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How to prove that all Heronian triangles can be found using formulas described here?

I understand that the described substitution will give Heronian triangle, but how to prove that using the described substitution will give all Heronian triangles (with scaling solutions, for example $(12,10,10)$ is obtained when multiplying $(6,5,5)$ by $2$)?

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    Perhaps related: http://math.stackexchange.com/questions/114112/heronian-triangle-generator2012-03-01
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    [This](http://www.gutenberg.org/files/20073/20073-pdf.pdf) appears to be the Carmichael publication referred to in the Wikipedia article.2012-05-01

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