G.84 rectangle on whole and part — Code

II.3

If a segment is cut at random, the rectangle contained by the whole and one of the parts equals the rectangle contained by the parts together with the square on that part.
A C B F D E 
"""Programmatic construction for Book II, Proposition 3 (II.3).

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

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure for Book II, Proposition 3 using geometor.model."""
            model = Model("II.3")

            # Straight line AB cut at random at C
            A = model.set_point(18.5, -29.5, classes=["given"], ID="A")
            C = model.set_point(71.5, -29.5, classes=["given"], ID="C")
            B = model.set_point(173.5, -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 CDEB described on CB [I. 46], ED drawn through to F, and AF parallel to CD/BE [I. 31]
            F = model.set_point(18.5, -129.5, ID="F")
            D = model.set_point(71.5, -129.5, ID="D")
            E = model.set_point(173.5, -129.5, ID="E")

            model.construct_line(E, F)
            model.set_segment(F, E)
            model.set_segment(F, D)
            model.set_segment(D, E)

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

            # Whole rectangle ABEF (AE), rectangle ACDF (AD), and square CDEB (CE / DB)
            model.set_polygon([A, B, E, F])
            model.set_polygon([A, C, D, F])
            model.set_polygon([C, B, E, D])

            return model


        if __name__ == "__main__":
            construct_g1()