3-Proportion and Theorem

<p>A 3-Proportion is an expression a:b:c where a, b, c ∈ Rational Numbers (Rat), not 0, with the convention that:

<i>a:b:c =&#160;λa:λb:λc for any </i>λ≠0

&#160;

Theorem:

a:b:c = d:e:f ⇔ ae-bd = 0, af-cd = 0, bf-ce = 0

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Three 2-proportions put together:

1. Ignore the 3rd element
   
2. Ignore the middle elements
   
3. Ignore the first elements</p>