Proof: By Euclid

(related to Proposition: 1.02: Constructing a Segment Equal to an Arbitrary Segment)

fn1. This proposition admits of a number of different cases, depending on the relative positions of the point $A$ and the line $BC$. In such situations, Euclid invariably only considers one particular case - usually, the most difficult - and leaves the remaining cases as exercises for the reader (translator's note).

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Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"