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Computable Euclid

Proposition 30

Theorem

If two lines (AB, CD) are parallel to the same line (EF), then they are parallel to one another.

Commentary

  • Let AB be parallel to EF and let CD also be parallel to EF.
  • Then AB and CD are parallel.
  • This proposition is equivalent to Postulate 5, and also Playfair's axiom.

  • Original statement

    αἱ τῇ αὐτῇ ϵὐθϵίᾳ παράλληλοι καὶ ἀλλήλαις ϵἰσὶ παράλληλοι.

    English translation

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


    Computable version


    Additional instances


    Dependency graphs