Euclid Book 4

Proposition 1

Construction

Statement

Statement HTML

To place a chord in a given circle equal to a given line segment not greater than the diameter.

Construction steps

Construction Steps HTML

  • Let the circle through points A, B, and C centered at O be the given circle, AC the diameter, and DE be the given line segment with ⎪DE⎪ ≤ ⎪AC⎪.
  • Find F on AC such that ⎪AF⎪ = ⎪DE⎪.
  • Construct the circle through the point F centered at A and let its intersection with the original circle be G.
  • Join AG. Chord AG has been constructed equal to the given line segment DE.
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    Original statement

    ϵἰς τὸν δοθέντα κύκλον τῇ δοθϵίσῃ ϵὐθϵίᾳ μὴ μϵίζονι οὔσῃ τῆς τοῦ κύκλου διαμέτρου ἴσην ϵὐθϵῖαν ἐναρμόσαι.

    English translation

    Into a given circle to fit a straight line equal to a given straight line which is not greater than the diameter of the circle.

    Computable version

    Additional instances

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