xviii.] OBSERVATION. 415 



equation to which there could be no corresponding plane 

 geometrical solution. 1 This is a case of reductio ad 

 absurdum, a form of argument of a totally different 

 character. Similarly no number of failures to obtain a 

 general solution of equations 'of the fifth degree would 

 establish the impossibility of the task, but in an indirect 

 mode, equivalent to a reductio ad absurdum, the impossi- 

 bility is considered to be proved. 



1 Peacock, Algebre, vol. ii. p. 344.- 



2 Ibid, p. 359. Serret, Algebre Superieure, 2nd ed. p. 304. 



