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A Property of Proportions

by

Ángel M. Carreras Jusino

Goal:

• Show that if and , then .

Let and for some a, b, c, d, f, and g ∈ ℜ.

This implies that c = ka and d = kb for some k ∈ ℜ.

Similarly f = la and g = lb for some ∈ ℜ.

Now, lets check what is .

∴ If and , then

In a similar way can also be shown that if and , then:

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