a problem with the "golden section"

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A problem with the golden section. It is also prop 1, in Euclid's Elements Book XIII.

Let AB be a line segment and let C a point between A and B divide it into the golden section: |AB| : |AC| :: |AC| : |CB|

Using point D to the left of A such that |DA| is half of |AB|, show that the square on |CD| is five (5) times the area of the square on
|AD|.

Note: read |XY| as the length of the line segment XY.

D --------------A----------------C---------B

If you want to try it geometrically, do not cheat by looking at book XIII first. Otherwise show by algebraic means that it is so.

BTW, the algebraic proof was longer and more error prone than Euclid's geometric proof.

ruveyn