G.290 numbers find least — Code

VII.34

Given two numbers, to find the least number which they measure.

g1.py

A B C D E F 
"""Programmatic construction for Book VII, Proposition 34, Case 1 (VII.34 - g1)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0342.g1 using geometor.model."""
            model = Model("VII.34.g1")

            # Given prime numbers A, B
            A_l = model.set_point(41.0, -17.0, classes=["given"], ID="A")
            A_r = model.set_point(98.0, -17.0, ID="A_r")

            B_l = model.set_point(128.0, -17.0, classes=["given"], ID="B")
            B_r = model.set_point(196.0, -17.0, ID="B_r")

            # Product C and lesser number D
            C_l = model.set_point(43.0, -42.0, classes=["given"], ID="C")
            C_r = model.set_point(199.0, -42.0, ID="C_r")

            D_l = model.set_point(46.0, -65.0, classes=["given"], ID="D")
            D_r = model.set_point(156.0, -65.0, ID="D_r")

            # Unit counts E, F
            E_l = model.set_point(24.0, -95.0, classes=["given"], ID="E")
            E_r = model.set_point(78.0, -95.0, ID="E_r")

            F_l = model.set_point(126.0, -95.0, classes=["given"], ID="F")
            F_r = model.set_point(167.0, -95.0, ID="F_r")

            # Segments
            model.set_segment(A_l, A_r)
            model.set_segment(B_l, B_r)
            model.set_segment(C_l, C_r)
            model.set_segment(D_l, D_r)
            model.set_segment(E_l, E_r)
            model.set_segment(F_l, F_r)

            return model


        if __name__ == "__main__":
            construct_g1()

g2.py

A B F E C D G H 
"""Programmatic construction for Book VII, Proposition 34, Case 2 (VII.34 - g2)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g2() -> Model:
            """Construct the figure 0343.g1 using geometor.model."""
            model = Model("VII.34.g2")

            # Given numbers A, B (not prime to one another)
            A_l = model.set_point(22.0, -23.0, classes=["given"], ID="A")
            A_r = model.set_point(90.0, -23.0, ID="A_r")

            B_l = model.set_point(124.0, -23.0, classes=["given"], ID="B")
            B_r = model.set_point(227.0, -23.0, ID="B_r")

            # Least numbers F, E in the same ratio with A, B
            F_l = model.set_point(23.0, -49.0, classes=["given"], ID="F")
            F_r = model.set_point(69.0, -49.0, ID="F_r")

            E_l = model.set_point(116.0, -49.0, classes=["given"], ID="E")
            E_r = model.set_point(184.0, -49.0, ID="E_r")

            # Product C and lesser number D
            C_l = model.set_point(23.0, -76.0, classes=["given"], ID="C")
            C_r = model.set_point(165.0, -76.0, ID="C_r")

            D_l = model.set_point(27.0, -99.0, classes=["given"], ID="D")
            D_r = model.set_point(132.0, -99.0, ID="D_r")

            # Unit counts G, H
            G_l = model.set_point(40.0, -126.0, classes=["given"], ID="G")
            G_r = model.set_point(75.0, -126.0, ID="G_r")

            H_l = model.set_point(123.0, -126.0, classes=["given"], ID="H")
            H_r = model.set_point(147.0, -126.0, ID="H_r")

            # Segments
            model.set_segment(A_l, A_r)
            model.set_segment(B_l, B_r)
            model.set_segment(F_l, F_r)
            model.set_segment(E_l, E_r)
            model.set_segment(C_l, C_r)
            model.set_segment(D_l, D_r)
            model.set_segment(G_l, G_r)
            model.set_segment(H_l, H_r)

            return model


        if __name__ == "__main__":
            construct_g2()