Where exactly do radians come from?

Question

I'm aware that the angle in radians is 1 when the arc length is equal to the radius. However, I wonder if this is exactly where radians come from. Have we set radians like this (like we set $i^2$ to $-1$) or is there something more to it?

Answer 1

According to Earliest Known Uses of Some of the Words of Mathematics, the term "radian" was coined independently by James Moore and William Thompson (Lord Kelvin) in the 19th century.