G.404 find two rational segments commensurable in square only — Code¶
Find two rational segments commensurable in square only and such that the square on the greater is greater than the square on the less by the square on a segment incommensurable in length with the greater.
"""Programmatic construction for Book X, Proposition 30 (X.30)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0072.g1 using geometor.model."""
model = Model("X.30")
# Diameter AB, center O, and point F on semicircle AFB
A = model.set_point(19.0, -111.5, classes=["given"], ID="A")
B = model.set_point(224.0, -111.5, classes=["given"], ID="B")
O = model.set_point(121.5, -111.5, ID="O")
F = model.set_point(91.5, -13.5, ID="F")
# Number line CD divided at E
C = model.set_point(46.0, -139.5, classes=["given"], ID="C")
E = model.set_point(92.0, -139.5, ID="E")
D = model.set_point(178.0, -139.5, classes=["given"], ID="D")
# Base lines and circle (semicircle AFB)
model.construct_line(A, B)
model.construct_circle(O, A)
model.construct_line(A, F)
model.construct_line(F, B)
model.construct_line(C, D)
# Segments
model.set_segment(A, B)
model.set_segment(A, F)
model.set_segment(F, B)
model.set_segment(C, D)
model.set_segment(C, E)
model.set_segment(E, D)
model.set_section([C, E, D])
# Inscribed right triangle AFB and right angle at F
model.set_polygon([A, F, B])
model.set_wedge(F, A, A, B)
return model
if __name__ == "__main__":
construct_g1()