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Euclid's Postulates

Euclid was a Greek mathematician who has been referred to as the 'father of geometry,' due in large part to a book he wrote called Elements. In this 13-volume book, he covers plane geometry, solid geometry, number theory, arithmetic theory, and irrational numbers. Quite possibly the most essential idea of Elements is the manner in which Euclid devised the logical steps necessary in proving assumptions. These assumptions are called axioms or postulates and are statements that are accepted as true without proof. He divided his ten axioms, which he called postulates, into two groups.

In simple language, Euclid's ten postulates are as follows:

  3. If equals are subtraced from equals, the remainders are equal
  5. The whole is greater than the part
  6. Between any two points a straight line may be drawn
  7. A straight line segment can be extended forever
  8. Given a line segment, a circle may be drawn having one endpoint as the center and the segment as the radius
  9. All right angles are congruent
  10. If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, then the straight lines, if extended indefinitely, meet on the side on which the angles lie (this is known as the Parallel Postulate)

In our geometry class, we will be learning about the fundamental ideas as indicated in Euclid's last five postulates.

So, what is the difference between an axiom and a postulate?

An axiom is a statement that is a 'given' and does not have to be proven. A postulate forms the basis for a theorem; it is the starting point.

©2014 Sherry Skipper Spurgeon for Geometry Bugs Me

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