ABSURD

, or Absurdum, a term commonly used in demonstrating converse propositions; a mode of demonstration, in which the proposition intended is not proved in a direct manner, by principles before laid down; but it proves that the contrary is absurd or impossible; and so indirectly as it were proves the proposition itself. The 4th proposition in the first book of Euclid, is the first in which he makes use of this mode of proof; where he shews that if the extremities of two lines coincide, those lines will coincide in all their parts, otherwise they would inclose a space, which is absurd or contrary to the 10th axiom. Most converse propositions are proved in this way, which mode of proof is called reductio ad absurdum.