Proposition I

The first proposition in Euclid's Elements is the construction of an equilateral triangle with compass and straightedge.
"On a given finite straight line to construct an equilateral triangle."




The side AB is the radius of the circles BCD and ACE.
The side AC is the radius of the circle BCD.
The side BC is the radius of the circle ACE.
Therefore the line segments AB, AC and BC are equal.
Therefore the triangle is equilateral.
It is a simple and beautiful construction.