\begin{definition}[Definition:Harmonic Pencil]
Let $A$ and $B$ be points on a straight line.
Let $P$ and $Q$ lie on $AB$ such that $\tuple {AB, PQ}$ is a harmonic range.
Let $O$ be a point which is not on the straight line $AB$.
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Then the pencil $\map O {AB, PQ}$ formed by joining $O$ to the four points $A$, $B$, $P$ and $Q$ is said to be a '''harmonic pencil'''.
\end{definition}