

JOURNAL 



OF 



NATURAL PHILOSOPHY, CHEMISTRY 



AND 



THE ARTS. 



DECEMBER, 1805. 

 ARTICLE I. 



On the Divijion of an Arch of a Circle into two fuch Parts, that 

 their Sines, or Cofines, or Verfed-Sines, Jhall Iiave a given Re- 

 lation. In a Letter from John Gough, Efq. 



To Mr. NICHOLSON. 

 SIR, 



JDEING at prefent on a vifit to my friend Michael Fryer, Introductory 

 teacher of the mathematics at this place, I have availed myfelf letter ' 

 of the opportunity to confult his very extenlive mathema- 

 tical library, with a view to difcover how far the following 

 theorems and problems are original ; thinking it poffible, at 

 leaft, that fimilar propositions might be met with in the works 

 of the early geometricians, particularly in the traces on An- 

 gular Sections, by Viela, Oughtred, Wallis, and others, which 

 I had never before been able to meet .with ; but I have found 

 only one of them to have been already treated, of which no- 

 tice (hall be taken in its proper place : neverthelefs, it is not 

 improbable but that fimilar theorems and problems are fcatteted 

 up and down in the different works on geometry at prefent in 

 ^xiftence : As this eflay, however, may claim the merit of 

 Voe. XII.— December, 1805. Q c*» 



