A demonstration of the Pythagoras' theorem [Une démonstration du théorème de Pythagore].

See the useful geometrical figures for this demonstration:

Please note that: Then:
  Surface(Green Square)   =     Surface(Red Square)    +  4.Surface(Blue Triangle)
= +

          2                       2                          1      
     (X+Y)          =            Z             +         4.(---.X.Y)
           ___          ___ 
 2    2   /   \    2   /   \
X  + Y  + 2.X.Y = Z  + 2.X.Y
          \___/        \___/

  2    2    2
X  + Y  = Z


(Z, X and Y denoting respectively the hypotenuse and the two other sides of the four right angled triangles)

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