- Introduction to Euclidean ConstructionsProposition 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