G.494 rational area medial — Code

X.108

If from a rational area a medial area be subtracted, the “side” of the remaining area becomes one of two irrational segments, either an apotome or a minor segment.

"""Programmatic construction for Book X, Proposition 108 (X.108)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0239.g1 using geometor.model."""
            model = Model("X.108")

            # Top rectangle AEB-CD
            A = model.set_point(85.5, -19.0, classes=["given"], ID="A")
            E = model.set_point(170.0, -19.0, ID="E")
            B = model.set_point(195.5, -19.0, classes=["given"], ID="B")
            C = model.set_point(85.5, -113.5, classes=["given"], ID="C")
            D = model.set_point(170.0, -113.5, ID="D")
            B_b = model.set_point(195.5, -113.5, ID="B_b")

            # Bottom rectangle H_t-L-G / H-K-F
            H_t = model.set_point(18.0, -143.5, ID="H_t")
            L = model.set_point(187.5, -143.5, ID="L")
            G = model.set_point(275.0, -143.5, classes=["given"], ID="G")
            H = model.set_point(18.0, -190.5, ID="H")
            K = model.set_point(187.5, -190.5, ID="K")
            F = model.set_point(275.0, -190.5, classes=["given"], ID="F")

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

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

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

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

            # Sections
            model.set_section([A, E, B])
            model.set_section([H, K, F])

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

            return model


        if __name__ == "__main__":
            construct_g1()