G.374 commensurable magnitudes find — Code

X.3

Given two commensurable magnitudes, to find their greatest common measure.

"""Programmatic construction for Book X, Proposition 3 (X.3)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the magnitude bars G, AB, CD for Book X, Proposition 3 (X.3)."""
            model = Model("X.3")

            # Single-letter magnitude G
            G_l = model.set_point(29.0, -20.5, classes=["given"], ID="G")
            G_r = model.set_point(76.0, -20.5, ID="G_r")

            # Subdivided magnitude AB (divided at F)
            A = model.set_point(179.0, -23.0, classes=["given"], ID="A")
            F = model.set_point(193.0, -23.0, ID="F")
            B = model.set_point(300.0, -23.0, classes=["given"], ID="B")

            # Subdivided magnitude CD (divided at E)
            C = model.set_point(19.0, -51.0, classes=["given"], ID="C")
            E = model.set_point(54.0, -51.0, ID="E")
            D = model.set_point(298.0, -51.0, classes=["given"], ID="D")

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

            # Magnitude G
            model.set_segment(G_l, G_r)

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

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

            # Sections
            model.set_section([A, F, B])
            model.set_section([C, E, D])

            return model


        if __name__ == "__main__":
            construct_g1()