# Definition:Euclid's Definitions - Book X/3 - Rational Line Segment

## Definition

In the words of Euclid:

*With these hypotheses, it is proved that there exist straight lines infinite in multitude which are commensurable and incommensurable respectively, some in length only, and others in square also, with an assigned straight line. Let then the assigned straight line be called***rational**, and those straight lines which are commensurable with it, whether in length and in square or square only,**rational**, but those which are incommensurable with it**irrational**.

(*The Elements*: Book $\text{X}$: Definition $3$)

## Sources

- 1926: Sir Thomas L. Heath:
*Euclid: The Thirteen Books of The Elements: Volume 3*(2nd ed.) ... (previous) ... (next): Book $\text{X}$. Definitions