In introduction to Euclid’s Geometry Class 9 I have explained all axioms & postulates given by Euclid.
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Euclid’d definition, axioms & postulates
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(i) A point is that which has no part
(ii)A line is breadthless length
(iii)The end of a line are points
(iv)A straight line is a line which lies evenly with the points on itself
(v)A surface which has length and breadth only
(vi) The edges of a surface are lines
(vii) A plane surface is a surface which lies evenly with the straight
lines on itself
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Euclids’ Axioms – Introduction to Euclid’s Geometry
(i) Things which are equal to the same things 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 thing are equal to one another.
Euclid’s Five postulates
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(i) A straight line may be drawn from any one point to any other points
(ii) A terminated line can be produced indefinitely
(iii) a circle can be drawn with any centre and any radius.
(iv)All right angles are equal to one another
(v)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 the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles
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Postulate 5 batayiea