G.128 no two similar unequal circle segments on the same chord — Code¶
On the same segment and on the same side of it, there cannot be constructed two similar and unequal segments of circles.
"""Programmatic construction for Book III, Proposition 23 (III.23)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0058.g2 using geometor.model."""
model = Model("III.23")
# Base points A, B and circle centers O1 (for ACB) and O2 (for ADB) (y-inverted)
A = model.set_point(28.00, -66.00, classes=["given"], ID="A")
B = model.set_point(164.00, -66.00, classes=["given"], ID="B")
O1 = model.set_point(96.00, -127.97, ID="O1")
O2 = model.set_point(96.00, -104.21, ID="O2")
C = model.set_point(105.21, -36.43, ID="C")
D = model.set_point(121.08, -30.35, ID="D")
# Circles for segments ACB and ADB
model.construct_circle(O1, A)
model.construct_circle(O2, A)
# Segments and secant ACD
model.set_segment(A, B)
model.set_segment(A, C)
model.set_segment(C, D)
model.set_segment(A, D)
model.set_segment(C, B)
model.set_segment(D, B)
model.set_section([A, C, D])
# Polygons
model.set_polygon([A, C, B])
model.set_polygon([A, D, B])
model.set_polygon([C, D, B])
# Angles (wedges)
model.set_wedge(C, A, A, B)
model.set_wedge(D, A, A, B)
return model
if __name__ == "__main__":
construct_g1()