G.441 square bimedial segment — Code

X.61

The square on the first bimedial segment applied to a rational segment produces as breadth the second binomial.

"""Programmatic construction for Book X, Proposition 61 (X.61)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0139.g1 using geometor.model."""
            model = Model("X.61")

            # First bimedial straight line AB divided into its medials at C
            A = model.set_point(53.0, -139.5, classes=["given"], ID="A")
            C = model.set_point(138.0, -139.5, classes=["given"], ID="C")
            B = model.set_point(182.0, -139.5, classes=["given"], ID="B")

            # Parallelogram DF applied to rational straight line DE, divided by KH, ML, NO
            D = model.set_point(21.5, -18.0, classes=["given"], ID="D")
            K = model.set_point(102.5, -18.0, ID="K")
            M = model.set_point(126.5, -18.0, ID="M")
            N = model.set_point(169.0, -18.0, ID="N")
            G = model.set_point(212.5, -18.0, ID="G")

            E = model.set_point(21.5, -112.5, classes=["given"], ID="E")
            H = model.set_point(102.5, -112.5, ID="H")
            L = model.set_point(126.5, -112.5, ID="L")
            O = model.set_point(169.0, -112.5, ID="O")
            F = model.set_point(212.5, -112.5, ID="F")

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

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

            # Segments on DEFG
            model.set_segment(D, G)
            model.set_segment(D, K)
            model.set_segment(D, M)
            model.set_segment(D, N)
            model.set_segment(K, M)
            model.set_segment(K, N)
            model.set_segment(K, G)
            model.set_segment(M, N)
            model.set_segment(M, G)
            model.set_segment(N, G)

            model.set_segment(E, F)
            model.set_segment(E, H)
            model.set_segment(E, L)
            model.set_segment(E, O)
            model.set_segment(H, L)
            model.set_segment(H, O)
            model.set_segment(H, F)
            model.set_segment(L, O)
            model.set_segment(L, F)
            model.set_segment(O, F)

            model.set_segment(D, E)
            model.set_segment(K, H)
            model.set_segment(M, L)
            model.set_segment(N, O)
            model.set_segment(G, F)

            # Sections
            model.set_section([A, C, B])
            model.set_section([D, K, M])
            model.set_section([D, M, G])
            model.set_section([M, N, G])

            # Polygons
            model.set_polygon([D, E, F, G])
            model.set_polygon([D, E, H, K])
            model.set_polygon([K, H, L, M])
            model.set_polygon([D, E, L, M])
            model.set_polygon([M, L, F, G])
            model.set_polygon([M, L, O, N])
            model.set_polygon([N, O, F, G])

            return model


        if __name__ == "__main__":
            construct_g1()