# Axiom:Euclid's Second Postulate

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## Postulate

A straight line segment can be extended indefinitely to form a straight line.

In the words of Euclid:

*To produce a finite straight line continuously in a straight line.*

(*The Elements*: Book $\text{I}$: Postulates: Euclid's Second Postulate)

### Production

The process of extending a straight line segment is called **production**.

Such a straight line segment is said to be **produced**.

The line segment can be extended in either direction, thus producing an infinite half-line, or in both directions, thus producing an infinite straight line.

## Sources

- 1926: Sir Thomas L. Heath:
*Euclid: The Thirteen Books of The Elements: Volume 1*(2nd ed.) ... (previous) ... (next): Book $\text{I}$. Postulates - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**Euclid's axioms**