G.381 squares segments commensurable — Code¶
The squares on segments commensurable in length have to one another the ratio which a square number has to a square number; and squares which have to one another the ratio which a square number has to a square number will also have their sides commensurable in length. But the squares on segments incommensurable in length have not to one another the ratio which a square number has to a square number; and squares which have not to one another the ratio which a square number has to a square number will not have their sides commensurable in length either.
"""Programmatic construction for Book X, Proposition 9 (X.9)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0033.g1 using geometor.model."""
model = Model("X.9")
# Single-letter straight line segment A
A_l = model.set_point(16.0, -24.0, classes=["given"], ID="A")
A_r = model.set_point(153.0, -24.0, ID="A_r")
# Single-letter straight line segment B
B_l = model.set_point(191.0, -23.5, classes=["given"], ID="B")
B_r = model.set_point(291.0, -23.5, ID="B_r")
# Single-letter number segment C
C_l = model.set_point(124.0, -43.5, classes=["given"], ID="C")
C_r = model.set_point(178.0, -43.5, ID="C_r")
# Single-letter number segment D
D_l = model.set_point(124.0, -66.5, classes=["given"], ID="D")
D_r = model.set_point(166.0, -66.5, ID="D_r")
# Base lines
model.construct_line(A_l, A_r)
model.construct_line(B_l, B_r)
model.construct_line(C_l, C_r)
model.construct_line(D_l, D_r)
# Magnitude and number segments
model.set_segment(A_l, A_r)
model.set_segment(B_l, B_r)
model.set_segment(C_l, C_r)
model.set_segment(D_l, D_r)
return model
if __name__ == "__main__":
construct_g1()