ON THE 



INSCRIPTION 



OF A 



REGULAR POLYGON OF SEVENTEEN SIDES IN A CIRCLE ; 



OR DIVISION OF THE CIRCUMFERENCE INTO SEVENTEEN 



EQUAL PARTS. 



BY SAMUEL JAMES, ESQ. 



PRESENTED BY THE Rev. FRANCIS SADLEIR, D. D. F.T.CD. M.R.I. A. 



Read, January 2+, 1820. 



The inscription of all r^ular polygons in a circle, besides those 

 of which the constructions are given in the elements of Euclid, and 

 those arising fi'om them by continual bisections, or taking their 

 differences, has been thought for ages to exceed the powers of 

 elementary geometry ; and, through the progress of mathematical 

 discovery from the time of the ancient Greek geometricians, no 

 addition to the number, as known to them, appears to have been 

 made until about the beginning of the present century ; when an 

 unexpected discovery was made by M. Gauss of certain other regular 

 polygons, which yet admitted of being inscribed geometrically in a 

 circle. This discovery was announced to the public in a work pub- 

 lishisd by him at Leipsic in the year 1801, entitled, Disquisitiones 



