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.

Welcome to Mathematics Stack Exchange. How about if $a/b=c/d$ and $e/f=c/d$ then $a/b=e/f$? — J. W. Tanner, May 21 '20 at 20:28

score -1 · Accepted Answer · answered May 21 '20 at 20:46

-1

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

answered May 21 '20 at 20:46

Allawonder

Euclid's "ratios" are not the same as rational numbers. (They are essentially equivalent to positive real numbers.) – Eric Wofsey May 21 '20 at 21:00
@EricWofsey, We should supposedly take your word for it, huh? – Allawonder May 21 '20 at 21:29

1 Answers1