G.260 number parts number — Code

VII.8

If a number be the same parts of a number that a number subtracted is of a number subtracted, the remainder is the same parts of the remainder that the whole is of the whole.

"""Programmatic construction for Book VII, Proposition 8 (VII.8)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0313.g1 using geometor.model."""
            model = Model("VII.8")

            # Top horizontal number segment CD (divided at F)
            C = model.set_point(13.0, -24.0, classes=["given"], ID="C")
            F = model.set_point(157.0, -24.0, ID="F")
            D = model.set_point(231.0, -24.0, classes=["given"], ID="D")

            # Middle horizontal number segment GH (divided at M, K, N)
            G = model.set_point(13.0, -55.0, classes=["given"], ID="G")
            M = model.set_point(65.0, -55.0, ID="M")
            K = model.set_point(88.0, -55.0, ID="K")
            N = model.set_point(140.0, -55.0, ID="N")
            H = model.set_point(164.0, -55.0, classes=["given"], ID="H")

            # Bottom horizontal number segment AB (divided at L, E)
            A = model.set_point(12.0, -81.0, classes=["given"], ID="A")
            L = model.set_point(63.0, -81.0, ID="L")
            E = model.set_point(115.0, -81.0, ID="E")
            B = model.set_point(162.0, -81.0, classes=["given"], ID="B")

            # Base lines
            model.construct_line(C, D)
            model.construct_line(G, H)
            model.construct_line(A, B)

            # Segments on CD
            model.set_segment(C, D)
            model.set_segment(C, F)
            model.set_segment(F, D)

            # Segments on GH
            model.set_segment(G, H)
            model.set_segment(G, M)
            model.set_segment(M, K)
            model.set_segment(K, N)
            model.set_segment(N, H)
            model.set_segment(G, K)
            model.set_segment(K, H)
            model.set_segment(G, N)
            model.set_segment(M, N)
            model.set_segment(M, H)

            # Segments on AB
            model.set_segment(A, B)
            model.set_segment(A, L)
            model.set_segment(L, E)
            model.set_segment(E, B)
            model.set_segment(A, E)
            model.set_segment(L, B)

            # Collinear sections
            model.set_section([C, F, D])
            model.set_section([G, K, H])
            model.set_section([G, M, K])
            model.set_section([K, N, H])
            model.set_section([A, L, E])
            model.set_section([A, E, B])

            return model


        if __name__ == "__main__":
            construct_g1()