G.511 straight lines parallel — Code

XI.9

Straight lines which are parallel to the same segment and are not in the same plane with it are also parallel to one another.
B H A F G E D K C 
"""Programmatic construction for Book XI, Proposition 9 (XI.9).

        Straight lines which are parallel to the same straight line and are not in the
        same plane with it are also parallel to one another.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book XI, Proposition 9 using geometor.model."""
            model = Model("XI.9")

            # 1. Let each of the straight lines AB, CD be parallel to EF, not being in
            #    the same plane with it.
            G = model.set_point(0, 0, classes=["given"], ID="G")
            F = model.set_point(sp.Rational(-84, 84), 0, classes=["given"], label="F")
            E = model.set_point(sp.Rational(85, 84), 0, classes=["given"], label="E")

            B = model.set_point(sp.Rational(-34, 84), sp.Rational(54, 84), classes=["given"], label="B")
            H = model.set_point(sp.Rational(39, 84), sp.Rational(54, 84), label="H")
            A = model.set_point(sp.Rational(134, 84), sp.Rational(55, 84), classes=["given"], label="A")

            D = model.set_point(sp.Rational(-41, 84), sp.Rational(-35, 84), classes=["given"], label="D")
            K = model.set_point(sp.Rational(38, 84), sp.Rational(-34, 84), label="K")
            C = model.set_point(sp.Rational(147, 84), sp.Rational(-33, 84), classes=["given"], label="C")

            # Collinear lines and sub-segments
            model.construct_line(B, A)
            model.set_section([B, H, A])
            model.set_segment(B, H)
            model.set_segment(H, A)
            model.set_segment(A, B)

            model.construct_line(F, E)
            model.set_section([F, G, E])
            model.set_segment(F, G)
            model.set_segment(G, E)
            model.set_segment(E, F)

            model.construct_line(D, C)
            model.set_section([D, K, C])
            model.set_segment(D, K)
            model.set_segment(K, C)
            model.set_segment(C, D)

            # 2. Perpendiculars GH and GK from G to EF in the respective planes
            model.set_segment(G, H)
            model.set_segment(G, K)

            # Planes through GH, GK; through EF, AB; and through FE, CD
            model.set_polygon([H, G, K])
            model.set_polygon([B, A, E, F])
            model.set_polygon([F, E, C, D])

            return model


        if __name__ == "__main__":
            construct_g1()