G.386 segments proportional square — Code¶
If four segments be proportional, and the square on the first be greater than the square on the second by the square on a segment commensurable with the first, the square on the third is greater than the square on the fourth by the square on a segment commensurable with the third. And, if the square on the first be greater than the square on the second by the square on a segment incommensurable with the first, the square on the third is greater than the square on the fourth by the square on a segment incommensurable with the third.
"""Programmatic construction for Book X, Proposition 14 (X.14)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0041.g1 using geometor.model."""
model = Model("X.14")
# Vertical straight lines A, B, E, C, D, F
A_t = model.set_point(19.5, -12.0, classes=["given"], ID="A")
A_b = model.set_point(19.5, -175.0, ID="A_b")
B_t = model.set_point(44.5, -33.0, classes=["given"], ID="B")
B_b = model.set_point(44.5, -175.0, ID="B_b")
E_t = model.set_point(78.5, -16.0, ID="E")
E_b = model.set_point(78.5, -98.0, ID="E_b")
C_t = model.set_point(103.5, -34.0, classes=["given"], ID="C")
C_b = model.set_point(103.5, -172.0, ID="C_b")
D_t = model.set_point(130.5, -58.0, classes=["given"], ID="D")
D_b = model.set_point(130.5, -178.0, ID="D_b")
F_t = model.set_point(153.5, -18.0, ID="F")
F_b = model.set_point(153.5, -91.0, ID="F_b")
for p_t, p_b in [
(A_t, A_b),
(B_t, B_b),
(E_t, E_b),
(C_t, C_b),
(D_t, D_b),
(F_t, F_b),
]:
model.construct_line(p_t, p_b)
model.set_segment(p_t, p_b)
return model
if __name__ == "__main__":
construct_g1()