G.90 four rectangles plus square on difference — Code¶
If a segment is cut at random, four times the rectangle contained by the whole and one of the parts together with the square on the remaining part equals the square on the whole and the first part as one segment.
"""Programmatic construction for Book II, Proposition 8 (II.8)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure for 0404.g1 (II.8) using geometor.model."""
model = Model("II.8")
# 1. Points
A = model.set_point(30.0, -29.0, classes=["given"], ID="A")
C = model.set_point(152.0, -29.0, classes=["given"], ID="C")
B = model.set_point(192.0, -29.0, classes=["given"], ID="B")
D = model.set_point(232.0, -29.0, ID="D")
M = model.set_point(30.0, -69.0, ID="M")
G = model.set_point(152.0, -69.0, ID="G")
K = model.set_point(192.0, -69.0, ID="K")
N = model.set_point(232.0, -69.0, ID="N")
O = model.set_point(30.0, -109.0, ID="O")
Q = model.set_point(152.0, -109.0, ID="Q")
R = model.set_point(192.0, -109.0, ID="R")
P = model.set_point(232.0, -109.0, ID="P")
E = model.set_point(30.0, -231.0, ID="E")
H = model.set_point(152.0, -231.0, ID="H")
L = model.set_point(192.0, -231.0, ID="L")
F = model.set_point(232.0, -231.0, ID="F")
# Gnomon markers
S = model.set_point(124.0, -109.0, ID="S")
T = model.set_point(208.0, -53.0, ID="T")
U = model.set_point(152.0, -137.0, ID="U")
# 2. Segments
# Horizontal Row 1: A, C, B, D
model.set_segment(A, C)
model.set_segment(C, B)
model.set_segment(B, D)
model.set_segment(A, B)
model.set_segment(C, D)
model.set_segment(A, D)
# Horizontal Row 2: M, G, K, N
model.set_segment(M, G)
model.set_segment(G, K)
model.set_segment(K, N)
model.set_segment(M, K)
model.set_segment(G, N)
model.set_segment(M, N)
# Horizontal Row 3: O, Q, R, P
model.set_segment(O, Q)
model.set_segment(Q, R)
model.set_segment(R, P)
model.set_segment(O, R)
model.set_segment(Q, P)
model.set_segment(O, P)
# Horizontal Row 4: E, H, L, F
model.set_segment(E, H)
model.set_segment(H, L)
model.set_segment(L, F)
model.set_segment(E, L)
model.set_segment(H, F)
model.set_segment(E, F)
# Vertical Col 1: A, M, O, E
model.set_segment(A, M)
model.set_segment(M, O)
model.set_segment(O, E)
model.set_segment(A, O)
model.set_segment(M, E)
model.set_segment(A, E)
# Vertical Col 2: C, G, Q, H
model.set_segment(C, G)
model.set_segment(G, Q)
model.set_segment(Q, H)
model.set_segment(C, Q)
model.set_segment(G, H)
model.set_segment(C, H)
# Vertical Col 3: B, K, R, L
model.set_segment(B, K)
model.set_segment(K, R)
model.set_segment(R, L)
model.set_segment(B, R)
model.set_segment(K, L)
model.set_segment(B, L)
# Vertical Col 4: D, N, P, F
model.set_segment(D, N)
model.set_segment(N, P)
model.set_segment(P, F)
model.set_segment(D, P)
model.set_segment(N, F)
model.set_segment(D, F)
# Diagonal: D, K, Q, E
model.set_segment(D, K)
model.set_segment(K, Q)
model.set_segment(Q, E)
model.set_segment(D, Q)
model.set_segment(K, E)
model.set_segment(D, E)
# 3. Polygons (Squares, Rectangles, Gnomon)
model.set_polygon([A, E, F, D])
model.set_polygon([O, Q, H, E])
model.set_polygon([C, B, K, G])
model.set_polygon([B, D, N, K])
model.set_polygon([G, K, R, Q])
model.set_polygon([K, N, P, R])
model.set_polygon([C, D, P, Q])
model.set_polygon([A, C, G, M])
model.set_polygon([M, G, Q, O])
model.set_polygon([Q, R, L, H])
model.set_polygon([R, P, F, L])
model.set_polygon([M, K, L, E])
model.set_polygon([A, B, K, M])
model.set_polygon([A, D, F, H, Q, O])
model.set_polygon([S, T, U])
return model
if __name__ == "__main__":
construct_g1()