G.171 there number magnitudes — Code

V.1

If there be any number of magnitudes whatever which are, respectively, equimultiples of any magnitudes equal in multitude, then, whatever multiple one of the magnitudes is of one, that multiple also will all be of all.

"""Programmatic construction for Book V, Proposition 1 (V.1)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0144.g1 using geometor.model."""
            model = Model("V.1")

            # Points on AB (divided at G) and CD (divided at H)
            A = model.set_point(30.0, -29.0, classes=["given"], ID="A")
            G = model.set_point(68.0, -29.0, ID="G")
            B = model.set_point(106.0, -29.0, classes=["given"], ID="B")

            C = model.set_point(196.0, -29.0, classes=["given"], ID="C")
            H = model.set_point(251.0, -29.0, ID="H")
            D = model.set_point(306.0, -29.0, classes=["given"], ID="D")

            # Single-letter magnitudes E and F
            E_l = model.set_point(26.0, -63.0, classes=["given"], ID="E")
            E_r = model.set_point(66.0, -63.0, ID="E_r")
            F_l = model.set_point(194.0, -63.0, classes=["given"], ID="F")
            F_r = model.set_point(249.0, -63.0, ID="F_r")

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

            # Whole and subdivided segments
            model.set_segment(A, B)
            model.set_segment(A, G)
            model.set_segment(G, B)
            model.set_segment(C, D)
            model.set_segment(C, H)
            model.set_segment(H, D)
            model.set_segment(E_l, E_r)
            model.set_segment(F_l, F_r)

            # Collinear sections
            model.set_section([A, G, B])
            model.set_section([C, H, D])

            return model


        if __name__ == "__main__":
            construct_g1()