G.434 area contained rational — Code

X.54

If an area be contained by a rational segment and the first binomial, the “side” of the area is the irrational segment which is called binomial.

"""Programmatic construction for Book X, Proposition 54 (X.54)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0121.g1 using geometor.model."""
            model = Model("X.54")

            # Left rectangle ABCD divided by vertical segments GH, EK, FL
            A = model.set_point(20.5, -18.5, classes=["given"], ID="A")
            G = model.set_point(120.0, -18.5, ID="G")
            E = model.set_point(136.5, -18.5, classes=["given"], ID="E")
            F = model.set_point(180.5, -18.5, ID="F")
            D = model.set_point(220.5, -18.5, classes=["given"], ID="D")

            B = model.set_point(20.5, -69.5, classes=["given"], ID="B")
            H = model.set_point(120.0, -69.5, ID="H")
            K = model.set_point(136.5, -69.5, ID="K")
            L = model.set_point(180.5, -69.5, ID="L")
            C = model.set_point(220.5, -69.5, classes=["given"], ID="C")

            # Right square SQ divided by MO and RP intersecting at N
            Q_tl = model.set_point(309.5, -18.5, ID="Q_tl")
            R = model.set_point(383.5, -18.5, ID="R")
            Q = model.set_point(416.0, -18.5, ID="Q")

            M = model.set_point(309.5, -51.5, ID="M")
            N = model.set_point(383.5, -51.5, ID="N")
            O = model.set_point(416.0, -51.5, ID="O")

            S = model.set_point(309.5, -123.5, ID="S")
            P = model.set_point(383.5, -123.5, ID="P")
            S_br = model.set_point(416.0, -123.5, ID="S_br")

            # Base lines
            for p1, p2 in [
                (A, D), (B, C), (A, B), (G, H), (E, K), (F, L), (D, C),
                (Q_tl, Q), (M, O), (S, S_br), (Q_tl, S), (R, P), (Q, S_br),
            ]:
                model.construct_line(p1, p2)

            # Top and bottom segments of ABCD
            top_pts = [A, G, E, F, D]
            bot_pts = [B, H, K, L, C]
            for pts in (top_pts, bot_pts):
                for i in range(len(pts)):
                    for j in range(i + 1, len(pts)):
                        model.set_segment(pts[i], pts[j])

            # Vertical segments of ABCD
            for p1, p2 in [(A, B), (G, H), (E, K), (F, L), (D, C)]:
                model.set_segment(p1, p2)

            # Segments of square SQ
            for p1, p2 in [
                (Q_tl, Q), (Q_tl, R), (R, Q),
                (M, O), (M, N), (N, O),
                (S, S_br), (S, P), (P, S_br),
                (Q_tl, S), (Q_tl, M), (M, S),
                (R, P), (R, N), (N, P),
                (Q, S_br), (Q, O), (O, S_br),
            ]:
                model.set_segment(p1, p2)

            # Key collinear sections
            model.set_section([A, G, E])
            model.set_section([A, E, D])
            model.set_section([E, F, D])
            model.set_section([M, N, O])
            model.set_section([R, N, P])

            # Polygons (rectangles and squares)
            model.set_polygon([A, B, C, D])
            model.set_polygon([A, B, H, G])
            model.set_polygon([G, H, K, E])
            model.set_polygon([E, K, L, F])
            model.set_polygon([F, L, C, D])
            model.set_polygon([E, K, C, D])
            model.set_polygon([S, S_br, Q, Q_tl])
            model.set_polygon([S, P, N, M])
            model.set_polygon([N, O, Q, R])
            model.set_polygon([M, N, R, Q_tl])
            model.set_polygon([P, S_br, O, N])

            return model


        if __name__ == "__main__":
            construct_g1()