G.495 medial area rational — Code

X.109

If from a medial area a rational area be subtracted, there arise two other irrational segments, either a first apotome of a medial segment or a segment which produces with a rational area a medial whole.

"""Programmatic construction for Book X, Proposition 109 (X.109)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0241.g1 using geometor.model."""
            model = Model("X.109")

            # Left rectangle B-E-C_t / A-D-C
            B = model.set_point(21.0, -52.5, classes=["given"], ID="B")
            E = model.set_point(93.5, -52.5, ID="E")
            C_t = model.set_point(133.0, -52.5, ID="C_t")
            A = model.set_point(21.0, -137.5, classes=["given"], ID="A")
            D = model.set_point(93.5, -137.5, ID="D")
            C = model.set_point(133.0, -137.5, classes=["given"], ID="C")

            # Right rectangle F-K-H / G-L-H_b
            F = model.set_point(274.0, -21.5, classes=["given"], ID="F")
            K = model.set_point(312.0, -21.5, ID="K")
            H = model.set_point(335.0, -21.5, ID="H")
            G = model.set_point(274.0, -179.5, classes=["given"], ID="G")
            L = model.set_point(312.0, -179.5, ID="L")
            H_b = model.set_point(335.0, -179.5, ID="H_b")

            # Base lines
            model.construct_line(B, C_t)
            model.construct_line(A, C)
            model.construct_line(B, A)
            model.construct_line(E, D)
            model.construct_line(C_t, C)

            model.construct_line(F, H)
            model.construct_line(G, H_b)
            model.construct_line(F, G)
            model.construct_line(K, L)
            model.construct_line(H, H_b)

            # Segments
            model.set_segment(B, A)
            model.set_segment(E, D)
            model.set_segment(C_t, C)
            model.set_segment(A, C)
            model.set_segment(A, D)
            model.set_segment(D, C)
            model.set_segment(B, E)
            model.set_segment(E, C_t)
            model.set_segment(B, C_t)

            model.set_segment(F, G)
            model.set_segment(K, L)
            model.set_segment(H, H_b)
            model.set_segment(F, H)
            model.set_segment(F, K)
            model.set_segment(K, H)
            model.set_segment(G, L)
            model.set_segment(L, H_b)
            model.set_segment(G, H_b)

            # Sections
            model.set_section([A, D, C])
            model.set_section([F, K, H])

            # Polygons (rectangles)
            model.set_polygon([B, C_t, C, A])  # BC
            model.set_polygon([B, E, D, A])    # BD
            model.set_polygon([E, C_t, C, D])  # EC
            model.set_polygon([F, H, H_b, G])  # GH
            model.set_polygon([F, K, L, G])    # GK / FL
            model.set_polygon([K, H, H_b, L])  # LH

            return model


        if __name__ == "__main__":
            construct_g1()