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Concept

Axiom

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.
Diagram_Analogy

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.