Powered by Wolfram
Powered by Wolfram

Computable Euclid

Proposition 42

Construction

To construct a parallelogram equal to a given triangle, with one angle equal to a given angle.

Construction Steps

  • Let ABC be the given triangle and let DEF be the given angle.
  • Construct the infinite line infinite line CP parallel to AB.
  • Bisect AB at M.
  • Choose N on infinite line CP such that BMN = ∠DEF.
  • Construct a line through B that is parallel to MN and intersects infinite line CP at Q. The parallelogram BMNQ has been constructed equal to the given triangle ABC, with BMN equal to the given angle DEF.

  • Original statement

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

    English translation

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


    Computable version


    Additional instances


    Dependency graphs