G.83 square equals sum of rectangles on parts — Code

II.2

If a segment is cut at random, the sum of the rectangles contained by the whole and each of the parts equals the square on the whole.
A C B D F E 
"""Programmatic construction for Book II, Proposition 2 (II.2).

        If a straight line be cut at random, the rectangle contained by the whole and
        both of the segments is equal to the square on the whole.
        """

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book II, Proposition 2 using geometor.model."""
            model = Model("II.2")

            # Straight line AB cut at random at C
            A = model.set_point(20.5, -29.5, classes=["given"], ID="A")
            C = model.set_point(60.5, -29.5, classes=["given"], ID="C")
            B = model.set_point(137.5, -29.5, classes=["given"], ID="B")

            model.construct_line(A, B)
            model.set_segment(A, B)
            model.set_segment(A, C)
            model.set_segment(C, B)

            # Square ADEB described on AB [I. 46], and parallel CF to AD/BE [I. 31]
            D = model.set_point(20.5, -146.5, ID="D")
            F = model.set_point(60.5, -146.5, ID="F")
            E = model.set_point(137.5, -146.5, ID="E")

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

            # Square ADEB (AE) and sub-rectangles ACFD (AF) and CBEF (CE)
            model.set_polygon([A, D, E, B])
            model.set_polygon([A, C, F, D])
            model.set_polygon([C, B, E, F])

            return model


        if __name__ == "__main__":
            construct_g1()