EUCLID'S AXIOMS AND POSTULATES

AXIOMS

1. Things which are equal to same thing are equal to one another.
2. If equals are added to equals, the wholes are equal.
3. If equals are subtracted from equals, the remainders are equal.
4. Things which coincide with one another are equal to one another.
5. The whole is greater than a part.
6. Things which are double of the same things are equal to one another.
7. Things which are halves of the same things are equal to one another.

POSTULATES

1. A straight line may be drawn from any one point to any other point.
2. A terminated line can be produced infinitely.
3. A circle can be drawn with any centre and any radius.
4. All right angles are equal to one another.
5. If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then two straight lines, if produced infinitely, meet on that side on which the sum of angles is less than two right angles.

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