G.235 equiangular parallelograms ratio — Code

VI.23

Equiangular parallelograms have to one another the ratio compounded of the ratios of their sides.
K L M A D H B C G E F 
"""Programmatic construction for Book VI, Proposition 23 (VI.23).

        Equiangular parallelograms have to one another the ratio compounded of the ratios
        of their sides.
        """

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for 0253.g1 (VI.23) using geometor.model."""
            model = Model("VI.23")

            # 1. Equiangular parallelograms AC (ABCD), CF (CEFG), and completed DG (DCGH)
            A = model.set_point(161.0, -28.0, classes=["given"], ID="A")
            D = model.set_point(253.0, -28.0, classes=["given"], ID="D")
            H = model.set_point(366.0, -28.0, ID="H")

            B = model.set_point(156.0, -59.0, classes=["given"], ID="B")
            C = model.set_point(248.0, -59.0, classes=["given"], ID="C")
            G = model.set_point(361.0, -59.0, classes=["given"], ID="G")

            E = model.set_point(240.0, -109.0, classes=["given"], ID="E")
            F = model.set_point(353.0, -109.0, classes=["given"], ID="F")

            # 2. Auxiliary straight lines K, L, M
            K1 = model.set_point(30.0, -65.0, ID="K1")
            K2 = model.set_point(92.0, -65.0, ID="K2")
            model.set_segment(K1, K2)

            L1 = model.set_point(30.0, -87.0, ID="L1")
            L2 = model.set_point(105.0, -87.0, ID="L2")
            model.set_segment(L1, L2)

            M1 = model.set_point(30.0, -109.0, ID="M1")
            M2 = model.set_point(135.0, -109.0, ID="M2")
            model.set_segment(M1, M2)

            # 3. Construction lines
            model.construct_line(B, G)
            model.construct_line(D, E)

            # 4. Segments and sub-segments
            model.set_segment(A, D)
            model.set_segment(D, H)
            model.set_segment(A, H)

            model.set_segment(B, C)
            model.set_segment(C, G)
            model.set_segment(B, G)

            model.set_segment(E, F)

            model.set_segment(A, B)
            model.set_segment(D, C)
            model.set_segment(C, E)
            model.set_segment(D, E)
            model.set_segment(H, G)
            model.set_segment(G, F)
            model.set_segment(H, F)

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

            # 6. Parallelograms AC, CF, DG (CH)
            model.set_polygon([A, B, C, D])
            model.set_polygon([C, E, F, G])
            model.set_polygon([D, C, G, H])

            # 7. Equal vertical angles BCD and ECG
            model.set_wedge(C, B, B, D)  # < B C D )
            model.set_wedge(C, E, E, G)  # < E C G )

            return model


        if __name__ == "__main__":
            construct_g1()