% common-notions.tex — Euclid's five common notions (axioms of magnitudes).

\section*{Common Notions}
\label{sec:common-notions}

\begin{rrxivremark}[Common Notion~1]
\label{cn:1}
Things which are equal to the same thing are also equal to one another.
\end{rrxivremark}

\begin{rrxivremark}[Common Notion~2]
\label{cn:2}
If equals be added to equals, the wholes are equal.
\end{rrxivremark}

\begin{rrxivremark}[Common Notion~3]
\label{cn:3}
If equals be subtracted from equals, the remainders are equal.
\end{rrxivremark}

\begin{rrxivremark}[Common Notion~4]
\label{cn:4}
Things which coincide with one another are equal to one another.
\end{rrxivremark}

\begin{rrxivremark}[Common Notion~5]
\label{cn:5}
The whole is greater than the part.
\end{rrxivremark}