G.518 segments meeting parallel — Code

XI.15

If two segments meeting one another be parallel to two segments meeting one another, not being in the same plane, the planes through them are parallel.
B A C E G D H K F 
"""Programmatic construction for Book XI, Proposition 15 (XI.15).

        If two straight lines meeting one another be parallel to two straight lines
        meeting one another, not being in the same plane, the planes through them are
        parallel.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book XI, Proposition 15 using geometor.model."""
            model = Model("XI.15")

            # 1. Let the two straight lines AB, BC meeting one another be parallel to
            #    the two straight lines DE, EF meeting one another, not in the same plane.
            B = model.set_point(0, 1, classes=["given"], ID="B")
            A = model.set_point(sp.Rational(-43, 145), sp.Rational(112, 145), classes=["given"], label="A")
            C = model.set_point(sp.Rational(30, 145), sp.Rational(112, 145), classes=["given"], label="C")

            # 2. Let BG be drawn from B perpendicular to the plane through DE, EF, meeting it at G.
            G = model.set_point(sp.Rational(4, 145), 0, label="G")
            E = model.set_point(sp.Rational(27, 145), sp.Rational(41, 145), classes=["given"], label="E")
            D = model.set_point(sp.Rational(-31, 145), sp.Rational(-5, 145), classes=["given"], label="D")
            F = model.set_point(sp.Rational(79, 145), sp.Rational(-20, 145), classes=["given"], label="F")

            # 3. Through G let GH be drawn parallel to ED, and GK parallel to EF.
            H = model.set_point(sp.Rational(-29, 145), sp.Rational(-25, 145), label="H")
            K = model.set_point(sp.Rational(25, 145), sp.Rational(-24, 145), label="K")

            # Plane through AB, BC corners
            P1 = model.set_point(sp.Rational(-75, 145), sp.Rational(168, 145), label="P1")
            P2 = model.set_point(sp.Rational(65, 145), sp.Rational(168, 145), label="P2")
            P3 = model.set_point(sp.Rational(34, 145), sp.Rational(100, 145), label="P3")
            P4 = model.set_point(sp.Rational(-89, 145), sp.Rational(99, 145), label="P4")

            # Plane through DE, EF corners
            Q1 = model.set_point(sp.Rational(-24, 145), sp.Rational(57, 145), label="Q1")
            Q2 = model.set_point(sp.Rational(135, 145), sp.Rational(57, 145), label="Q2")
            Q3 = model.set_point(sp.Rational(93, 145), sp.Rational(-36, 145), label="Q3")
            Q4 = model.set_point(sp.Rational(-56, 145), sp.Rational(-36, 145), label="Q4")

            # Segments
            model.set_segment(A, B)
            model.set_segment(B, C)
            model.set_segment(D, E)
            model.set_segment(E, F)
            model.set_segment(B, G)
            model.set_segment(G, H)
            model.set_segment(G, K)

            # Planes
            model.set_polygon([P1, P2, P3, P4])
            model.set_polygon([Q1, Q2, Q3, Q4])
            model.set_polygon([A, B, C])
            model.set_polygon([D, E, F])

            # Wedges for angles BGH, BGK, GBA
            model.set_wedge(G, H, H, B)
            model.set_wedge(G, B, B, K)
            model.set_wedge(B, G, G, A)

            return model


        if __name__ == "__main__":
            construct_g1()