G.512 segments meeting parallel — Code

XI.10

If two segments meeting one another be parallel to two segments meeting one another not in the same plane, they will contain equal angles.
B C A E F D 
"""Programmatic construction for Book XI, Proposition 10 (XI.10).

        If two straight lines meeting one another be parallel to two straight lines
        meeting one another not in the same plane, they will contain equal angles.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book XI, Proposition 10 using geometor.model."""
            model = Model("XI.10")

            # Upper plane boundary corners
            U1 = model.set_point(sp.Rational(-30, 79), sp.Rational(19, 79), label="U1")
            U2 = model.set_point(sp.Rational(112, 79), sp.Rational(19, 79), label="U2")
            U3 = model.set_point(sp.Rational(68, 79), sp.Rational(-66, 79), label="U3")
            U4 = model.set_point(sp.Rational(-48, 79), sp.Rational(-66, 79), label="U4")

            # Lower plane boundary corners
            L1 = model.set_point(sp.Rational(25, 79), sp.Rational(-92, 79), label="L1")
            L2 = model.set_point(sp.Rational(222, 79), sp.Rational(-92, 79), label="L2")
            L3 = model.set_point(sp.Rational(178, 79), sp.Rational(-167, 79), label="L3")
            L4 = model.set_point(sp.Rational(-1, 79), sp.Rational(-167, 79), label="L4")

            # 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; and let BA, BC, ED, EF be cut off equal to one another.
            B = model.set_point(0, 0, classes=["given"], ID="B")
            A = model.set_point(sp.Rational(-17, 79), sp.Rational(-55, 79), classes=["given"], label="A")
            C = model.set_point(1, sp.Rational(-5, 79), classes=["given"], label="C")

            E = model.set_point(sp.Rational(78, 79), sp.Rational(-102, 79), classes=["given"], label="E")
            D = model.set_point(sp.Rational(62, 79), sp.Rational(-156, 79), classes=["given"], label="D")
            F = model.set_point(sp.Rational(157, 79), sp.Rational(-106, 79), classes=["given"], label="F")

            # 2. Join AD, CF, BE, AC, DF.
            model.set_segment(A, B)
            model.set_segment(B, C)
            model.set_segment(A, C)

            model.set_segment(D, E)
            model.set_segment(E, F)
            model.set_segment(D, F)

            model.set_segment(A, D)
            model.set_segment(B, E)
            model.set_segment(C, F)

            # Upper and lower plane boundaries
            model.set_polygon([U1, U2, U3, U4])
            model.set_polygon([L1, L2, L3, L4])

            # Triangles and parallelograms in the proof
            model.set_polygon([A, B, C])
            model.set_polygon([D, E, F])
            model.set_polygon([A, B, E, D])
            model.set_polygon([B, C, F, E])
            model.set_polygon([A, C, F, D])

            return model


        if __name__ == "__main__":
            construct_g1()