[ ^5^ ] 



^GENERAL DEMONSTRATION of the PROPERTY of tJie 

 CIRCLE difcovered by Mr. COTES deduced from the CIRCLE 

 only. By the Rev. J. BRINKLEY, ^. M. ANDREWS Pro- 

 feffor ofJJironomy, and M. R. I. A, 



HE very elegant property of the circle difcovered by the cele- ReadNov.4th 

 brated Cotes has for its extenfive ufes always been juftly efteemed '^^'' 

 among mathematicians. The inventor left no demonftration of 

 it; and although it immediately excited the attention of the moft 

 eminent cultivators of the fcience, yet no general invefligation 

 has been hitherto given, if we except one derived from the hyperbola 

 and ifnpoffible expreflions, which was firft given by De Moivre, 

 afterwards by Maclaurin and other authors. But the elegance of 

 the theorem and the ftridtnefs of mathematical reafoning feem to 

 require a very different kind of demonflration. The author of 

 " Epiftola ad Amicum de inventis Cotefii," has indeed attempted 

 a dem.onftration from the circle only ; however it will readily appear 

 on examination that it is not general, even conceding the demon- 

 flration 



