zhou bi suan jing gnomons

Next we will deal with the diagram of the Zhou Bi Suan Jing that most closely
precursors the “Pythagorean” triangle as we know it today: as the 3,4,5 rt. triangle.
On the left we see the common expression, with the “Pythagorean” triangle of 3,4,5
between the squares of each of its legs, thus 3^2+4^2=5^2, proving the “Pythagorean”
theorem. However, in the Zhou Bi Suan Jing variation, there is also depicted a square
of area 9 (3^2) within the borders of the area 25 (5^2) square. Such, again, is the
nature of the “Gnomon.”


On the right we see the “Gnomon” expressed as a square divided from within another
square not by the method of a surrounding border of 1 base-unit square on each side,
but such only on two sides, as like a carpenter’s square. We see the square of 25 (5^2)
here divided into a square of 16 (4^2) by the method of reducing the former on only
two sides. Such, again, is the nature of the “Gnomon” as it was studied in the Zhou Bi
Suan Jing of China around 1045(-)YP.