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Proposition: 1.30: Transitivity of Parallel Lines

(Proposition 30 from Book 1 of Euclid's “Elements”)

(Straight-lines) parallel to the same straight line are also parallel to one another.

• Let each of the (straight lines) $AB$ and $CD$ be parallel to $EF$.
• I say that $AB$ is also parallel to $CD$.

Modern Formulation

Straight lines parallel to the same straight line are also parallel to one another, i.e. if \(AB\parallel EF\) and \(EF\parallel CB\) then \(AB\parallel CB\).

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2

Thank you to the contributors under CC BY-SA 4.0!

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non-Github:

@Calahan

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@Fitzpatrick

References

Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"

Adapted from (subject to copyright, with kind permission)

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