G.580 square segment five — Code

XIII.2

If the square on a segment be five times the square on a segment of it, then, when the double of the said segment is cut in extreme and mean ratio, the greater segment is the remaining part of the original segment.
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"""Programmatic construction for Book XIII, Proposition 2 (XIII.2).

        If the square on a straight line be five times the square on a segment of it,
        then, when the double of the said segment is cut in extreme and mean ratio,
        the greater segment is the remaining part of the original straight line.
        """

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book XIII, Proposition 2 using geometor.model."""
            model = Model("XIII.2")

            # Straight line AB with segment AC, and CD = 2 AC
            A = model.set_point(15.0, -172.0, classes=["given"], ID="A")
            C = model.set_point(79.0, -172.0, classes=["given"], ID="C")
            B = model.set_point(163.0, -172.0, classes=["given"], ID="B")
            D = model.set_point(214.0, -172.0, classes=["given"], ID="D")

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

            # Square ALFB (AF) on AB, divided through C and H
            L = model.set_point(15.0, -24.0, ID="L")
            R = model.set_point(79.0, -24.0, ID="R")
            F = model.set_point(163.0, -24.0, ID="F")
            P = model.set_point(15.0, -108.0, ID="P")
            H = model.set_point(79.0, -108.0, ID="H")
            Q = model.set_point(163.0, -108.0, ID="Q")

            # Square CDGK (CG) on CD, divided by BE
            K = model.set_point(79.0, -307.0, ID="K")
            E = model.set_point(163.0, -307.0, ID="E")
            G = model.set_point(214.0, -307.0, ID="G")

            # Horizontal segments in AF and CG
            model.set_segment(L, F)
            model.set_segment(L, R)
            model.set_segment(R, F)
            model.set_segment(P, Q)
            model.set_segment(P, H)
            model.set_segment(H, Q)
            model.set_segment(K, G)
            model.set_segment(K, E)
            model.set_segment(E, G)

            # Vertical segments in AF and CG
            model.set_segment(L, A)
            model.set_segment(L, P)
            model.set_segment(P, A)
            model.set_segment(R, K)
            model.set_segment(R, H)
            model.set_segment(H, C)
            model.set_segment(C, K)
            model.set_segment(F, E)
            model.set_segment(F, Q)
            model.set_segment(Q, B)
            model.set_segment(B, E)
            model.set_segment(D, G)

            # Diagonal AF
            model.set_segment(A, F)
            model.set_segment(A, H)
            model.set_segment(H, F)

            # Polygons (squares, rectangles, and gnomon MNO)
            model.set_polygon([A, L, F, B])
            model.set_polygon([C, D, G, K])
            model.set_polygon([A, P, H, C])
            model.set_polygon([H, R, F, Q])
            model.set_polygon([P, L, R, H])
            model.set_polygon([C, H, Q, B])
            model.set_polygon([C, B, E, K])
            model.set_polygon([B, D, G, E])
            model.set_polygon([P, L, F, B, C, H])

            return model


        if __name__ == "__main__":
            construct_g1()