Introduction to Euclidean Constructions

Trent Burchard, Aug 24, 2020


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

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

Construct an equilateral triangle on segment AB
– Trent Burchard

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