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An axiom or a postulate is a statement that is accepted without a proof. It is used as the basis for further reasoning and inferences to study the consequences that follow it. Consider the following analogy. An axiom can be thought of as a tree trunk. The roots relate to the mathematical definitions, the branches to theorems, and the leaves to corollaries.

In the book "The Elements of Geometry," written by the ancient Greek mathematician Euclid, he created a comprehensive model showing how all properties and theorems of geometry can be logically studied. The following five axioms detail Euclid's model.

  1. It is always possible to draw a straight line between any two points.
  2. Any straight line can be extended indefinitely.
  3. It is always possible to draw a circle with any given point as the center and any given radius.
  4. All right angles are equal.
  5. For any given line and a given point not lying on that line, there is exactly one line passing through that point that does not meet the given line.