G.547 segments proportional parallelepipedal — Code

XI.37

If four segments be proportional, the parallelepipedal solids on them which are similar and similarly described is proportional; and, if the parallelepipedal solids on them which are similar and similarly described be proportional, the segments will themselves also be proportional.

"""Programmatic construction for Book XI, Proposition 37 (XI.37).

        Four proportional straight lines AB, CD, EF, GH and the similar and similarly
        situated parallelepipedal solids KA, LC, ME, NG described on them.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


        def _add_box(
            model: Model,
            x1: int, y1: int,
            x2: int, y2: int,
            dx: int, dy: int,
            lbl_bl: str, lbl_br: str, lbl_tr: str,
        ) -> None:
            """Add a parallelepiped box to the model."""
            p_tl1 = model.set_point(sp.Rational(x1, 100), sp.Rational(191 - y1, 100), label=f"{lbl_bl}_tl1")
            p_tr1 = model.set_point(sp.Rational(x2, 100), sp.Rational(191 - y1, 100), classes=["given"], label=lbl_tr)
            p_br1 = model.set_point(sp.Rational(x2 - 3, 100), sp.Rational(191 - y2, 100), label=f"{lbl_bl}_br1")
            p_bl1 = model.set_point(sp.Rational(x1 - 3, 100), sp.Rational(191 - y2, 100), label=f"{lbl_bl}_bl1")

            p_tl2 = model.set_point(sp.Rational(x1 + dx, 100), sp.Rational(191 - (y1 + dy), 100), label=f"{lbl_bl}_tl2")
            p_tr2 = model.set_point(sp.Rational(x2 + dx, 100), sp.Rational(191 - (y1 + dy), 100), label=f"{lbl_bl}_tr2")
            p_br2 = model.set_point(sp.Rational(x2 - 3 + dx, 100), sp.Rational(191 - (y2 + dy), 100), classes=["given"], label=lbl_br)
            p_bl2 = model.set_point(sp.Rational(x1 - 3 + dx, 100), sp.Rational(191 - (y2 + dy), 100), classes=["given"], label=lbl_bl)

            for p1, p2 in [
                (p_tl1, p_tr1), (p_tr1, p_br1), (p_br1, p_bl1), (p_bl1, p_tl1),
                (p_tl2, p_tr2), (p_tr2, p_br2), (p_br2, p_bl2), (p_bl2, p_tl2),
                (p_tl1, p_tl2), (p_tr1, p_tr2), (p_br1, p_br2), (p_bl1, p_bl2),
            ]:
                model.set_segment(p1, p2)

            model.set_polygon([p_bl1, p_br1, p_br2, p_bl2])
            model.set_polygon([p_tl2, p_tr2, p_br2, p_bl2])


        def construct_g1() -> Model:
            """Construct the four similar parallelepipeds KA, LC, ME, NG for XI.37."""
            model = Model("XI.37")

            _add_box(model, 30, 92, 98, 134, 16, 23, "A", "B", "K")
            _add_box(model, 168, 77, 256, 131, 20, 27, "C", "D", "L")
            _add_box(model, 338, 65, 442, 129, 24, 31, "E", "F", "M")
            _add_box(model, 482, 36, 616, 122, 30, 36, "G", "H", "N")

            return model


        if __name__ == "__main__":
            construct_g1()