112 THE SQUARING OF THE CIRCLE. 



Bovillius, and Orontius Finmis. — In the beginuiug of the sixteenth 

 century a certain Bovillius appears, who announccMl anew the construc- 

 tion of Cusa, meeting, however, with no notice. But about tlie mitUlle 

 of the sixteenth century a book was published which the scholars of 

 the time at first received with interest. It bore the proud title "i>e 

 Rebus MathematkiH Hactenus DesideratisP Its author, Orontius 

 Fiuams, represented that he had overcome all the difficulties that had 

 ever stood in the way of geometrical investigators; and incidentally he 

 also communicated to the world the " true quadrature" of the circle. 

 His fame was short-lived. For afterwards, in a book entitled "De 

 Erratis Orontii,'^ the Portuguese Petrus Nonius demonstrated that 

 Orontius's <iuadrature, like most of his other professed discoveries, was 

 incorrect. 



Simon Van Eyck, — In the period following this the number of cirde- 

 squarers so increased that we shall have to limit ourselves to those 

 whom mathematicians recognize. And particularly is Simon Van Eyck 

 to be mentioned, who towards the close of the sixteenth century pub- 

 lished a quadrature which was so approximate that the value of n de- 

 rived from it was more exact than that of Archimedes ; and to'disprove 

 it the mathematician Peter Metius was obliged to seek a still more 

 accurate value than 3}. The erroneous quadrature of Van Eyck was 

 thus the occasion of Metius's discovery that the ratio 355 : 113, or '^^{\j^ 

 varied from the true value of - by less than one one millionth, eclipsing 

 accordingly all values hitherto obtained. Moreover it is demonstrable 

 by the theory of continued fractions that, admitting figures to four 

 ])laces only, no two numbers more exactly represent the value of n thau 

 355 and 113. 



Joseph Scaliger. — In the same way the quadrature of the great phi- 

 lologist, Joseph Scaliger, led to refutations. Like most circle-squarers 

 who believe in their discovery, Scaliger also was little versed in the 

 elements of geometry. lie solved, however — at least in his own opin- 

 ion he did — tiie famous problem ; and published in 1502 a book up(m 

 it, which bore the pretentious title ^' Nova Cyclometria,^^ and in which 

 the name of Archimedes was derided. The worthlessness of his sup- 

 posed discovery was demonstrated to him by the greatest mathematic- 

 ians of his time, namely, Vieta, Adrianns Komanus, and Clavius. 



Longomontamis, John Porta, and Gregorii of St. Vincent. — Of the erring 

 circle-squarers that nourished before the middle of the seventeenth 

 century three others deserve particular mention; — Longomontanus of 

 Copenhagen, who rendered such gieat services to astronomy, the Nea- 

 politan John Porta, and Gregory of St. Vincent. Longomontanus made 

 ;r=3j'jV,Vrc'oi 'i"<^l ^^'^s s*> convinced of the correctness of his result that 

 he thanked God fervently, in the i)reface to his work ^^ Inventio Quad- 

 raturce Circuli,^^ that He had granteil him in his high old age the 

 strength to comiuer tlu' celebrated difficulty. John Porta followed the 

 initiative of Hippocrates, and believed he had solved the problem by 



