88 Mr. Hellins's Second Appendix to the improved 



1 



+ 



3 

 8 



CC 



+ • 



3-5 

 8.8 



c 4 



a 



— 



i 



7 



CC 





3 



4.8 



c" 



a 



+ 



3 



8 



acc-{- 



3-5 

 8.8 



at 4 





— 



I 



T 



cc 



— 



3 

 4.8 



3 

 4.8 



c 4 



■c 4 



a +T a "'+17^ 4 



8.8 



CC —- C*. 



16 



Now the terms — \ cc and — T 3 ¥ c 4 may very easily be added 

 to the terms fee and gc 4 , i.e. to 0-1036802 cc and 0-0687064,^, 

 which will then become — 0-1463198 cc, and — 01 187936c 4 ; 

 and, by denoting the coefficients of these new terms by the 

 Roman letters — f and — g respectively, the first theorem in 

 the Art. before mentioned, or the value of A, is 



i — |_ e — fee — gc 4 



1 1 



(a + b) 



+ a + 4acc + 



44- ac 4 . 



3. The expression a, (— -f -~ cc -j- 3 ' t 5 2 21 c 4 ), which occurs 

 in the value of A', in Art. 12. of the first Appendix, is = 



4 



+ 3 ' 5 cc-l- 

 ■4.12 ■ 



3-5-2 1 -4 

 4.12.32 





a 



1 



~" 7 



-2- c 4 



4.8 





4 



a 4- -^-a cc 



4.12 



_L 3.5-" 



1 41232 



ac 4 





16 



3-5 

 12.16 



c 4 







9 



r* 



3-5 



3-5 21 



a 4. _£Z_ ac<? + -*^- 



1 4.12 '4.12.5 



— ~ cc ■— 

 16 



19 

 8.16 



ar 



r. 



8.16 



Here again the terms ^cc and — ^^ c 4 may very easily 



be added to the terms ice and kc 4 , i.e. to 00551502 cc and 



