Proposition: 1.27: Parallel Lines I
(Proposition 27 from Book 1 of Euclid's “Elements”)
If a straight line falling across two straight lines makes the alternate angles equal to one another then the (two) straight lines will be parallel to one another.
Modern Formulation
If a straight line \((EF)\) intersects two straight lines \((AB)\), \((CD)\) such that the alternate angles are equal \((\angle{AEF}=\angle{DFE})\), then these lines are parallel \((AB\parallel CD)\).
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4 5
Propositions: 6
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References
Adapted from CC BYSA 3.0 Sources:
 Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014
Adapted from (Public Domain)
 Casey, John: "The First Six Books of the Elements of Euclid"
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"