1. The act of demonstrating; an exhibition; proof; especially, proof beyond the possibility of doubt; indubitable evidence, to the senses or reason. Those intervening ideas which serve to show the agreement of any two others are called proofs; and where agreement or disagreement is by this means plainly and clearly perceived, it is called demonstration. (Locke)
2. An expression, as of the feelings, by outward signs; a manifestation; a show. Did your letters pierce the queen to any demonstration of grief? (Shak) Loyal demonstrations toward the prince. (Prescott)
6. (Science: mathematics) 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.
(Science: logic) direct, or positive, demonstration, 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 i 3c8 ncorrect.