[Page 11]

Systematic Treatise on Computing Methods, Volume Six


Quotient: 3 paces	Area: 9 paces	Quotient: 30 paces	Area: 900 paces
Quotient: 4 paces	Area: 16 paces	Quotient: 40 paces	Area: 1,600 paces
Quotient: 5 paces	Area: 25 paces	Quotient: 50 paces	Area: 2,500 paces
Quotient: 6 paces	Area: 36 paces	Quotient: 60 paces	Area: 3,600 paces
Quotient: 7 paces	Area: 49 paces	Quotient: 70 paces	Area: 4,900 paces
Quotient: 8 paces	Area: 64 paces	Quotient: 80 paces	Area: 6,400 paces
Quotient: 9 paces	Area: 81 paces	Quotient: 90 paces	Area: 8,100 paces

The rule states: Set the total area as the dividend original: 實, shi. In Chinese mathematics, the 'solid' number being operated upon.. Separately place one counting rod, called the lower method original: 下法, xia fa. A auxiliary unit used to track decimal places during root extraction., beneath the digits of the dividend.

From the last digit to the first, always skip every other place to estimate the dividend's magnitude.
For a single unit, the lower method is fixed at the ones place.
For hundreds, the lower method is fixed at the tens place.
For ten-thousands, the lower method is fixed at the hundreds place.
For millions, the lower method is fixed at the thousands place.

Above the dividend, place the first digit of the quotient the square root being sought. Below the dividend, also place that same quotient digit, which is now called the square method original: 方法, fang fa. This represents the side of the square being subtracted from the area.. Multiply the quotient by this square method and subtract the result from the dividend.