# Summary

Euclid defined a point, a line and a plane. But these definitions are not accepted by mathematicians. We take a point, line and plane as undefined terms.

Axioms or postulates are only assumptions which are obvious truths. They are not proved.

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Some of the Euclidâ€™s axioms were :

(i) Things which are equal to the same thing are equal to one another.

(ii) If equals are added to equals, the wholes are equal.

(iii) If equals are subtracted from equals, the remainders are equal.

(iv) Things which coincide with one another are equal to one another.

(v) The whole is greater than the part.

(vi) Things which are double of the same things are equal to one another.

(vii) Things which are halves of the same things are equal to one other.

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Euclidâ€™s Postulates were :

Postulate 1: A straight line may be drawn from any one point to any other point.

Postulate 2: A terminated line can be produced indefinitely

Postulate 3: A circle can be drawn with any centre and any radius.

Postulate 4: All right angles are equal to one another.Postulate 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; the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles

Two equivalent versions of Euclidâ€™s fifth postulate are

(i) â€˜For every line* l * and for every point P not lying on *l*, there exists a unique line *m * passing through P and parallel to *l*â€™.