G.179 magnitudes equimultiples magnitudes — Code

V.6

If two magnitudes be equimultiples of two magnitudes, and any magnitudes subtracted from them be equimultiples of the same, the remainders also are either equal to the same or equimultiples of them.
A G B E K C H D F 
"""Programmatic construction for Book V, Proposition 6 (V.6)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0153.g1 for Book V, Proposition 6 using geometor.model."""
            model = Model("V.6")

            # Magnitude AB subdivided at G (with intermediate multiple marks A_1, A_2)
            A = model.set_point(27.0, -28.0, classes=["given"], ID="A")
            A_1 = model.set_point(71.0, -28.0, ID="A_1")
            A_2 = model.set_point(115.0, -28.0, ID="A_2")
            G = model.set_point(159.0, -28.0, classes=["given"], ID="G")
            B = model.set_point(204.0, -28.0, classes=["given"], ID="B")

            # Standalone magnitude E
            E_1 = model.set_point(27.0, -52.0, classes=["given"], ID="E_1")
            E_2 = model.set_point(71.0, -52.0, classes=["given"], ID="E_2")

            # Magnitude KD subdivided at C and H (with intermediate multiple marks C_1, C_2)
            K = model.set_point(27.0, -84.0, ID="K")
            C = model.set_point(56.0, -84.0, classes=["given"], ID="C")
            C_1 = model.set_point(85.0, -84.0, ID="C_1")
            C_2 = model.set_point(115.0, -84.0, ID="C_2")
            H = model.set_point(144.0, -84.0, classes=["given"], ID="H")
            D = model.set_point(173.0, -84.0, classes=["given"], ID="D")

            # Standalone magnitude F
            F_1 = model.set_point(27.0, -107.0, classes=["given"], ID="F_1")
            F_2 = model.set_point(56.0, -107.0, classes=["given"], ID="F_2")

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

            # Segments along AB
            model.set_segment(A, B)
            model.set_segment(A, G)
            model.set_segment(G, B)

            # Standalone magnitude E
            model.set_segment(E_1, E_2)

            # Segments along KD
            model.set_segment(K, D)
            model.set_segment(C, D)
            model.set_segment(C, H)
            model.set_segment(H, D)
            model.set_segment(C, K)
            model.set_segment(K, H)

            # Standalone magnitude F
            model.set_segment(F_1, F_2)

            return model


        if __name__ == "__main__":
            construct_g1()