G.452 medial areas incommensurable — Code

X.72

If two medial areas incommensurable with one another be added together, the remaining two irrational segments arise, namely either a second bimedial or a side of the sum of two medial areas.
A C B D E F H G K I 
"""Programmatic construction for Book X, Proposition 72 (X.72)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0159.g1 using geometor.model."""
            model = Model("X.72")

            # Left area AD composed of two incommensurable medial areas AB, CD
            A = model.set_point(21.5, -16.5, classes=["given"], ID="A")
            C = model.set_point(105.5, -16.5, classes=["given"], ID="C")
            C_r = model.set_point(147.5, -16.5, ID="C_r")
            A_b = model.set_point(21.5, -104.0, ID="A_b")
            B = model.set_point(105.5, -104.0, classes=["given"], ID="B")
            D = model.set_point(147.5, -104.0, classes=["given"], ID="D")

            # Right rectangle EI applied to rational straight line EF
            E = model.set_point(274.5, -41.0, classes=["given"], ID="E")
            F = model.set_point(478.0, -41.0, classes=["given"], ID="F")
            H = model.set_point(274.5, -83.0, ID="H")
            G = model.set_point(478.0, -83.0, ID="G")
            K = model.set_point(274.5, -100.0, ID="K")
            I = model.set_point(478.0, -100.0, 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, F)
            model.construct_line(H, G)
            model.construct_line(K, I)
            model.construct_line(E, K)
            model.construct_line(F, 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, F)
            model.set_segment(H, G)
            model.set_segment(K, I)
            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)

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

            return model


        if __name__ == "__main__":
            construct_g1()