Page 4 - Lesson Notes-Euclid Definitions,Axioms and Postulates Ch-5(Introduction to Euclid')

Euclid‟s Axioms and Postulates

Euclid assumed some properties which were actually „obvious universal

truth‟. He had bifurcated them in two types: Axioms and postulates.

AXIOMS

The basic facts (obvious and universal truths) which are taken for granted, without
proof and are used throughout in mathematics are called Axioms.

Some of Euclid Axioms are-

1. Things which are equal to the same thing are equal to one another.

If p = q and s = q, then p = s.

2. If equals are added to equals, then the wholes are equal.

If p = q and we add s to both p and q then the result will also be equal.

p + s = q + s

3. If equals are subtracted from equals, then the remainders are equal.

This is same as above, if p = q and we subtract the same number from both,
then the result will be the same.

p – s = q – s

4. Things which coincide with one another are equal to one another.

If two figures fit into each other completely then these must be equal to one
another.

5. The whole is greater than the part.

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