G.32 bisect a segment — Code

I.10

Bisect a given segment.
C A D B 
"""Programmatic construction for Book I, Proposition 10 (I.10).

        To bisect a given finite straight line.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


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

            # 1. Let AB be the given finite straight line.
            A = model.set_point(0, 0, classes=["given"], ID="A")
            B = model.set_point(1, 0, classes=["given"], ID="B")
            model.set_segment(A, B)

            # 2. Construct equilateral triangle ABC on AB [I. 1]
            C = model.set_point(sp.Rational(1, 2), sp.sqrt(3) / 2, label="C")
            model.set_segment(A, C)
            model.set_segment(B, C)
            model.set_polygon([A, B, C])

            # 3. Bisect angle ACB by straight line CD meeting AB at D [I. 9]
            D = model.set_point(sp.Rational(1, 2), 0, label="D")
            model.set_section([A, D, B])
            model.set_segment(A, D)
            model.set_segment(D, B)
            model.set_segment(C, D)

            model.set_polygon([A, C, D])
            model.set_polygon([B, C, D])

            return model


        if __name__ == "__main__":
            construct_g1()