G.237 construct one and the same figure similar to — Code¶
Construct one and the same figure similar to a given polygon and equal to another given polygon.
"""Programmatic construction for Book VI, Proposition 25 (VI.25).
To construct one and the same figure similar to a given rectilineal figure ABC
and equal to another given rectilineal figure D.
"""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure for 0259.g1 (VI.25) using geometor.model."""
model = Model("VI.25")
# 1. Given triangle ABC and applied parallelograms BE (BLEC) and CM/EF (CEMF)
A = model.set_point(26.0, -51.0, classes=["given"], ID="A")
B = model.set_point(47.0, -125.0, classes=["given"], ID="B")
C = model.set_point(119.0, -125.0, classes=["given"], ID="C")
F = model.set_point(199.0, -125.0, ID="F")
L = model.set_point(36.0, -164.0, ID="L")
E = model.set_point(108.0, -164.0, ID="E")
M = model.set_point(188.0, -164.0, ID="M")
model.construct_line(B, F)
model.construct_line(L, M)
model.set_segment(A, B)
model.set_segment(A, C)
model.set_segment(B, C)
model.set_segment(C, F)
model.set_segment(B, F)
model.set_segment(L, E)
model.set_segment(E, M)
model.set_segment(L, M)
model.set_segment(B, L)
model.set_segment(C, E)
model.set_segment(F, M)
model.set_section([B, C, F])
model.set_section([L, E, M])
model.set_polygon([A, B, C])
model.set_polygon([B, L, E, C])
model.set_polygon([C, E, M, F])
model.set_polygon([B, L, M, F])
# 2. Given rectilineal figure D
D1 = model.set_point(156.0, -84.0, classes=["given"], ID="D1")
D2 = model.set_point(252.0, -48.0, classes=["given"], ID="D2")
D3 = model.set_point(296.0, -94.0, classes=["given"], ID="D3")
D4 = model.set_point(221.0, -110.0, classes=["given"], ID="D4")
model.set_segment(D1, D2)
model.set_segment(D2, D3)
model.set_segment(D3, D4)
model.set_segment(D4, D1)
model.set_polygon([D1, D2, D3, D4])
# 3. Constructed similar triangle KGH on mean proportional GH
K = model.set_point(356.0, -56.0, ID="K")
G = model.set_point(385.0, -162.0, ID="G")
H = model.set_point(490.0, -162.0, ID="H")
model.set_segment(K, G)
model.set_segment(K, H)
model.set_segment(G, H)
model.set_polygon([K, G, H])
# 4. Angles FCE and CBL
model.set_wedge(C, F, F, E) # < F C E )
model.set_wedge(B, C, C, L) # < C B L )
return model
if __name__ == "__main__":
construct_g1()