I am learning the
number theory. I am not a native English speaker. I encountered the word
commensurable from time to time. Such as:
the Pythagoreans discovered when they found that the diagonal of certain geometric fgures may be incommensurable with their sides.
I guess I need to understand the motivation/origin/construction of the word
commensurable to get its real meaning.
As I googled, there can be 3 meanings as below. I think the
1 is reasonable based on the word's origin. But how come it leads to ratio in
2 and especially, ratio of integers in
3??? What's the mind flow of a native English speaker for this?