"""Programmatic construction for Book XII, Proposition 18 (XII.18).
Spheres ABC (diameter BC), DEF (diameter EF) concentric with lesser sphere GHK
(diameter HK), and greater sphere LMN.
"""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0439.g1 using geometor.model."""
model = Model("XII.18")
# Top-left sphere ABC
O1 = model.set_point(90.2, -92.0, ID="O1")
A = model.set_point(90.2, -22.8, classes=["given"], ID="A")
B = model.set_point(21.0, -92.0, classes=["given"], ID="B")
C = model.set_point(159.4, -92.0, classes=["given"], ID="C")
# Top-right concentric spheres DEF and GHK
O2 = model.set_point(360.8, -105.0, ID="O2")
D = model.set_point(392.0, -27.2, classes=["given"], ID="D")
E = model.set_point(277.0, -105.0, classes=["given"], ID="E")
F = model.set_point(444.6, -105.0, classes=["given"], ID="F")
G = model.set_point(382.0, -34.3, classes=["given"], ID="G")
H = model.set_point(287.0, -105.0, classes=["given"], ID="H")
K = model.set_point(434.6, -105.0, classes=["given"], ID="K")
# Bottom sphere LMN
O3 = model.set_point(228.8, -286.8, ID="O3")
L = model.set_point(228.8, -190.0, classes=["given"], ID="L")
M = model.set_point(132.0, -286.8, classes=["given"], ID="M")
N = model.set_point(325.6, -286.8, classes=["given"], ID="N")
# Spheres (modeled as circles)
model.construct_circle(O1, B)
model.construct_circle(O2, E)
model.construct_circle(O2, H)
model.construct_circle(O3, M)
# Diameters and sub-segments
for p1, p2 in [
(B, C),
(E, H), (H, K), (K, F), (E, F),
]:
model.set_segment(p1, p2)
return model
if __name__ == "__main__":
construct_g1()
