G.579 segment cut extreme — Code

XIII.1

If a segment be cut in extreme and mean ratio, the square on the greater segment added to the half of the whole is five times the square on the half.

"""Programmatic construction for Book XIII, Proposition 1 (XIII.1).

        If a straight line be cut in extreme and mean ratio, the square on the greater
        segment added to the half of the whole is five times the square on the half.
        """

        from __future__ import annotations

        from geometor.model import Model


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

            # Straight line AB cut in extreme and mean ratio at C, with AD = 1/2 AB
            D = model.set_point(21.0, -172.0, classes=["given"], ID="D")
            A = model.set_point(88.0, -172.0, classes=["given"], ID="A")
            C = model.set_point(170.0, -172.0, classes=["given"], ID="C")
            B = model.set_point(221.0, -172.0, classes=["given"], ID="B")

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

            # Square DLFC (DF) on DC, divided through A and H
            L = model.set_point(21.0, -23.0, ID="L")
            R = model.set_point(88.0, -23.0, ID="R")
            F = model.set_point(170.0, -23.0, ID="F")
            P = model.set_point(21.0, -105.0, ID="P")
            H = model.set_point(88.0, -105.0, ID="H")
            Q = model.set_point(170.0, -105.0, ID="Q")

            # Square ABEK (AE) on AB, divided by CG
            K = model.set_point(88.0, -305.0, ID="K")
            G = model.set_point(170.0, -305.0, ID="G")
            E = model.set_point(221.0, -305.0, ID="E")

            # Horizontal segments in DF and AE
            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, E)
            model.set_segment(K, G)
            model.set_segment(G, E)

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

            # Diagonal DF
            model.set_segment(D, F)
            model.set_segment(D, H)
            model.set_segment(H, F)

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

            return model


        if __name__ == "__main__":
            construct_g1()