G.474 find the fifth apotome — Code

X.89

Find the fifth apotome.

"""Programmatic construction for Book X, Proposition 89 (X.89)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0190.g1 using geometor.model."""
            model = Model("X.89")

            # Vertical single-letter magnitude segments A and H
            A_t = model.set_point(27.0, -19.0, classes=["given"], ID="A")
            A_b = model.set_point(27.0, -154.0, ID="A_b")

            H_t = model.set_point(60.0, -57.0, classes=["given"], ID="H")
            H_b = model.set_point(60.0, -169.0, ID="H_b")

            # Vertical line BG divided at C
            B = model.set_point(104.0, -20.0, classes=["given"], ID="B")
            C = model.set_point(104.0, -88.0, classes=["given"], ID="C")
            G = model.set_point(104.0, -147.0, classes=["given"], ID="G")

            # Vertical number line DE divided at F
            D = model.set_point(130.0, -14.0, classes=["given"], ID="D")
            F = model.set_point(130.0, -146.0, classes=["given"], ID="F")
            E = model.set_point(130.0, -199.0, classes=["given"], ID="E")

            # Base lines
            model.construct_line(A_t, A_b)
            model.construct_line(H_t, H_b)
            model.construct_line(B, G)
            model.construct_line(D, E)

            # Segments
            model.set_segment(A_t, A_b)
            model.set_segment(H_t, H_b)
            model.set_segment(B, G)
            model.set_segment(B, C)
            model.set_segment(C, G)
            model.set_segment(D, E)
            model.set_segment(D, F)
            model.set_segment(F, E)

            # Collinear sections
            model.set_section([B, C, G])
            model.set_section([D, F, E])

            return model


        if __name__ == "__main__":
            construct_g1()