HisroRT of the socitrr, 5 



]\lem. .Acad. Sciences, 1756, p. 301. There is a fifth rule, it 

 muft be obferved, neceffary for the cafe, when the three fides, 

 or three angles of the triangle, are given, as this cafe refufes to 

 fubmit to Napier's rule in any form of it. 



The author of the paper, now communicated to the Society, 

 has alfo been fuccefsful in his attempt to render the rules of tri- 

 gonometry eafily retained in the memory. He employs the 

 circular parts, and makes ufe of fewer rules than M. Pingre, 

 as he has only four, including one for the cafe jufb mentioned. 



The theorems Mr Fisher employs are not new, but they 

 are judicioufly feledled, and are lefs embarrafling in the ap- 

 plication than either thofe of Napier or Pingre, They are as 

 little as pofTible fubjedl to ambiguity ; they do not require the 

 letting fall a perpendicular, and they apply both to plane and 

 fpherical triangles. 



1. M denotes the middle part of the triangle, and muft al« 

 ways be affumed betwixt two given parts. It is either a fide or 

 the fupplement of an angle. 



2. A and a are the two parts adjacent to the middle, and of 

 a different denomination from it. 



3. O and o denote the two parts oppofite to the adjacent 

 parts, and of the fame denomination with the middle part. 



4. 1 is the laft or moft diftant part, and of a different deno-- 

 mination from the middle part. 



THEOR. 



