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Computable Euclid

Proposition 45

Construction

To construct a parallelogram equal to a given polygon, and having an angle equal to a given angle.

Construction Steps

  • Let ADCB be the given polygon and let FEG be the given angle.
  • Join BD.
  • Construct a parallelogram HJKL that has the same area as triangle ADB, with LHJ = ∠FEG.
  • Extend HJ to construct a parallelogram JNMK that has the same area as triangle BDC, with KJN = ∠FEG. Parallelogram HNML equal to the given polygon ADBC has been constructed with LHN equal to the given angle FEG.

  • Original statement

    τῷ δοθέντι ϵὐθυγράμμῳ ἴσον παραλληλόγραμμον συστήσασθαι ἐν τῇ δοθϵίσῃ γωνίᾳ ϵὐθυγράμμῳ.

    English translation

    To construct, in a given rectilinear angle, a parallelogram equal to a given rectilinear figure.


    Computable version


    Additional instances


    Dependency graphs