G.172 magnitude multiple fifth — Code¶
If a first magnitude be the same multiple of a second that a third is of a fourth, and a fifth also be the same multiple of the second that a sixth is of the fourth, the sum of the first and fifth is the same multiple of the second that the sum of the third and sixth is of the fourth.
"""Programmatic construction for Book V, Proposition 2 (V.2)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0145.g1 using geometor.model."""
model = Model("V.2")
# Points on AG (divided at B) and DH (divided at E)
A = model.set_point(26.0, -27.0, classes=["given"], ID="A")
B = model.set_point(134.0, -27.0, classes=["given"], ID="B")
G = model.set_point(206.0, -27.0, classes=["given"], ID="G")
D = model.set_point(26.0, -81.0, classes=["given"], ID="D")
E = model.set_point(176.0, -81.0, classes=["given"], ID="E")
H = model.set_point(276.0, -81.0, classes=["given"], ID="H")
# Single-letter magnitudes C and F
C_l = model.set_point(26.0, -57.0, classes=["given"], ID="C")
C_r = model.set_point(62.0, -57.0, ID="C_r")
F_l = model.set_point(26.0, -109.0, classes=["given"], ID="F")
F_r = model.set_point(76.0, -109.0, ID="F_r")
# Base lines
model.construct_line(A, G)
model.construct_line(D, H)
# Whole and subdivided segments
model.set_segment(A, G)
model.set_segment(A, B)
model.set_segment(B, G)
model.set_segment(D, H)
model.set_segment(D, E)
model.set_segment(E, H)
model.set_segment(C_l, C_r)
model.set_segment(F_l, F_r)
# Collinear sections
model.set_section([A, B, G])
model.set_section([D, E, H])
return model
if __name__ == "__main__":
construct_g1()