% postulates.tex — The five postulates of Euclidean plane geometry.
%
% Postulates are recorded as rrxivremark blocks so the parser
% addresses them but doesn't confuse them with falsifiable claims.

\section*{Postulates}
\label{sec:postulates}

\begin{rrxivremark}[Postulate~1]
\label{post:1}
To draw a straight line from any point to any point.
\end{rrxivremark}

\begin{rrxivremark}[Postulate~2]
\label{post:2}
To produce a finite straight line continuously in a straight line.
\end{rrxivremark}

\begin{rrxivremark}[Postulate~3]
\label{post:3}
To describe a circle with any centre and distance.
\end{rrxivremark}

\begin{rrxivremark}[Postulate~4]
\label{post:4}
That all right angles are equal to one another.
\end{rrxivremark}

\begin{rrxivremark}[Postulate~5 (the parallel postulate)]
\label{post:5}
That, if a straight line falling on two straight lines makes the
interior angles on the same side less than two right angles, the two
straight lines, if produced indefinitely, meet on that side on which
are the angles less than the two right angles.
\end{rrxivremark}
