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Computable Euclid

Proposition 14

Construction

To construct a square equal to a given polygon.

Construction Steps

1. Let ADCB be the given polygon.
2. Construct a rectangle EFGH such that it has the same area as polygon ADCB.
3. Extend EF to J such that FJ = FG.
4. Bisect EJ at K.
5. Construct the circle through the point J centered at K that intersects the extension of GF at P.
6. Construct a square PFMN with FP as a side. The square PFMN has been constructed equal (in area) to the given polygon ABCD.

Original statement

τῷ δοθέντι ϵὐθυγράμμῳ ἴσον τϵτράγωνον συστήσασθαι.

English translation

To construct a square equal to a given rectilinear figure.


Computable version


Additional instances


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