Systematic Treatise on Computing Methods, Volume Six

Gradually calculate, continue the quotient, and double the corner;original: 隅, yu. In the traditional Chinese square root algorithm, the "corner" refers to the specific divisor term that is updated and doubled as one moves to the next decimal place or digit.

Simply follow this method to occupy the empty spaces.

The explanation states: A square is the area original: 積, ji produced by a side multiplied by itself. To extract is to seek the value of that side.

"For one hundred, ten is fixed without doubt" means that if the area is 100 paces original: 步, bu. A unit of length, or square paces when referring to area., the side can be estimated as 10 paces without any uncertainty. "For one thousand, thirty with a remainder" means that if the area is 1,000 paces, the side can be estimated as 30-some paces. "For nine thousand, nine times nine is not far from ten" means that if the area is 9,000 paces, the side is approximately 90 paces, because 90 times 90 is 8,100. "Ten thousand is always one hundred paces" means that 100 paces multiplied by itself yields an area of 10,000 paces. This section provides the mnemonic for estimating the initial quotient original: 初商, chu shang. This is the first digit of the square root.. A table of quotients and areas is appended below.

Mnemonic for Determining the First Digit of the Initial Quotient in Square Root Extraction

This is based on the number multiplied by itself.


Quotient: 10 paces	Quotient: 20 paces	Quotient: 1 pace	Quotient: 2 paces
Area: 100 paces	Area: 400 paces	Area: 1 pace	Area: 4 paces