zhou bi suan jing gnomon

In this extract from the Zhou Bi Suan Jing, we see the standard form of the “Gnomon”
with which the text in this section most commonly works: a paraelleogram (square)
divided by sections to form a smaller paralellogram (square) inside it. Here, the outer
square’s area is given as 42 (7^2), while the inner-most square consists of only one
unit at the center.Arranged around this central, base-unit square, we have 4
rectangles of 3 by 4 squares each, and each of these is divided by a diaganol, forming
a third square, of area 25 (5^2). This tripartite nature defines the “Gnomon.”

What is particularly significant in this arrangement is the diaganols that form the
sides of the third square, oriented at an angle to the outer, base-42, and inner, base-1
squares. Each of these diaganol lines bisects one of the 3X4 rectangles, and thus forms
the familiar “Pythagorean” theorem triangle, the right triangle of legs 3 and 4. That
the hypontenuse of this triangle is 5, although not apparently mentioned, is the
proof that the interior, tilted square’s area is 25 (5^2).