G.399 rectangle contained medial — Code¶
The rectangle contained by medial segments commensurable in square only is either rational or medial.
"""Programmatic construction for Book X, Proposition 25 (X.25)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0060.g1 using geometor.model."""
model = Model("X.25")
# Left composite figure: square AD, rectangle AC, square BE (also called CO)
A = model.set_point(94.0, -18.5, classes=["given"], ID="A")
B = model.set_point(94.0, -93.0, classes=["given"], ID="B")
C = model.set_point(140.0, -93.0, classes=["given"], ID="C")
D = model.set_point(19.0, -93.0, ID="D")
O = model.set_point(94.0, -139.0, ID="O")
E = model.set_point(140.0, -139.0, ID="E")
D_t = model.set_point(19.0, -18.5, ID="D_t")
C_t = model.set_point(140.0, -18.5, ID="C_t")
# Right composite figure: rectangles GH, MK (HN), NL on FG
F = model.set_point(194.5, -18.0, classes=["given"], ID="F")
G = model.set_point(256.0, -18.0, classes=["given"], ID="G")
H = model.set_point(194.5, -112.5, ID="H")
M = model.set_point(256.0, -112.5, ID="M")
K = model.set_point(194.5, -165.5, ID="K")
N = model.set_point(256.0, -165.5, ID="N")
L = model.set_point(194.5, -198.5, ID="L")
L_r = model.set_point(256.0, -198.5, ID="L_r")
# Base lines
model.construct_line(D_t, C_t)
model.construct_line(D, C)
model.construct_line(O, E)
model.construct_line(D_t, D)
model.construct_line(A, O)
model.construct_line(C_t, E)
model.construct_line(F, L)
model.construct_line(G, L_r)
model.construct_line(F, G)
model.construct_line(H, M)
model.construct_line(K, N)
model.construct_line(L, L_r)
# Segments on left figure
model.set_segment(A, B)
model.set_segment(B, O)
model.set_segment(A, O)
model.set_segment(D, B)
model.set_segment(B, C)
model.set_segment(D, C)
model.set_segment(O, E)
model.set_segment(C, E)
model.set_segment(D_t, D)
model.set_segment(D_t, C_t)
model.set_segment(C_t, E)
# Segments on right figure
model.set_segment(F, G)
model.set_segment(H, M)
model.set_segment(K, N)
model.set_segment(L, L_r)
model.set_segment(F, H)
model.set_segment(H, K)
model.set_segment(K, L)
model.set_segment(F, K)
model.set_segment(H, L)
model.set_segment(F, L)
model.set_segment(G, L_r)
# Collinear sections
model.set_section([A, B, O])
model.set_section([D, B, C])
model.set_section([F, H, K])
model.set_section([H, K, L])
model.set_section([F, H, L])
# Polygons
model.set_polygon([A, B, D, D_t])
model.set_polygon([A, B, C, C_t])
model.set_polygon([B, C, E, O])
model.set_polygon([F, G, M, H])
model.set_polygon([H, M, N, K])
model.set_polygon([K, N, L_r, L])
return model
if __name__ == "__main__":
construct_g1()