Ruler Only Constructions


Reference: A.S. Smogorzhevskii, The Ruler in Geometrical Constructions, Blaisdell, 1961.


Given the midpoint C of a line segment AB, to construct a line parallel to AB passing through a given point D.
Reference: A.S. Smogorzhevskii, The Ruler in Geometrical Constructions, Blaisdell, 1961, pp. 51-52.

The straight lines l and m are parallel, to construct the midpoint of A and B on m.
Reference: A.S. Smogorzhevskii, The Ruler in Geometrical Constructions, Blaisdell, 1961, p. 52.

Through the point A lying outside the given straight line l and m, draw a straight line parallel to the given ones.
Reference: A.S. Smogorzhevskii, The Ruler in Geometrical Constructions, Blaisdell, 1961, p. 52.

Given A, B on m and l parallel to m, construct C on m with AB = BC.
Reference: A.S. Smogorzhevskii, The Ruler in Geometrical Constructions, Blaisdell, 1961, pp. 52-53.

Given a circle and its center, construct an inscribed square.
Reference: A.S. Smogorzhevskii, The Ruler in Geometrical Constructions, Blaisdell, 1961, p. 60.

Given a parallelogram, a straight line, and a point,
to construct a line through the point parallel to the line.
References:
Math. Gaz. Oct. 1908, p. 334, problem # 284 (M.I. Trachtenberg).
Math. Gaz. problem # 318 (J.M. Child).

Given a regular hexagon with unit length on each side:
to construct segement of length 1/2, 1/3, 1/4, 1/5, 1/6 etc. Solution


Given two intersecting circles
to construct their centers. Solution
Source: nGXܴ, pp. 42-43.