Why do we typically use $h$ for

$$\frac{\mathrm{d}f}{\mathrm{d}x}=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$$

A student asked me this the other day. My guess was that it was originally height, because Newton was originally applying it to gravity and he was looking at change in height, and then it stuck.

Anyone have any insight into this?

Cross posted to Math StackExchange: http://math.stackexchange.com/questions/1135284/use-of-h-in-the-newton-quotient