G.133 equal angles stand on equal arcs — Code¶
In equal circles, equal angles stand on equal arcs, whether they stand at the centers or at the circumferences.
"""Programmatic construction for Book III, Proposition 26 (III.26)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0063.g1 using geometor.model."""
model = Model("III.26")
# Left circle ABC with center G and arc point K (y-inverted)
G = model.set_point(101.00, -86.00, ID="G")
A = model.set_point(68.00, -37.09, classes=["given"], ID="A")
B = model.set_point(52.09, -119.00, classes=["given"], ID="B")
C = model.set_point(149.91, -119.00, classes=["given"], ID="C")
K = model.set_point(101.00, -145.00, ID="K")
# Right circle DEF with center H and arc point L (y-inverted)
H = model.set_point(281.00, -86.00, ID="H")
D = model.set_point(333.96, -60.00, classes=["given"], ID="D")
E = model.set_point(232.09, -119.00, classes=["given"], ID="E")
F = model.set_point(329.91, -119.00, classes=["given"], ID="F")
L = model.set_point(281.00, -145.00, ID="L")
# Equal circles ABC and DEF
model.construct_circle(G, A)
model.construct_circle(H, D)
# Segments
model.set_segment(A, B)
model.set_segment(A, C)
model.set_segment(B, G)
model.set_segment(G, C)
model.set_segment(B, C)
model.set_segment(D, E)
model.set_segment(D, F)
model.set_segment(E, H)
model.set_segment(H, F)
model.set_segment(E, F)
# Polygons
model.set_polygon([A, B, C])
model.set_polygon([B, G, C])
model.set_polygon([D, E, F])
model.set_polygon([E, H, F])
# Angles (wedges)
model.set_wedge(G, B, B, C)
model.set_wedge(H, E, E, F)
model.set_wedge(A, B, B, C)
model.set_wedge(D, E, E, F)
return model
if __name__ == "__main__":
construct_g1()