Writing Euclid's proposition "Ratios which are the same with the same ratio are also the same with one another" in contemporary style

Question

I need to write the Proposition 11 in Book 5 of Euclid's Elements according to contemporary style. It states that:

Ratios which are the same with the same ratio are also the same with one another.

The clue in book says that it is about transitivity. However I could not indicate it mathematically.

May you help me to write it by using an if-then statement or another way? Thanks for your helps.

Answer 1

Let a, b and c be rational. If $a=b$ and $b=c,$ then $a=c.$