G.510 segments parallel right — Code

XI.8

If two segments be parallel, and one of them be at right angles to any plane, the remaining one is at right angles to the same plane.

"""Programmatic construction for Book XI, Proposition 8 (XI.8).

        If two straight lines be parallel, and one of them be at right angles to any
        plane, the remaining one will also be at right angles to the same plane.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book XI, Proposition 8 using geometor.model."""
            model = Model("XI.8")

            # Plane of reference boundary corners
            P1 = model.set_point(sp.Rational(-20, 102), sp.Rational(45, 102), label="P1")
            P2 = model.set_point(sp.Rational(148, 102), sp.Rational(45, 102), label="P2")
            P3 = model.set_point(sp.Rational(101, 102), sp.Rational(-56, 102), label="P3")
            P4 = model.set_point(sp.Rational(-39, 102), sp.Rational(-56, 102), label="P4")

            # 1. Let AB, CD be two parallel straight lines, and let AB be at right
            #    angles to the plane of reference, meeting it at B, D.
            B = model.set_point(0, 0, classes=["given"], ID="B")
            A = model.set_point(0, 1, classes=["given"], ID="A")
            D = model.set_point(sp.Rational(100, 102), 0, classes=["given"], label="D")
            C = model.set_point(sp.Rational(100, 102), sp.Rational(100, 102), classes=["given"], label="C")

            # 2. Let BD be joined, and let DE be drawn in the plane of reference at
            #    right angles to BD, with DE equal to AB.
            E = model.set_point(sp.Rational(85, 102), sp.Rational(-42, 102), label="E")

            # 3. Join BE, AE, AD.
            model.set_segment(A, B)
            model.set_segment(C, D)
            model.set_segment(B, D)
            model.set_segment(D, E)
            model.set_segment(B, E)
            model.set_segment(A, E)
            model.set_segment(A, D)

            # Plane of reference boundary
            model.set_segment(P1, P2)
            model.set_segment(P2, P3)
            model.set_segment(P3, P4)
            model.set_segment(P4, P1)
            model.set_polygon([P1, P2, P3, P4])

            # Planes and triangles in the proof
            model.set_polygon([A, B, D])
            model.set_polygon([E, D, B])
            model.set_polygon([A, B, E])
            model.set_polygon([E, D, A])
            model.set_polygon([A, B, D, C])

            return model


        if __name__ == "__main__":
            construct_g1()