# Why is there "modulus" word in the "distance modulus" term?

The difference of apparent (m) and absolute (M) magnitudes of an object is called "distance modulus", which is related to the distance $$d$$ to the object in parsecs with equation

$$m - M = 5 \log \Big(\frac{d}{10 \ \textrm{pc}}\Big) \tag{1}.$$

I'm trying to understand why $$m - M$$ is called "distance modulus". The word "distance" makes sense, because there is a distance d term in Eq. (1). But what is "modulus" word doing there? In math, modulus means the remainder after division of two numbers. For example, modulus of 5 and 3 is 2.

Another meaning of "modulus" is length of a vector. I don't see how either of these two meanings can be relevant to Eq. 1.