112 THE SQUARING OF THE CIRCLE. 



Bovillius, and Orontius Finceus. — In the beginuing of the sixteenth 

 century a certain Bovillius appears, who announced anew tlie construc- 

 tion of Cusa, meeting, however, with no notice. But about the middle 

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

 the time at first received with interest. It bore the proud title "De 

 Rebus Mathematicis Hactenus DesideratisP Its author, Orontius 

 Fiuffius, 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 quadrature, like most of his other professed discoveries, was 

 incorrect. 



Simon Van Eyck. — In the period following this the number of circle- 

 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 3i. The erroneous quadrature of Van Eyck was 

 thus the occasion of Metius's discovery that the ratio 355: 113, or 3yL^3, 

 varied from the true value of n 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 

 places only, no two numbers more exactly represent the value of n than 

 355 and 113. 



Joseph Scaliger. — In the same way the quadrature of the great i)hi- 

 lologist, Josei)h Scaliger, led to refutations. Like most circle-squarers 

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

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

 ion he did — the famous problem ; and published in 1592 a book upon 

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

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

 posed discovery was demonstrated to him by the gieatest mathematic- 

 ians of his time, namely, Vieta, Adriauus Eomanus, and Olavius. 



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

 circle-squarers that fiourished before the middle of the seventeenth 

 century three others deserve particular mention; — Longomontanus of 

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

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

 7r=3j^^-^^^%, and was so convinced of the correctness of his result that 

 he thanked God fervently, in the preface to his work '•'■ Inventlo Quad- 

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

 strength to conquer the celebrated difficulty. John Porta followed the 

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



