G.415 segments incommensurable square — Code¶
If two segments incommensurable in square which make the sum of the squares on them medial, and the rectangle contained by them medial and also incommensurable with the sum of the squares on them, be added together, the whole segment is irrational; and let it be called the side of the sum of two medial areas.
"""Programmatic construction for Book X, Proposition 41 (X.41)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0094.g1 using geometor.model."""
model = Model("X.41")
# Straight line AC divided into straight lines AB, BC
A = model.set_point(23.0, -259.5, classes=["given"], ID="A")
B = model.set_point(94.0, -259.5, classes=["given"], ID="B")
C = model.set_point(146.0, -259.5, classes=["given"], ID="C")
# Parallelogram DH (K, H at top; G, F in middle; D, E at bottom)
K = model.set_point(53.5, -18.5, ID="K")
H = model.set_point(118.5, -18.5, ID="H")
G = model.set_point(53.5, -103.5, ID="G")
F = model.set_point(118.5, -103.5, ID="F")
D = model.set_point(53.5, -236.0, classes=["given"], ID="D")
E = model.set_point(118.5, -236.0, classes=["given"], ID="E")
# Base lines
model.construct_line(A, C)
model.construct_line(D, K)
model.construct_line(E, H)
model.construct_line(D, E)
model.construct_line(G, F)
model.construct_line(K, H)
# Segments
model.set_segment(A, C)
model.set_segment(A, B)
model.set_segment(B, C)
model.set_segment(D, E)
model.set_segment(G, F)
model.set_segment(K, H)
model.set_segment(D, G)
model.set_segment(G, K)
model.set_segment(D, K)
model.set_segment(E, F)
model.set_segment(F, H)
model.set_segment(E, H)
# Sections
model.set_section([A, B, C])
model.set_section([D, G, K])
model.set_section([E, F, H])
# Polygons: whole rectangle DH, lower rectangle DF, upper rectangle GH
model.set_polygon([D, E, H, K])
model.set_polygon([D, E, F, G])
model.set_polygon([G, F, H, K])
return model
if __name__ == "__main__":
construct_g1()