Definition:Commensurable/Notation

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 $11$