G.463 apotome medial segment — Code

X.81

To a second apotome of a medial segment only one medial segment can be annexed which is commensurable with the whole in square only and which contains with the whole a medial rectangle.

"""Programmatic construction for Book X, Proposition 81 (X.81)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0174.g1 using geometor.model."""
            model = Model("X.81")

            # Top straight line AD divided at B and C
            A = model.set_point(16.0, -21.5, classes=["given"], ID="A")
            B = model.set_point(80.0, -21.5, classes=["given"], ID="B")
            C = model.set_point(122.0, -21.5, classes=["given"], ID="C")
            D = model.set_point(154.0, -21.5, classes=["given"], ID="D")

            # Rectangle FEIN divided horizontally by LH and GM
            F = model.set_point(29.0, -45.5, classes=["given"], ID="F")
            E = model.set_point(121.0, -45.5, classes=["given"], ID="E")

            L = model.set_point(29.0, -65.5, ID="L")
            H = model.set_point(121.0, -65.5, ID="H")

            G = model.set_point(29.0, -237.0, ID="G")
            M = model.set_point(121.0, -237.0, ID="M")

            I = model.set_point(29.0, -335.0, ID="I")
            N = model.set_point(121.0, -335.0, ID="N")

            # Base lines
            model.construct_line(A, D)
            model.construct_line(F, E)
            model.construct_line(L, H)
            model.construct_line(G, M)
            model.construct_line(I, N)
            model.construct_line(F, I)
            model.construct_line(E, N)

            # Segments on AD
            model.set_segment(A, D)
            model.set_segment(A, C)
            model.set_segment(A, B)
            model.set_segment(B, D)
            model.set_segment(B, C)
            model.set_segment(C, D)

            # Horizontal segments on rectangle FEIN
            model.set_segment(F, E)
            model.set_segment(L, H)
            model.set_segment(G, M)
            model.set_segment(I, N)

            # Vertical segments on left side FI
            model.set_segment(F, I)
            model.set_segment(F, G)
            model.set_segment(F, L)
            model.set_segment(L, I)
            model.set_segment(L, G)
            model.set_segment(G, I)

            # Vertical segments on right side EN
            model.set_segment(E, N)
            model.set_segment(E, M)
            model.set_segment(E, H)
            model.set_segment(H, N)
            model.set_segment(H, M)
            model.set_segment(M, N)

            # Sections
            model.set_section([A, B, C])
            model.set_section([A, B, D])
            model.set_section([A, C, D])
            model.set_section([B, C, D])
            model.set_section([F, L, G])
            model.set_section([F, L, I])
            model.set_section([F, G, I])
            model.set_section([L, G, I])
            model.set_section([E, H, M])
            model.set_section([E, H, N])
            model.set_section([E, M, N])
            model.set_section([H, M, N])

            # Polygons (rectangles)
            model.set_polygon([F, E, N, I])
            model.set_polygon([F, E, M, G])
            model.set_polygon([F, E, H, L])
            model.set_polygon([L, H, M, G])
            model.set_polygon([L, H, N, I])
            model.set_polygon([G, M, N, I])

            return model


        if __name__ == "__main__":
            construct_g1()