G.21 cut off an equal segment — Code

I.3

Cut off from the greater of two unequal segments a segment equal to the less.
C D A E B F 
"""Programmatic construction for Book I, Proposition 3 (I.3).

        Given two unequal straight lines, to cut off from the greater a straight line
        equal to the less.
        """

        from __future__ import annotations

        import sympy as sp
        from geometor.model import Model


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

            # 1. Let AB, C be the two given unequal straight lines, and let AB be the greater.
            A = model.set_point(0, 0, classes=["given"], ID="A")
            B = model.set_point(3, 0, classes=["given"], ID="B")
            model.set_segment(A, B)

            # Standalone given straight line C (of length 2)
            C_start = model.set_point(-sp.Rational(1, 2), sp.Rational(5, 2), classes=["given"])
            C_end = model.set_point(sp.Rational(3, 2), sp.Rational(5, 2), classes=["given"], label="C")
            model.set_segment(C_start, C_end)

            # 2. At the point A let AD be placed equal to the straight line C [I. 2]
            D = model.set_point(-sp.Rational(8, 5), sp.Rational(6, 5), label="D")
            model.set_segment(A, D)

            # 3. With centre A and distance AD let the circle DEF be described [Post. 3]
            model.construct_circle(A, D)

            # Circumference point F and intersection point E on AB
            E = model.set_point(2, 0, ID="E")
            F = model.set_point(sp.Rational(6, 5), -sp.Rational(8, 5), label="F")

            # 4. Cut-off segment AE and remainder EB along AB
            model.set_segment(A, E)
            model.set_segment(E, B)
            model.set_section([A, E, B])

            return model


        if __name__ == "__main__":
            construct_g1()