Axiom:Euclid's Second Postulate

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): Euclid's axioms