[ 343 ] 



.. . ^J^h ^ .. 8/3 

 2/x + 2^^ = r>= — ^ — or <7 = X' = 



3. . .. \ 2o8/5 t \_ q6/* 

 2 /at + 2. 3 ;c;<^ = B = Tj or a = iv — ^ 



2 



7* 2-3^^ t, 24C0/' 5 ? c:6o/5 



llx + , = B — : or tf = ;f — 



• • ~ r* ~ r^ 



2. 4. XX 



2. ^xx I ? / 7232 /« 

 2 /x5 + .. 5 = B _ _ 34624 or <? = ^ = 



2.10 A' A' ^ 



&c. &c. 



Hence while / by flowing from becomes /, a from a femi- 

 quadrant becomes = 



a femiquadr. + / - — + ~ — - — + -^ — — — + &c. 

 r 3/-^ 3r3 3r+ 45^5 



The two laft examples are feries of Gregory's from the Comm. 

 Epift. For an account and different methods of inveftigating 

 them fee Scrip. Log. Vol. III. preface and pages 443, &c. 

 , 480, &c. 



Ex.iMPLE V. To expand the mviltinomial. 



a + i> z + c z^ ^ dz'i + Scc^ where n is of any denomination 

 whole, negative or fradional. (De Moivrc Mifcell. Analytica, 

 p. 87). 



Let 



