"""Programmatic construction for Book XI, Proposition 14 (XI.14).
Planes to which the same straight line is at right angles will be parallel.
"""
from __future__ import annotations
import sympy as sp
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure for Book XI, Proposition 14 using geometor.model."""
model = Model("XI.14")
# 1. Let any straight line AB be at right angles to each of the planes CD, EF.
A = model.set_point(0, 1, classes=["given"], ID="A")
B = model.set_point(sp.Rational(3, 69), 0, classes=["given"], label="B")
# Plane CD corners
C1 = model.set_point(sp.Rational(-25, 69), sp.Rational(85, 69), label="C1")
C = model.set_point(sp.Rational(42, 69), sp.Rational(85, 69), classes=["given"], label="C")
C3 = model.set_point(sp.Rational(29, 69), sp.Rational(54, 69), label="C3")
D = model.set_point(sp.Rational(-35, 69), sp.Rational(54, 69), classes=["given"], label="D")
# Plane EF corners
F1 = model.set_point(sp.Rational(-45, 69), sp.Rational(19, 69), label="F1")
F = model.set_point(sp.Rational(41, 69), sp.Rational(19, 69), classes=["given"], label="F")
F3 = model.set_point(sp.Rational(26, 69), sp.Rational(-17, 69), label="F3")
E = model.set_point(sp.Rational(-54, 69), sp.Rational(-17, 69), classes=["given"], label="E")
# 2. Suppose they meet at common section GH, and let point K be taken on GH.
G = model.set_point(sp.Rational(200, 69), sp.Rational(92, 69), label="G")
H = model.set_point(sp.Rational(152, 69), sp.Rational(-19, 69), label="H")
K = model.set_point(sp.Rational(180, 69), sp.Rational(46, 69), label="K")
# Segments and section
model.set_segment(A, B)
model.set_segment(G, H)
model.set_segment(G, K)
model.set_segment(K, H)
model.set_section([G, K, H])
model.set_segment(A, K)
model.set_segment(B, K)
# Planes CD, EF and triangle ABK
model.set_polygon([C1, C, C3, D])
model.set_polygon([F1, F, F3, E])
model.set_polygon([A, B, K])
# Wedges for angles ABK and BAK
model.set_wedge(B, A, A, K)
model.set_wedge(A, K, K, B)
return model
if __name__ == "__main__":
construct_g1()
