6. (Math.) A course of reasoning showing that a certain result is a necessary consequence of assumed premises; -- these premises being definitions, axioms, and previously established propositions.
Direct, or Positive, demonstration (Logic & Math.), one in which the correct conclusion is the immediate sequence of reasoning from axiomatic or established premises; -- opposed to Indirect, or Negative, demonstration (called also reductio ad absurdum), in which the correct conclusion is an inference from the demonstration that any other hypothesis must be incorrect.
De*mon"stra*tive (?), a. [F. démonstratif, L. demonstrativus.] 1. Having the nature of demonstration; tending to demonstrate; making evident; exhibiting clearly or conclusively. "Demonstrative figures." Dryden.
An argument necessary and demonstrative.
Hooker.
2. Expressing, or apt to express, much; displaying feeling or sentiment; as, her nature was demonstrative.