Thursday, March 9, 2023

Euclid's five postulates


Postulate 1

A straight Line may be drawn from any one point to any other point.

In other words , we can say that, at least one straight line passes though two distinct point.


Postulate 2

A terminated line can be produced indefinitely.

Terminated line means line segment . So according to the postulate, a line segment can be extended on either side to form a line



Postulate 3

A circle can be drawn with any centre and any radius.

Postulate 4

All right angles are equal to one another.

In other words , we can say that , atleast one straight line passes though two distinct point.

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, then the two straight lines, if produced infinitely , meet on that side on which the sum of angles is less than two right angles.


For example , the line PQ in above figure falls on lines AB and CD such that the sum of the interior angles is less than 180 degrees (less than two right angles as per the Euclid) on left side of the line PQ. Therefore , the lines AB and CD will eventually  intersect on the left side of the PQ.

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