G.499 square rational segment — Code¶
The square on a rational segment, if applied to an apotome, produces as breadth the binomial segment the terms of which are commensurable with the terms of the apotome and in the same ratio; and further the binomial so arising has the same order as the apotome.
"""Programmatic construction for Book X, Proposition 113 (X.113)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0252.g1 using geometor.model."""
model = Model("X.113")
# Single-letter vertical magnitude segments A and G
A_t = model.set_point(28.0, -18.0, classes=["given"], ID="A")
A_b = model.set_point(28.0, -110.0, ID="A_b")
G_t = model.set_point(137.5, -19.0, classes=["given"], ID="G")
G_b = model.set_point(137.5, -73.0, ID="G_b")
# Vertical line CB divided at D
C = model.set_point(63.0, -18.0, classes=["given"], ID="C")
D = model.set_point(63.0, -110.0, classes=["given"], ID="D")
B = model.set_point(63.0, -171.0, classes=["given"], ID="B")
# Vertical line KH divided at E and F
K = model.set_point(103.0, -18.0, ID="K")
E = model.set_point(103.0, -82.0, ID="E")
F = model.set_point(103.0, -107.0, ID="F")
H = model.set_point(103.0, -142.0, ID="H")
# Base lines
model.construct_line(A_t, A_b)
model.construct_line(C, B)
model.construct_line(K, H)
model.construct_line(G_t, G_b)
# Segments
model.set_segment(A_t, A_b)
model.set_segment(G_t, G_b)
model.set_segment(C, B)
model.set_segment(C, D)
model.set_segment(D, B)
model.set_segment(K, H)
model.set_segment(K, F)
model.set_segment(K, E)
model.set_segment(E, H)
model.set_segment(E, F)
model.set_segment(F, H)
# Sections
model.set_section([C, D, B])
model.set_section([K, E, F])
model.set_section([K, F, H])
model.set_section([E, F, H])
return model
if __name__ == "__main__":
construct_g1()