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 $Q+N\,4+4$.
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($N$ stays for unknown and $Q$ for its square.)


Can you give me the other examples?



History of Mathematical Notation
For a quite extensive overview with many examples, you might want to check out [The origins and development of mathematical notation](http://math.unipa.it/~grim/mathnotation.pdf).
I also enjoyed reading Stephen Wolfram's take on [Mathematical Notation – past and future,](http://www.stephenwolfram.com/publications/mathematical-notation-past-future/) with a great variety of illustrations.




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The OP asks specifically for the evolution of one formula, "to see the big picture". Here is one example, taken from [Math through the ages](https://books.google.nl/books/about/Math_Through_the_Ages.html?id=JAXNVaPt7uQC&redir_esc=y):


![](https://ilorentz.org/beenakker/MO/math_notation.png)


