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The Elements
All propositions

Proposition I.1

The equilateral triangle

On a given finite straight line, to construct an equilateral triangle.

The first proposition of the Elements is a construction, not a theorem. It shows the compass and straightedge at work, and quietly uses the common notions to conclude equality. Everything else grows from this.

Step 1 of 5

The given segment

Given

Let AB be the given finite straight line. This is all we are handed — two points, and the segment between them.