son who could prove that it was incorrect. Hesse of Berlin wrote 

 an arithmetic in 1776, in which a true quadrature was also "made 

 known," n being exactly equal to 3^$. About the same time Pro- 

 fessor Bischoff of Stettin defended a quadrature previously pub- 

 lished by Captain Leistner, Preacher Merkel, and Schoolmaster 



