\begin{definition}[Definition:Harmonic Range]
Let $A$ and $B$ be points on a straight line.
Let $P$ and $Q$ lie on $AB$ such that $P$ is on the line segment $AB$ while $Q$ is outside the line segment $AB$.
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Let $P$ and $Q$ be positioned such that:
:$\dfrac {AP} {PB} = -\dfrac {AQ} {QB}$
Then $\tuple {AB, PQ}$ are said to be a '''harmonic range'''.
\end{definition}