I'm reading through some geometry proofs, and I can see something like
$AB^2:PM\times EB::BC^2\ :CD\times PQ$
So I understand that $A:B$ is equivalent to $\frac{A}{B}$, but what does the $::$ mean?
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HINT
$$ A:B :: C:D \equiv \implies \dfrac{A}{B} = \dfrac{C}{D} $$
The notation is called proportion.
$A$ is to $B$ as $C$ is to $D$.
hjpotter92
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I wonder why they could not have just simply said A:B=C:D instead, which is much less ambiguous. – Trogdor Sep 14 '14 at 07:21
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2How is this a "hint"...? – Najib Idrissi Sep 14 '14 at 12:00
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Is $B=D=0$ allowed on the left hand side (at least when $A \not =0$ and $D \not = 0$) but not on the right? – Henry May 28 '19 at 12:34
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Assuming it says $CD \times PQ$ instead of $CD \times : PQ$, I believe the above statement is equivalent to \begin{align*} \frac{AB^2}{PM \times EB} = \frac{BC^2}{CD \times PQ} \end{align*}
symmetricuser
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