G.496 medial area there — Code¶
If from a medial area there be subtracted a medial area incommensurable with the whole, the two remaining irrational segments arise, either a second apotome of a medial segment or a segment which produces with a medial area a medial whole.
"""Programmatic construction for Book X, Proposition 110 (X.110)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0242.g1 using geometor.model."""
model = Model("X.110")
# Left rectangle B-E-C_t / A-D-C
B = model.set_point(22.0, -48.0, classes=["given"], ID="B")
E = model.set_point(93.5, -48.0, ID="E")
C_t = model.set_point(134.5, -48.0, ID="C_t")
A = model.set_point(22.0, -130.5, classes=["given"], ID="A")
D = model.set_point(93.5, -130.5, ID="D")
C = model.set_point(134.5, -130.5, classes=["given"], ID="C")
# Right rectangle F-K-H / G-L-H_b
F = model.set_point(277.0, -18.5, classes=["given"], ID="F")
K = model.set_point(315.0, -18.5, ID="K")
H = model.set_point(336.5, -18.5, ID="H")
G = model.set_point(277.0, -177.5, classes=["given"], ID="G")
L = model.set_point(315.0, -177.5, ID="L")
H_b = model.set_point(336.5, -177.5, ID="H_b")
# Base lines
model.construct_line(B, C_t)
model.construct_line(A, C)
model.construct_line(B, A)
model.construct_line(E, D)
model.construct_line(C_t, C)
model.construct_line(F, H)
model.construct_line(G, H_b)
model.construct_line(F, G)
model.construct_line(K, L)
model.construct_line(H, H_b)
# Segments
model.set_segment(B, A)
model.set_segment(E, D)
model.set_segment(C_t, C)
model.set_segment(A, C)
model.set_segment(A, D)
model.set_segment(D, C)
model.set_segment(B, E)
model.set_segment(E, C_t)
model.set_segment(B, C_t)
model.set_segment(F, G)
model.set_segment(K, L)
model.set_segment(H, H_b)
model.set_segment(F, H)
model.set_segment(F, K)
model.set_segment(K, H)
model.set_segment(G, L)
model.set_segment(L, H_b)
model.set_segment(G, H_b)
# Sections
model.set_section([A, D, C])
model.set_section([F, K, H])
# Polygons (rectangles)
model.set_polygon([B, C_t, C, A]) # BC
model.set_polygon([B, E, D, A]) # BD
model.set_polygon([E, C_t, C, D]) # EC
model.set_polygon([F, H, H_b, G]) # GH
model.set_polygon([F, K, L, G]) # GK / FL
model.set_polygon([K, H, H_b, L]) # LH
return model
if __name__ == "__main__":
construct_g1()