G.31 bisect an angle — Code

I.9

Bisect a given angle.

"""Programmatic construction for Book I, Proposition 9 (I.9).

        To bisect a given rectilineal angle.
        """

        from __future__ import annotations

        from geometor.model import Model


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

            # 1. Given rectilineal angle BAC
            A = model.set_point(52, -12, classes=["given"], ID="A")
            B = model.set_point(19, -114, classes=["given"], ID="B")
            C = model.set_point(85, -114, classes=["given"], ID="C")

            model.construct_line(A, B)
            model.construct_line(A, C)

            # 2. Point D taken at random on AB, and AE cut off from AC equal to AD [I. 3]
            D = model.set_point(33, -72, ID="D")
            E = model.set_point(71, -72, ID="E")

            model.set_section([A, D, B])
            model.set_segment(A, D)
            model.set_segment(D, B)
            model.set_segment(A, B)

            model.set_section([A, E, C])
            model.set_segment(A, E)
            model.set_segment(E, C)
            model.set_segment(A, C)

            # 3. Join DE, construct equilateral triangle DEF on DE [I. 1], and join AF
            F = model.set_point(52, -105, ID="F")
            model.set_segment(D, E)
            model.set_segment(D, F)
            model.set_segment(E, F)
            model.set_segment(A, F)

            model.set_polygon([A, D, E])
            model.set_polygon([D, E, F])
            model.set_polygon([A, D, F])
            model.set_polygon([A, E, F])

            return model


        if __name__ == "__main__":
            construct_g1()