G.97 construct a square equal to a polygon — Code

II.14

Construct a square equal in area to a given rectilineal figure.
A B C D E F G H 
"""Programmatic construction for Book II, Proposition 14 (II.14).

        To construct a square equal to a given rectilineal figure.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book II, Proposition 14 using geometor.model."""
            model = Model("II.14")

            # 1. Rectangular parallelogram BCDE (BD) equal to the given rectilineal figure A
            B = model.set_point(0, 0, classes=["given"], ID="B")
            C = model.set_point(0, -1, classes=["given"], ID="C")
            D = model.set_point(3, -1, classes=["given"], ID="D")
            E = model.set_point(3, 0, classes=["given"], ID="E")
            model.set_polygon([B, C, D, E])

            # 2. Produce BE to F with EF = ED
            model.construct_line(B, E)
            F = model.set_point(4, 0, ID="F")

            # 3. Bisect BF at G
            G = model.set_point(2, 0, ID="G")

            # 4. With centre G and distance GB or GF describe the semicircle BHF
            model.construct_circle(G, B)

            # 5. Produce DE to H on the semicircle, and join GH
            model.construct_line(D, E)
            H = model.set_point(3, sp.sqrt(3), label="H")

            # Right triangle GEH
            model.set_polygon([G, E, H])

            # Collinear sections
            model.set_section([B, G, F])
            model.set_section([B, E, F])
            model.set_section([D, E, H])

            # Segments
            for p1, p2 in [
                (B, C), (C, D), (D, E), (B, E),
                (E, F), (B, F), (G, B), (G, F), (G, E),
                (E, H), (D, H), (G, H),
            ]:
                model.set_segment(p1, p2)

            return model


        if __name__ == "__main__":
            construct_g1()