G.409 find two segments incommensurable in square which make — Code¶
Find two segments incommensurable in square which make the sum of the squares on them medial and the rectangle contained by them medial and moreover incommensurable with the sum of the squares on them.
"""Programmatic construction for Book X, Proposition 35 (X.35)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0085.g1 using geometor.model."""
model = Model("X.35")
# Diameter AB extended to C, with E bisecting BC, F on AB, and D on semicircle ADB
A = model.set_point(19.0, -109.0, classes=["given"], ID="A")
F = model.set_point(186.5, -109.0, ID="F")
B = model.set_point(204.0, -109.0, classes=["given"], ID="B")
E = model.set_point(257.0, -109.0, ID="E")
C = model.set_point(310.0, -109.0, classes=["given"], ID="C")
O = model.set_point(111.5, -109.0, ID="O")
D = model.set_point(186.5, -54.9, ID="D")
# Base lines and semicircle ADB
model.construct_line(A, C)
model.construct_circle(O, A)
model.construct_line(A, D)
model.construct_line(D, B)
model.construct_line(F, D)
# Segments
model.set_segment(A, B)
model.set_segment(B, C)
model.set_segment(B, E)
model.set_segment(E, C)
model.set_segment(A, F)
model.set_segment(F, B)
model.set_segment(F, D)
model.set_segment(A, D)
model.set_segment(D, B)
model.set_segment(A, C)
model.set_segment(A, E)
model.set_segment(F, C)
model.set_segment(F, E)
# Sections
model.set_section([A, F, B])
model.set_section([B, E, C])
model.set_section([A, B, C])
# Inscribed right triangles ADB, ADF, DFB
model.set_polygon([A, D, B])
model.set_polygon([A, D, F])
model.set_polygon([D, F, B])
# Right angles at D and F
model.set_wedge(D, A, A, B)
model.set_wedge(F, D, A, D)
model.set_wedge(F, D, D, B)
return model
if __name__ == "__main__":
construct_g1()