Chapter 14 Section 7 Rules and Guidelines

Now, the word "rule" is often used to express certain standards, rules or habits, and describe a person's behavior is correct, in line with standards or common sense; the word "guidelines" is used to describe the principles or standards on which speech, action, etc. are based.In fact, the original rules and guidelines are three tools for drawing, measuring and testing. "Gauge" is a compass, "moment" is a rectangular ruler, and the yardstick is a rope.According to the legend, Fuxi invented the rules, and Nuwa invented the moment, and it is also said that the rules, moments, and principles are all invented by skillful workers.In the legend of Dayu's water control, it is said that he held the guideline in his left hand and the rules and measures in his right hand to carry out topographical surveys, and only then did he complete the task of water control.

Although ancient Chinese geometry did not form a Euclidean geometry system like ancient Greece, they had a long-standing understanding of geometric figures, especially circles, squares, and straights.This can be seen from the Neolithic pottery shapes, the outlines of architectural sites, and a large number of bronze ware shapes from the Xia, Shang and Zhou dynasties.Rules and yardsticks generally appeared along with these geometric shapes, and became the commonly used tools for drawing shapes and measuring in the production of carpenters, potters, and lathes.It is said that Xi Zhong, a Chezheng (an official in charge of car manufacturing) in the Xia Dynasty, made cars in accordance with the rules and standards when he built cars. Therefore, the cars he built were reasonable in structure, durable and fast in movement. In "Kao Gong Ji", when checking whether the wheels are qualified, it is required to use gauges to calibrate whether the wheels are round, use torque to check whether the wheel surface is flat, and use a yardstick to measure whether the spokes are straight.Even today, some carpenters still use these three tools when making wood.

On the basis of practical experience, the understanding of some geometric figures in the Spring and Autumn Period and the Warring States Period has begun to rise to the rational stage.In the book "Mo Jing" at that time, there are circles that are "one center and the same length", squares that have four equal sides and are perpendicular to each other, three points that are collinear and straight, and two lines that are equal in distance from each other. And the definitions that lines are composed of points, surfaces are composed of lines, and volumes are composed of surfaces.It is a pity that the germination of this rational geometry was not well inherited and developed in later generations, but was overshadowed by the pragmatic trend.