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  • Introduction to Euclidean Constructions
      Proposition 1: To construct an equilateral triangle on a given finite straight line.
      Proposition 2: To place a straight line equal to a given straight line with one end at a given point.
      Proposition 3: To cut off from the greater of two given unequal straight lines a straight line equal to the less.
      Proposition 9: To bisect a given rectilinear angle.
      Proposition 10: To bisect a given finite straight line.
      Proposition 11: To draw a straight line at right angles to a given straight line from a given point on it.
      Proposition 12: To draw a straight line perpendicular to a given infinite straight line from a given point not on it.
      Proposition 46: To describe a square on a given straight line.
      Challenge! Given a segment of length 1 unit, construct a segment of length square root 2 units

Introduction to Euclidean Constructions

Author:
Trent Burchard
Topic:
Constructions

  • Proposition 1: To construct an equilateral triangle on a given finite straight line.

  • Proposition 2: To place a straight line equal to a given straight line with one end at a given point.

  • Proposition 3: To cut off from the greater of two given unequal straight lines a straight line equal to the less.

  • Proposition 9: To bisect a given rectilinear angle.

  • Proposition 10: To bisect a given finite straight line.

  • Proposition 11: To draw a straight line at right angles to a given straight line from a given point on it.

  • Proposition 12: To draw a straight line perpendicular to a given infinite straight line from a given point not on it.

  • Proposition 46: To describe a square on a given straight line.

  • Challenge! Given a segment of length 1 unit, construct a segment of length square root 2 units

Next
Proposition 1: To construct an equilateral triangle on a given finite straight line.

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