G.498 square rational segment — Code¶
The square on a rational segment applied to the binomial segment produces as breadth an apotome the terms of which are commensurable with the terms of the binomial and moreover in the same ratio; and further the apotome so arising will have the same order as the binomial segment.
"""Programmatic construction for Book X, Proposition 112 (X.112)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0247.g1 using geometor.model."""
model = Model("X.112")
# Single-letter magnitude segments A and G
A_l = model.set_point(18.0, -20.5, classes=["given"], ID="A")
A_r = model.set_point(138.0, -20.5, ID="A_r")
G_l = model.set_point(247.0, -46.5, classes=["given"], ID="G")
G_r = model.set_point(563.0, -46.5, ID="G_r")
# Line BC divided at D
B = model.set_point(18.0, -50.5, classes=["given"], ID="B")
D = model.set_point(72.0, -50.5, classes=["given"], ID="D")
C = model.set_point(183.0, -50.5, classes=["given"], ID="C")
# Line KH divided at E and F
K = model.set_point(76.0, -85.5, ID="K")
E = model.set_point(142.0, -85.5, ID="E")
F = model.set_point(232.0, -85.5, ID="F")
H = model.set_point(455.0, -85.5, ID="H")
# Base lines
model.construct_line(A_l, A_r)
model.construct_line(B, C)
model.construct_line(G_l, G_r)
model.construct_line(K, H)
# Segments
model.set_segment(A_l, A_r)
model.set_segment(G_l, G_r)
model.set_segment(B, C)
model.set_segment(B, D)
model.set_segment(D, C)
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([B, D, C])
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()