# Euclidean algorithm in Euclid's words

When describing the Euclidean algorithm in his book, Elements, Euclid says the following:

When the less of the numbers $$a$$ and $$b$$ is continually subtracted from the greater, some number is left which measures the one before it.

So when looking for a GCD of, say, $$25$$ and $$15$$, we can subtract $$15$$ from $$25$$ and get $$10$$. So $$10$$ is the number left which should measure(divide) the one before it. It measures neither $$15$$ nor $$25$$.

Can anyone interpret what Euclid wanted to say with that sentence?

In your example: $$(25,15) \to (10,15) \to (10,5)$$ and now $$5$$ measures $$10$$ and we're done.
When the less of the numbers $$a$$ and $$b$$ is continually subtracted from the greater, eventually some number is left which measures the one before it.