G.17 construct an equilateral triangle — Code

I.1

Construct an equilateral triangle on a given segment.
C D A B E 
"""Programmatic construction for Book I, Proposition 1 (I.1).

        On a given finite straight line to construct an equilateral triangle.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book I, Proposition 1 using geometor.model."""
            model = Model("I.1")

            # 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)

            # Extended horizontal line [ A B ] to determine circumference points D and E
            model.construct_line(A, B)

            # 2. With centre A and distance AB let the circle BCD be described [Post. 3]
            circle_BCD = model.construct_circle(A, B)

            # 3. With centre B and distance BA let the circle ACE be described [Post. 3]
            circle_ACE = model.construct_circle(B, A)

            # Label the upper intersection of circles ( A B ) and ( B A ) as C,
            # and the outer diameter intersections on [ A B ] as D and E.
            C = model.set_point(sp.Rational(1, 2), sp.sqrt(3) / 2, label="C")
            D = model.set_point(-1, 0, ID="D")
            E = model.set_point(2, 0, ID="E")

            # 4. From C to A, B let the straight lines CA, CB be joined [Post. 1]
            model.set_segment(C, A)
            model.set_segment(C, B)

            # 5. Therefore the triangle ABC is equilateral
            model.set_polygon([A, B, C])

            return model


        if __name__ == "__main__":
            construct_g1()