84 OBSERFATIONS on the 



ftiticflion of the tables contained in this trigonometry, that I 

 now beg leave to ofter a few remarks. 



2. It is necelTary to begin with obferving, that the cir- 

 cumference of the circle is here divided into 360 equal parts, 

 each of which is again fubdivided into 60, and fo on. The 

 fame divifion was followed by the Greek mathematicians ; 

 and this coincidence is the more to be remarked, that it re- 

 lates to a matter of arbitrary arrangement, and one by no 

 means neceflarily connected with the properties of the circle. 

 There are indeed fome very obvious properties of that curve, 

 that make it, though not neceffary, at leaft convenient, that the 

 number of parts, into which the circumference is divided, fhould 

 be a number divifible both by 3 and by 4, that is, that it fhould 

 be a multiple of 1 2 ; but nothing more precife can be determin- 

 ed from the nature of the curve itfelf. The agreement of 

 / two nations, therefore, in dividing the circumference of the 



circle precifely in the fame manner, as it cannot well be attri- 

 buted to chance, mufl be fuppofed to refult from fome communi- 

 cation having taken place between them, if it were not that ano- 

 ther very probable caufe may be affigned for it. In Greece, and 

 no doubt in every other country, the divifion of the circle, i ito 

 equal parts, is of a much older date than the origin of trigono- 

 metry, and muft be as ancient as tlie firft circular inftruments 

 ufed for meafurlng angles in the heavens. The inventors of 

 thofe inftruments naturally fought to make the divifions on them 

 correfpond to the fpace which the fun defcribed daily in the 

 ecliptic ; and they could eafily difcover, without any very pre- 

 ' cife knowledge of the length of the folar year, that this might 



be nearly effetfted by making each of them the 360th part of 

 the whole circumference. Accordingly the famous circle of 

 OsYMANDiAs, in Egypt, defcribed by Herodotus, was divided 

 into 360 eqtial parts. 



This 



