E. Cobham Brewer 1810–1897. Dictionary of Phrase and Fable. 1898. 
 Reductio ad Absurdum.  
A proof of inference arising from the demonstration that every other hypothesis involves an absurdity. Thus, suppose I want to prove that the direct road from two given places is the shortest, I should say, “It must either be the shortest or not the shortest. If not the shortest, then some other road is the direct road; but there cannot be two shortest roads, therefore the direct road must be the shortest.”  1 


