G.507 segment set right — Code

XI.5

If a segment be set up at right angles to three segments which meet one another, at their common point of section, the three segments are in one plane.

"""Programmatic construction for Book XI, Proposition 5 (XI.5).

        If a straight line be set up at right angles to three straight lines which meet
        one another, at their common point of section, the three straight lines are in
        one 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 5 using geometor.model."""
            model = Model("XI.5")

            # Perspective plane of reference corners
            P1 = model.set_point(sp.Rational(-34, 77), sp.Rational(41, 77), label="P1")
            P2 = model.set_point(sp.Rational(112, 77), sp.Rational(41, 77), label="P2")
            P3 = model.set_point(sp.Rational(100, 77), sp.Rational(-46, 77), label="P3")
            P4 = model.set_point(sp.Rational(-50, 77), sp.Rational(-46, 77), label="P4")

            # 1. Let a straight line AB be set up at right angles to the three straight
            #    lines BC, BD, BE, at their point of meeting at B.
            B = model.set_point(0, 0, classes=["given"], ID="B")
            A = model.set_point(0, 1, classes=["given"], ID="A")
            C = model.set_point(sp.Rational(40, 77), sp.Rational(66, 77), classes=["given"], label="C")
            D = model.set_point(sp.Rational(79, 77), 0, classes=["given"], label="D")
            E = model.set_point(sp.Rational(40, 77), sp.Rational(-34, 77), classes=["given"], label="E")

            # 2. Let the plane through AB, BC be produced; let it make as common section
            #    in the plane of reference the straight line BF.
            F = model.set_point(sp.Rational(30, 77), sp.Rational(32, 77), label="F")

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

            # 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])

            # Plane through BD, BE and plane through AB, BC
            model.set_polygon([B, D, E])
            model.set_polygon([A, B, C])
            model.set_polygon([A, B, F])

            return model


        if __name__ == "__main__":
            construct_g1()