G.466 segment produces medial — Code¶
To a segment which produces with a medial area a medial whole only one segment can be annexed which is incommensurable in square with the whole segment and which with the whole segment makes the sum of the squares on them medial and twice the rectangle contained by them both medial and also incommensurable with the sum of the squares on them.
"""Programmatic construction for Book X, Proposition 84 (X.84)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0179.g1 using geometor.model."""
model = Model("X.84")
# Top straight line AD divided at B and C
A = model.set_point(105.0, -20.5, classes=["given"], ID="A")
B = model.set_point(147.0, -20.5, classes=["given"], ID="B")
C = model.set_point(213.0, -20.5, classes=["given"], ID="C")
D = model.set_point(242.0, -20.5, classes=["given"], ID="D")
# Rectangle EFIN divided vertically by HL and MG
E = model.set_point(16.0, -51.5, classes=["given"], ID="E")
H = model.set_point(36.5, -51.5, ID="H")
M = model.set_point(205.5, -51.5, ID="M")
N = model.set_point(303.5, -51.5, ID="N")
F = model.set_point(16.0, -145.5, classes=["given"], ID="F")
L = model.set_point(36.5, -145.5, ID="L")
G = model.set_point(205.5, -145.5, ID="G")
I = model.set_point(303.5, -145.5, ID="I")
# Base lines
model.construct_line(A, D)
model.construct_line(E, N)
model.construct_line(F, I)
model.construct_line(E, F)
model.construct_line(H, L)
model.construct_line(M, G)
model.construct_line(N, I)
# Segments on AD
model.set_segment(A, D)
model.set_segment(A, C)
model.set_segment(A, B)
model.set_segment(B, D)
model.set_segment(B, C)
model.set_segment(C, D)
# Vertical segments on rectangle EFIN
model.set_segment(E, F)
model.set_segment(H, L)
model.set_segment(M, G)
model.set_segment(N, I)
# Horizontal segments on top side EN
model.set_segment(E, N)
model.set_segment(E, M)
model.set_segment(E, H)
model.set_segment(H, N)
model.set_segment(H, M)
model.set_segment(M, N)
# Horizontal segments on bottom side FI
model.set_segment(F, I)
model.set_segment(F, G)
model.set_segment(F, L)
model.set_segment(L, I)
model.set_segment(L, G)
model.set_segment(G, I)
# Sections
model.set_section([A, B, C])
model.set_section([A, B, D])
model.set_section([A, C, D])
model.set_section([B, C, D])
model.set_section([E, H, M])
model.set_section([E, H, N])
model.set_section([E, M, N])
model.set_section([H, M, N])
model.set_section([F, L, G])
model.set_section([F, L, I])
model.set_section([F, G, I])
model.set_section([L, G, I])
# Polygons (rectangles)
model.set_polygon([E, F, I, N])
model.set_polygon([E, F, G, M])
model.set_polygon([E, F, L, H])
model.set_polygon([H, L, G, M])
model.set_polygon([H, L, I, N])
model.set_polygon([M, G, I, N])
return model
if __name__ == "__main__":
construct_g1()