What does ':' and '::' mean in algebra?

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In the book I'm reading it says about ratios and proportions,

If $a:b::c:d;$ then $ad=bc$, and $\frac{a}{b}=\frac{c}{d}$

What do ':' and '::' mean? Also, it is not stating the above as a definition.

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1 Answer

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$a:b$ denotes the ratio of $a$ to $b$.

$a∶b∷c∶d$ is a proportion, a statement expressing the equality of the two ratios $a:b$ and $c:d$.

In English, it is often expressed as follows: $a$ is to $b$ as $c$ is to $d$.

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