Constructing a Parallel Line from a Line and a Point

Geometric Proof

(related to "Constructing a Parallel Line from a Line and a Point")

Take any point \(D\) on the straight line \(AB\) and join it with point \(C\) (axiom 1.1). By virtue of proposition 1.23, we can find a point \(E\) such that by joining points \(C\) and \(E\) we obtain \(\angle{ADC}=\angle{DCE}\). By proposition 1.27, \(AB\parallel CE\).

References

[628] Casey, John: “The First Six Books of the Elements of Euclid”, http://www.gutenberg.org/ebooks/21076, 2007
[626] Callahan, Daniel: “Euclid’s ‘Elements’ Redux”, http://starrhorse.com/euclid/, 2014

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