(1) I begin the demonstration with a typical set of nested squares & circles. This diagram is very easy to construct with unmarked compass & straightedge, so I won’t bother with extraneous details. Although measurement is not used to construct these figures, it is obviously required for the proof. Therefore, I will treat the innermost Green Circle as a Unit Circle; (Radius = 1, Area = Pi). The outer Blue Circle is twice the size of the Green Circle; (Radius = √2, Area = 2Pi). Also, you will notice that I’ve labeled key intersecting points with the letters A-E, and made two line extensions; one in the center & one at the bottom. These will come into play in succeeding diagrams.
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