G.130 complete a circle from a given segment — Code

III.25

Given a segment of a circle, complete the full circle of which it is a segment.

g1.py

"""Programmatic construction for Book III, Proposition 25 Case 1 (III.25 - g1)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0061.g1 using geometor.model."""
            model = Model("III.25.g1")

            # Points (y-inverted)
            A = model.set_point(44.00, -28.00, classes=["given"], ID="A")
            C = model.set_point(44.00, -152.00, classes=["given"], ID="C")
            D = model.set_point(44.00, -90.00, ID="D")
            B = model.set_point(27.34, -90.00, classes=["given"], ID="B")
            E = model.set_point(151.00, -90.00, ID="E")

            # Circle for segment ABC
            model.construct_circle(E, A)

            # Segments and sections
            model.set_segment(A, C)
            model.set_segment(A, D)
            model.set_segment(D, C)
            model.set_segment(B, D)
            model.set_segment(D, E)
            model.set_segment(B, E)
            model.set_segment(A, B)
            model.set_segment(A, E)
            model.set_segment(E, C)
            model.set_section([A, D, C])
            model.set_section([B, D, E])

            # Polygons
            model.set_polygon([A, B, D])
            model.set_polygon([A, B, E])
            model.set_polygon([A, D, E])
            model.set_polygon([C, D, E])
            model.set_polygon([A, E, C])

            # Angles (wedges)
            model.set_wedge(B, A, A, D)
            model.set_wedge(A, B, B, D)
            model.set_wedge(A, B, B, E)
            model.set_wedge(D, A, A, E)
            model.set_wedge(D, C, C, E)

            return model


        if __name__ == "__main__":
            construct_g1()
        

g2.py

"""Programmatic construction for Book III, Proposition 25 Case 2 (III.25 - g2)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g2() -> Model:
            """Construct the figure 0061.g2 using geometor.model."""
            model = Model("III.25.g2")

            # Points (y-inverted)
            D = model.set_point(85.00, -80.00, ID="D")
            A = model.set_point(85.00, -22.00, classes=["given"], ID="A")
            C = model.set_point(85.00, -138.00, classes=["given"], ID="C")
            B = model.set_point(27.00, -80.00, classes=["given"], ID="B")

            # Circle for semicircle ABC
            model.construct_circle(D, A)

            # Segments and sections
            model.set_segment(A, C)
            model.set_segment(A, D)
            model.set_segment(D, C)
            model.set_segment(B, D)
            model.set_segment(A, B)
            model.set_section([A, D, C])

            # Polygon
            model.set_polygon([A, B, D])

            # Angles (wedges)
            model.set_wedge(B, A, A, D)
            model.set_wedge(A, B, B, D)

            return model


        if __name__ == "__main__":
            construct_g2()
        

g3.py

"""Programmatic construction for Book III, Proposition 25 Case 3 (III.25 - g3)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g3() -> Model:
            """Construct the figure 0062.g1 using geometor.model."""
            model = Model("III.25.g3")

            # Points (y-inverted)
            E = model.set_point(83.00, -72.00, ID="E")
            D = model.set_point(110.00, -72.00, ID="D")
            A = model.set_point(110.00, -24.00, classes=["given"], ID="A")
            C = model.set_point(110.00, -120.00, classes=["given"], ID="C")
            B = model.set_point(27.93, -72.00, classes=["given"], ID="B")

            # Circle for segment ABC
            model.construct_circle(E, A)

            # Segments and sections
            model.set_segment(A, C)
            model.set_segment(A, D)
            model.set_segment(D, C)
            model.set_segment(B, D)
            model.set_segment(B, E)
            model.set_segment(E, D)
            model.set_segment(A, B)
            model.set_segment(A, E)
            model.set_segment(E, C)
            model.set_section([A, D, C])
            model.set_section([B, E, D])

            # Polygons
            model.set_polygon([A, B, D])
            model.set_polygon([A, B, E])
            model.set_polygon([A, E, D])

            # Angles (wedges)
            model.set_wedge(B, A, A, D)
            model.set_wedge(A, B, B, D)
            model.set_wedge(A, B, B, E)

            return model


        if __name__ == "__main__":
            construct_g3()