I would like to see a simple example which shows how mathematical notation were evolve in time and space.

Say, consider the formula $$(x+2)^2=x^2+4{\cdot}x+4.$$ If I understand correctly, Franciscus Vieta would write something like this. (Feel free to correct me.)

## $\overline{N+2}$ quadr. æqualia $Q+N\,4+4$.

($N$ stays for unknown and $Q$ for its square.)

Can you give me the other examples?

Enlightening Symbolshas an example of what you want? press.princeton.edu/titles/10204.html $\endgroup$ – Timothy Chow Nov 28 '15 at 15:19