G.550 there prisms equal — Code

XI.39

If there be two prisms of equal height, and one have a parallelogram as base and the other a triangle, and if the parallelogram be double of the triangle, the prisms is equal.

#!/usr/bin/env python3
        """
        Programmatic construction for Book XI, Proposition 39 (XI.39)
        using geometor.model.
        """
        from geometor.model import Model


        def build_model() -> Model:
            m = Model("XI.39")

            # Left prism ABCDEF and completed solid AO
            B = m.set_point(26, 26, classes=["given"], ID="B")
            D = m.set_point(138, 26, classes=["given"], ID="D")
            O = m.set_point(154, 42, classes=["constructed"], ID="O")
            B2 = m.set_point(42, 42, classes=["auxiliary"])
            A = m.set_point(26, 97, classes=["given"], ID="A")
            C = m.set_point(138, 97, classes=["given"], ID="C")
            F = m.set_point(154, 113, classes=["given"], ID="F")
            E = m.set_point(42, 113, classes=["given"], ID="E")

            # Right prism GHKLMN and completed solid GP
            M = m.set_point(275, 32, classes=["given"], ID="M")
            P = m.set_point(345, 32, classes=["constructed"], ID="P")
            N = m.set_point(378, 60, classes=["given"], ID="N")
            L = m.set_point(308, 60, classes=["given"], ID="L")
            H = m.set_point(275, 102, classes=["given"], ID="H")
            H2 = m.set_point(345, 102, classes=["auxiliary"])
            K = m.set_point(378, 130, classes=["given"], ID="K")
            G = m.set_point(308, 130, classes=["given"], ID="G")

            # Polygons (solids, prisms, parallelograms, triangles)
            m.set_polygon([B, D, O, F, E, A])  # Solid < A O >
            m.set_polygon([B, D, F, E, A])     # Prism < A B C D E F >
            m.set_polygon([A, C, F, E])        # Parallelogram < A F >
            m.set_polygon([M, P, N, K, G, H])  # Solid < G P >
            m.set_polygon([M, N, K, G, H])     # Prism < G H K L M N >
            m.set_polygon([H, H2, K, G])       # Parallelogram < H K >
            m.set_polygon([G, H, K])           # Triangle < G H K >

            # Segments
            for p1, p2 in [
                (B, D), (D, O), (O, B2), (B2, B),
                (A, C), (C, F), (F, E), (E, A),
                (B, A), (D, C), (O, F), (B2, E),
                (B, E), (D, F),
                (M, P), (P, N), (N, L), (L, M),
                (H, H2), (H2, K), (K, G), (G, H),
                (M, H), (P, H2), (N, K), (L, G),
                (M, N), (H, K),
            ]:
                m.set_segment(p1, p2)

            return m


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