The most important definition of Book 5 of Euclid's Elements which was never understood by any mainstream mathematics academic. In fact, not even understood by modern Greek math academics!

Book 5 - Definition 3:

Λόγος εστί δύο μεγεθών ομογενών ή κατά πηλικότητα ποια σχέσις.

A ratio is composed of two homogenous magnitudes with respect to how each magnitude might measure the other.

Sir Thomas Heath's translation missed the fact entirely by focusing on the sizes of the magnitudes.

The Greek word πηλικό means quotient. πηλικότητα means “quotientness”. There is no English equivalent. In other words, a ratio is simply the comparison of two random magnitudes p and q denoted by p : q and how each and/or parts of each might measure the other. The comparison is purely qualitative, not quantitative as number is only introduced in Book 7 through the abstract unit.

p : q literally means "p compared with q"

What interests intelligent people, is do these two magnitudes (p and q in the ratio) have a relationship? That is, do they have quotientness? In simple words, do they have a common divisor. If they do, then we can proceed to call the measure of the antecedent magnitude of the ratio by the name p/q, meaning p/q is a number - which DOES NOT mean "p divided by q".

More here:

https://youtu.be/2ZDrEPj0A00