G.444 square side rational — Code

X.64

The square on the side of a rational plus a medial area applied to a rational segment produces as breadth the fifth binomial.

"""Programmatic construction for Book X, Proposition 64 (X.64)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0146.g1 using geometor.model."""
            model = Model("X.64")

            # Side of a rational plus a medial area AB divided at C
            A = model.set_point(52.0, -131.5, classes=["given"], ID="A")
            C = model.set_point(139.0, -131.5, classes=["given"], ID="C")
            B = model.set_point(185.0, -131.5, classes=["given"], ID="B")

            # Parallelogram DF applied to rational straight line DE, divided by KH, ML, NO
            D = model.set_point(23.5, -18.0, classes=["given"], ID="D")
            K = model.set_point(101.5, -18.0, ID="K")
            M = model.set_point(124.5, -18.0, ID="M")
            N = model.set_point(168.5, -18.0, ID="N")
            G = model.set_point(212.5, -18.0, ID="G")

            E = model.set_point(23.5, -110.5, classes=["given"], ID="E")
            H = model.set_point(101.5, -110.5, ID="H")
            L = model.set_point(124.5, -110.5, ID="L")
            O = model.set_point(168.5, -110.5, ID="O")
            F = model.set_point(212.5, -110.5, 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()