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What are the formulas for proportional line segments?

If a/b=c/d, then ad=bc.

This is the basic nature.

From a/b=c/d, we can deduce the properties of the combination ratio: (a b)/b = (c d)/d, and a/(b a) = c/(d c).

There are also proportional properties: if a/b=c/d=…=m/n(b, d, …, m is not 0 and b+d+…+n≠0), then (a+c+…+m)/(b+d+…+n) = a/b.

Others are about geometry, which should be related to specific diagrams.

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