G.373 less unequal magnitudes — Code

X.2

If, when the less of two unequal magnitudes is continually subtracted in turn from the greater, that which is left never measures the one before it, the magnitudes is incommensurable.

"""Programmatic construction for Book X, Proposition 2 (X.2)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the magnitude bars E, AB, CD for Book X, Proposition 2 (X.2)."""
            model = Model("X.2")

            # Single-letter magnitude E
            E_l = model.set_point(70.0, -23.5, classes=["given"], ID="E")
            E_r = model.set_point(118.0, -23.5, ID="E_r")

            # Subdivided magnitude AB (divided at G)
            A = model.set_point(205.0, -23.5, classes=["given"], ID="A")
            G = model.set_point(230.0, -23.5, ID="G")
            B = model.set_point(339.0, -23.5, classes=["given"], ID="B")

            # Subdivided magnitude CD (divided at F)
            C = model.set_point(17.0, -50.0, classes=["given"], ID="C")
            F = model.set_point(75.0, -50.0, ID="F")
            D = model.set_point(337.0, -50.0, classes=["given"], ID="D")

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

            # Magnitude E
            model.set_segment(E_l, E_r)

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

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

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

            return model


        if __name__ == "__main__":
            construct_g1()