Proposition: Prop. 11.09: Lines Parallel to Same Line not in Same Plane are Parallel to each other

(Proposition 9 from Book 11 of Euclid's “Elements”)

(Straight-lines) parallel to the same straight line, and which are not in the same plane as it, are also parallel to one another. * For let $AB$ and $CD$ each be parallel to $EF$, not being in the same plane as it. * I say that $AB$ is parallel to $CD$.


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2 3

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Adapted from (subject to copyright, with kind permission)

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

Adapted from CC BY-SA 3.0 Sources:

  1. Prime.mover and others: "Pr∞fWiki",, 2016