TITLE: History of Mathematical Notation
QUESTION [28 upvotes]: 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?

REPLY [5 votes]: "The big picture" that can be seen in Carlo Beenakker's example is 


Rhetorical (verbal);   Syncopated  (abbreviated words);       Symbolic. 


However, this well-known picture is very algebra-oriented and does not say anything about the use of notations in say geometry as discussed here "
The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History
" or as asked here Uppercase Point Labels in High-School Diagrams. 
Thus, at least for me, the interesting answers to OP questions would be those that are not related to algebra.

REPLY [3 votes]: Find a quantity such that $\varsigma\;\overline{\beta}$ squared equals
  $$\Delta^{\Upsilon}\;\varsigma\overline{\delta}\;{\stackrel{o}{M}}\overline{\delta}$$

(My translation into English from Diophantes $\alpha\rho\iota\theta\mu\eta\tau\iota\kappa\eta$.)