G.438 area contained rational — Code

X.58

If an area be contained by a rational segment and the fifth binomial, the “side” of the area is the irrational segment called the side of a rational plus a medial area.

#!/usr/bin/env python3
        """
        Programmatic construction for Euclid Book X, Proposition 58 (X.58)
        using geometor.model.
        """
        from geometor.model import Model


        def build_model() -> Model:
            m = Model("X.58")

            # Left partitioned rectangle ABCD (with vertical dividers GH, EK, FL)
            A = m.set_point(17.0, 20.0, classes=["given"], ID="A")
            G = m.set_point(115.5, 20.0, classes=["constructed"], ID="G")
            E = m.set_point(133.5, 20.0, classes=["given"], ID="E")
            F = m.set_point(176.5, 20.0, classes=["constructed"], ID="F")
            D = m.set_point(218.0, 20.0, classes=["given"], ID="D")

            B = m.set_point(17.0, 72.5, classes=["given"], ID="B")
            H = m.set_point(115.5, 72.5, classes=["constructed"], ID="H")
            K = m.set_point(133.5, 72.5, classes=["constructed"], ID="K")
            L = m.set_point(176.5, 72.5, classes=["constructed"], ID="L")
            C = m.set_point(218.0, 72.5, classes=["constructed"], ID="C")

            # Top and bottom segments of ABCD
            m.set_segment(A, D)
            m.set_segment(A, E)
            m.set_segment(E, D)
            m.set_segment(E, F)
            m.set_segment(F, D)
            m.set_segment(A, G)
            m.set_segment(G, E)
            m.set_segment(B, C)
            m.set_segment(B, H)
            m.set_segment(H, K)
            m.set_segment(K, L)
            m.set_segment(L, C)

            # Vertical dividers of ABCD
            m.set_segment(A, B)
            m.set_segment(G, H)
            m.set_segment(E, K)
            m.set_segment(F, L)
            m.set_segment(D, C)

            # Polygons of ABCD
            m.set_polygon([A, B, C, D])  # AC
            m.set_polygon([A, B, K, E])  # AK
            m.set_polygon([A, B, H, G])  # AH
            m.set_polygon([G, H, K, E])  # GK / HE
            m.set_polygon([E, K, L, F])  # EL
            m.set_polygon([F, L, C, D])  # FC

            # Right square SQ with horizontal divider MO and vertical divider RP meeting at N
            TL = m.set_point(291.5, 20.0, classes=["constructed"], ID="TL")
            R = m.set_point(363.0, 20.0, classes=["constructed"], ID="R")
            Q = m.set_point(398.5, 20.0, classes=["constructed"], ID="Q")

            M = m.set_point(291.5, 54.5, classes=["constructed"], ID="M")
            N = m.set_point(363.0, 54.5, classes=["constructed"], ID="N")
            O = m.set_point(398.5, 54.5, classes=["constructed"], ID="O")

            S = m.set_point(291.5, 126.5, classes=["constructed"], ID="S")
            P = m.set_point(363.0, 126.5, classes=["constructed"], ID="P")
            BR = m.set_point(398.5, 126.5, classes=["constructed"], ID="BR")

            # Segments of SQ
            m.set_segment(M, O)
            m.set_segment(M, N)
            m.set_segment(N, O)
            m.set_segment(R, P)
            m.set_segment(R, N)
            m.set_segment(N, P)
            m.set_segment(M, S)
            m.set_segment(S, P)
            m.set_segment(O, Q)
            m.set_segment(R, Q)

            # Polygons of SQ
            m.set_polygon([TL, S, BR, Q])  # SQ
            m.set_polygon([M, S, P, N])    # SN (square on MN)
            m.set_polygon([N, O, Q, R])    # NQ (square on NO)
            m.set_polygon([TL, M, N, R])   # MR (rectangle MN, NO)
            m.set_polygon([N, P, BR, O])   # NP (rectangle MN, NO)

            return m


        if __name__ == "__main__":
            model = build_model()
            print(f"Constructed {model.name} with {len(model)} elements.")