G.546 segments proportional parallelepipedal — Code

XI.36

If three segments be proportional, the parallelepipedal solid formed out of the three is equal to the parallelepipedal solid on the mean which is equilateral, but equiangular with the aforesaid solid.

"""Programmatic construction for Book XI, Proposition 36 (XI.36).

        If three straight lines A, B, C be proportional, the parallelepipedal solid LH
        formed out of A, B, C is equal to the equilateral and equiangular
        parallelepipedal solid EK on the mean B.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the two equiangular parallelepipeds LH and EK and lines A, B, C for XI.36."""
            model = Model("XI.36")

            # Left parallelepiped LH
            H = model.set_point(sp.Rational(48, 100), sp.Rational(229, 100), classes=["given"], label="H")
            H_right = model.set_point(sp.Rational(174, 100), sp.Rational(229, 100), label="H_right")
            N_left = model.set_point(sp.Rational(108, 100), sp.Rational(181, 100), label="N_left")
            N = model.set_point(sp.Rational(234, 100), sp.Rational(181, 100), classes=["given"], label="N")

            O_left = model.set_point(sp.Rational(12, 100), sp.Rational(159, 100), label="O_left")
            O = model.set_point(sp.Rational(138, 100), sp.Rational(159, 100), classes=["given"], label="O")
            M = model.set_point(sp.Rational(72, 100), sp.Rational(111, 100), classes=["given"], label="M")
            L = model.set_point(sp.Rational(198, 100), sp.Rational(111, 100), classes=["given"], label="L")

            # Proportional lines A, B, C
            A1 = model.set_point(sp.Rational(74, 100), sp.Rational(79, 100), classes=["given"], label="A")
            A2 = model.set_point(sp.Rational(196, 100), sp.Rational(79, 100), label="A2")
            B1 = model.set_point(sp.Rational(74, 100), sp.Rational(51, 100), classes=["given"], label="B")
            B2 = model.set_point(sp.Rational(166, 100), sp.Rational(51, 100), label="B2")
            C1 = model.set_point(sp.Rational(74, 100), sp.Rational(23, 100), classes=["given"], label="C")
            C2 = model.set_point(sp.Rational(142, 100), sp.Rational(23, 100), label="C2")

            # Right parallelepiped EK
            K = model.set_point(sp.Rational(356, 100), sp.Rational(215, 100), classes=["given"], label="K")
            K_right = model.set_point(sp.Rational(468, 100), sp.Rational(215, 100), label="K_right")
            D_left = model.set_point(sp.Rational(416, 100), sp.Rational(167, 100), label="D_left")
            D = model.set_point(sp.Rational(528, 100), sp.Rational(167, 100), classes=["given"], label="D")

            G_left = model.set_point(sp.Rational(312, 100), sp.Rational(129, 100), label="G_left")
            G = model.set_point(sp.Rational(424, 100), sp.Rational(129, 100), classes=["given"], label="G")
            F = model.set_point(sp.Rational(372, 100), sp.Rational(81, 100), classes=["given"], label="F")
            E = model.set_point(sp.Rational(484, 100), sp.Rational(81, 100), classes=["given"], label="E")

            for p1, p2 in [
                (H, H_right), (H_right, N), (N, N_left), (N_left, H),
                (O_left, O), (O, L), (L, M), (M, O_left),
                (O_left, H), (O, H_right), (L, N), (M, N_left),
                (A1, A2), (B1, B2), (C1, C2),
                (K, K_right), (K_right, D), (D, D_left), (D_left, K),
                (G_left, G), (G, E), (E, F), (F, G_left),
                (G_left, K), (G, K_right), (E, D), (F, D_left),
            ]:
                model.set_segment(p1, p2)

            model.set_polygon([M, L, N, N_left])
            model.set_polygon([O_left, O, L, M])
            model.set_polygon([F, E, D, D_left])
            model.set_polygon([G_left, G, E, F])

            return model


        if __name__ == "__main__":
            construct_g1()