# Definition:Commensurable/Notation

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## Definition

There appears to be no universally acknowledged symbol to denote commensurability.

Thomas L. Heath in his edition of *Euclid: The Thirteen Books of The Elements: Volume 3, 2nd ed.* makes the following suggestions:

- $(1): \quad$ To denote that $A$ is commensurable or commensurable in length with $B$:
- $A \mathop{\frown} B$

- $(2): \quad$ To denote that $A$ is commensurable in square with $B$:
- $A \mathop{\frown\!\!-} B$

- $(3): \quad$ To denote that $A$ is incommensurable or incommensurable in length with $B$:
- $A \mathop{\smile} B$

- $(4): \quad$ To denote that $A$ is incommensurable in square with $B$:
- $A \mathop{\smile\!\!-} B$

This convention may be used on $\mathsf{Pr} \infty \mathsf{fWiki}$ if accompanied by a note which includes a link to this page.

## Sources

- 1926: Sir Thomas L. Heath:
*Euclid: The Thirteen Books of The Elements: Volume 3*(2nd ed.) ... (previous) ... (next): Book $\text{X}$. Propositions: Footnote to Proposition $11$