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Euclidean

Meaning & Application of Euclid’s Postulates

Euclid propounded some basic assumptions about line segment, circle and the congruent right angles. These assumptions are known as Euclid’s Postulates which are 5 in number and form one of the bases for his geometrical work of art called The Elements. The book also comprises of 23 definitions and 5 common notions.

Euclid's Postulates

A) Two points determine a line segment.
B) A line segment can be extended indefinitely along a line.
C) A circle can be drawn with a center and any radius.
D) All right angles are congruent.
E) If two lines are cut by a transversal, and the interior angles on the same side of the transversal have a total measure of less than 180 degrees, then the lines will intersect on that side of the transversal.

The last postulate is not as obvious as the other four, and Euclid himself was reluctant to use it. Later mathematicians, finding the fifth postulate to be complicated, thought it might be possible to derive it from the other four. However, they only succeeded in replacing it with equivalent statements.

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