G.451 rational medial area — Code

X.71

If a rational and a medial area be added together, four irrational segments arise, namely a binomial or a first bimedial or a major or a side of a rational plus a medial area.

"""Programmatic construction for Book X, Proposition 71 (X.71)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0156.g1 using geometor.model."""
            model = Model("X.71")

            # Left area AD composed of rational area AB and medial area CD
            A = model.set_point(21.0, -18.5, classes=["given"], ID="A")
            C = model.set_point(83.5, -18.5, classes=["given"], ID="C")
            C_r = model.set_point(107.0, -18.5, ID="C_r")
            A_b = model.set_point(21.0, -172.0, ID="A_b")
            B = model.set_point(83.5, -172.0, classes=["given"], ID="B")
            D = model.set_point(107.0, -172.0, classes=["given"], ID="D")

            # Right rectangle EI applied to rational straight line EF
            E = model.set_point(221.5, -47.5, classes=["given"], ID="E")
            H = model.set_point(312.5, -47.5, ID="H")
            K = model.set_point(367.5, -47.5, ID="K")
            F = model.set_point(221.5, -156.0, classes=["given"], ID="F")
            G = model.set_point(312.5, -156.0, ID="G")
            I = model.set_point(367.5, -156.0, ID="I")

            # Base lines
            model.construct_line(A, C_r)
            model.construct_line(A_b, D)
            model.construct_line(A, A_b)
            model.construct_line(C, B)
            model.construct_line(C_r, D)

            model.construct_line(E, K)
            model.construct_line(F, I)
            model.construct_line(E, F)
            model.construct_line(H, G)
            model.construct_line(K, I)

            # Segments
            model.set_segment(A, C_r)
            model.set_segment(A, C)
            model.set_segment(C, C_r)
            model.set_segment(A_b, D)
            model.set_segment(A_b, B)
            model.set_segment(B, D)
            model.set_segment(A, A_b)
            model.set_segment(C, B)
            model.set_segment(C_r, D)

            model.set_segment(E, K)
            model.set_segment(E, H)
            model.set_segment(H, K)
            model.set_segment(F, I)
            model.set_segment(F, G)
            model.set_segment(G, I)
            model.set_segment(E, F)
            model.set_segment(H, G)
            model.set_segment(K, I)

            # Sections
            model.set_section([E, H, K])
            model.set_section([F, G, I])

            # Polygons
            model.set_polygon([A, A_b, B, C])
            model.set_polygon([C, B, D, C_r])
            model.set_polygon([A, A_b, D, C_r])
            model.set_polygon([E, F, G, H])
            model.set_polygon([H, G, I, K])
            model.set_polygon([E, F, I, K])

            return model


        if __name__ == "__main__":
            construct_g1()