G.412 medial segments commensurable — Code¶
If two medial segments commensurable in square only and containing a medial rectangle be added together, the whole is irrational; and let it be called a second bimedial segment.
"""Programmatic construction for Book X, Proposition 38 (X.38)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0089.g1 using geometor.model."""
model = Model("X.38")
# Straight line AC divided into medial straight lines AB, BC
A = model.set_point(70.0, -17.5, classes=["given"], ID="A")
B = model.set_point(148.5, -17.5, classes=["given"], ID="B")
C = model.set_point(202.0, -17.5, classes=["given"], ID="C")
# Parallelogram DF (D, H, G on top; E, H_b, F on bottom)
D = model.set_point(19.5, -48.0, classes=["given"], ID="D")
H = model.set_point(148.5, -48.0, ID="H")
G = model.set_point(249.5, -48.0, ID="G")
E = model.set_point(19.5, -125.0, classes=["given"], ID="E")
H_b = model.set_point(148.5, -125.0, ID="H_b")
F = model.set_point(249.5, -125.0, ID="F")
# Base lines
model.construct_line(A, C)
model.construct_line(D, G)
model.construct_line(E, F)
model.construct_line(D, E)
model.construct_line(H, H_b)
model.construct_line(G, F)
# Segments
model.set_segment(A, C)
model.set_segment(A, B)
model.set_segment(B, C)
model.set_segment(D, E)
model.set_segment(D, G)
model.set_segment(D, H)
model.set_segment(H, G)
model.set_segment(E, F)
model.set_segment(E, H_b)
model.set_segment(H_b, F)
model.set_segment(H, H_b)
model.set_segment(G, F)
# Sections
model.set_section([A, B, C])
model.set_section([D, H, G])
# Polygons: whole parallelogram DF and constituent rectangles EH, HF
model.set_polygon([D, E, F, G])
model.set_polygon([D, E, H_b, H])
model.set_polygon([H, H_b, F, G])
return model
if __name__ == "__main__":
construct_g1()