The Great Qin Empire---Qin Li

When the north wind comes, it is the beginning of winter. The scenery is bleak and everything is empty. In the eastern suburbs of Shangcai in early October, there are a few more carriages and horses. Zhang Han and Qin Mocheng Shang took the carriage, and Hei Fu rode a horse. Under the protection of hundreds of soldiers, they left the camp and headed east.

The driver drove very slowly so that the military commander Zhang Han could carefully observe the surrounding terrain. When they drove to a section, Zhang Han shouted: "Stop!"

Setting up camp requires choosing a place, and so does building a fortress. Hei Fu saw that there was a marsh on the left, a flowing spring on the right, and a small hill behind. The view facing the east was very flat, and there was a road passing by. There were also forests and grasslands for firewood and grazing a few miles away. It can be said to be a place with four preparations.

Hei Fu took a look and said, "Isn't this the wild land in the eastern suburbs that Li Duwei mentioned? I heard that the father and son of the court judge often led yellow dogs to chase cunning rabbits here. It is indeed suitable for setting up camps and building fortifications."

The work of building barriers now to be done is also Zhang Han's "Chu Jun Ji" duty.

The "Ji" in "Chu Jun Ji" means to be safe and secure, which means that after the barrier is built, there is no need to worry about the enemy's sneak attack or strong attack, and the army can be stationed with peace of mind; if the construction tasks are allocated fairly and reasonably, there will be no chaos and contradictions.

While talking, Zhang Han also got off the car with everyone, and began to hold tools such as rulers, rules, squares, and ropes, and began to carry out construction measurements on the endless Shangcai Plain.

Zhang Han lifted the "ruler" with a heavy object hanging on it, got off the car to test the straightness, and compared the height differences between the terrain. Cheng Shang pulled the walking rope and measured carefully step by step on the ground, and there was a scribe next to him recording the distance.

As for the "ruler", it is a tool for calibrating circles, and the "ruler" is a tool for drawing squares, that is, a square. Zhang Han and Qin Mo have already played with this simple tool in many ways. It can not only determine the level, measure height, depth, and distance, but also draw circles and squares. When used, it can be placed in different positions, and it can also measure the height, distance, and size of objects. As for how much error there is, it all depends on the operator's experience.

Seeing Hei Fu's curious face, Zhang Han also explained: "It is said that when Dayu controlled the flood, he traveled on land by car, on water by boat, and on mud by sled. He traveled on the mountain by sedan chair, with a ruler on the left and a ruler on the right, carrying four lines to open up the nine states and connect the nine roads."

Although this is a legend, most people attribute the tools invented by skilled craftsmen to the sage king. In this way, they spent half a day to measure the sections of the fortification. Every hundred steps, they also inserted the blackened wooden poles deeply into the ground as a mark.

After returning to the camp in the evening, Zhang Han asked several accountants who were proficient in arithmetic to calculate the amount of work with the data measured today, so as to assign it to the laborers' brigade for construction.

Heifu was fortunate to see the dazzling amount of work calculations in this era.

In the open space of the tent, a large number of counting sticks were placed on the ground. Heifu was not unfamiliar with this thing, because the Qin State stipulated that local officials must have counting sticks to deal with emergencies. Mathematics is one of the six arts of gentlemen in the Spring and Autumn Period, and a necessary skill for Qin officials. When serving as an official in the local area, a large number of digital calculations must be performed for square fields, millet, equal transportation, and taxes. If a person does not know how to count, he is not even qualified to be a Dou Shi official!

In Xianyang and the county city, there are also special "accountants" who calculate the annual household registration, taxes, cultivated land, money and grain, thieves, and lawsuits in each county, and use them as a basis for performance evaluation, which is called Shangji. These people are equivalent to accountants in later generations. Their daily work is to deal with numbers. Accountants will also be recruited during wartime as specialized talents, as assistants to the military commander or military officer (logistics officer). They help measure the height of the hillside, measure the depth of the river, coordinate the baggage and millet, and dispatch the number of divisions and brigades.

At the moment, the accountants are sitting in the tent, sweating and fiddling with the counting sticks. Hei Fu went over to take a look and found that they were all calculating "Now there is a trench, the width is 16 feet and 3 inches on the top, 10 feet on the bottom, 6 feet and 3 inches deep, and 13 feet and 2 feet and 1 inch long. How much is the area?" "The work is 766 feet, and one-fifth of the work is excavated, and the work is determined to be 612 feet and 5 feet and four feet. How many people are needed?"

Although the accountants quickly fiddled with the counting sticks to calculate, in Hei Fu's opinion, it was still very complicated and troublesome.

Zhang Han did not feel this way, but smiled and said: "In the past, it was even more complicated to calculate earthwork and the number of people. Fortunately, there was an official in the Imperial Censorate who was in charge of books and classics. Based on the actual projects of building city walls, digging ditches, and building warehouses, he wrote an article "Shang Gong" and handed it to the Shaofu. Since then, when it comes to calculating the earthwork and the number of slaves required for building fortifications, you only need to put the number into the algorithm he set..."

The so-called Shang Gong is a method of measuring volume and calculating the labor used in engineering. Zhang Han also showed Hei Fu the volume of Shang Gong he carried with him. Each part is divided into problems, solutions, and formulas.

Hei Fu took a look and felt familiar. Isn't this the Nine Chapters of Arithmetic!

"Shao Rong, the official you are talking about, is it Zhang Cang?"

"Oh?" Zhang Han was a little surprised: "Does the commander know Zhang Cang?"

"I have heard of Xunzi's disciple of Lanling for a long time."

Hei Fu smiled and said, "Moreover, I was a patrol officer in Yangwu County, Dang County two years ago, and I met Zhang Cang's two uncles Zhang Fu and Zhang Bo. I also heard about Zihu's deeds from them. I never thought that he was so talented!"

"Of course, Zhang Zihu is a learner and a master of everything."

Zhang Cang is Li Si's junior brother, and is also a member of the "Li Si Party". As an official of the Shaofu, many things involve precise calculations. Zhang Han has dealt with Zhang Cang a lot, so he talked about an interesting story about Zhang Cang:

"When Zhang Cang first arrived at the Imperial Censorate, the Imperial Censor saw that he was fat and plump, and even had difficulty walking. He was quite unhappy, so he pointed at his big round belly and asked, what's in it? Zhang Zihu didn't take it as an offense, but just patted his belly and laughed, saying that it was full of knowledge and was full of erudition!"

"The Imperial Censor was also a great talent with a wealth of knowledge. He immediately asked Zhang Cang some questions, and he answered them all. There were even some obscure books that even the Imperial Censor had never read, so he asked him to take care of the books in the collection room. Zhang Cang loved books like his life, and often brought some dry food and sat in the pile of bamboo slips for several days. Now he might have finished reading all the books collected by the Imperial Censorate from Han, Zhao, Wei, and Yan. Everyone said that seeing that his belly was getting bigger and bigger, he might want to put all the knowledge in the world into it?"

Thinking of that extremely smart but increasingly fat guy, Zhang Han couldn't help laughing: "When you lead the army to Xianyang in the future, you will know what kind of person he is!"

"Definitely!"

Heifu was amazed. Most people just study hard, but Zhang Cang not only has a wide range of knowledge, but can also put what he has learned into practical application. This is amazing.

He glanced at the accountants who were fiddling with the counting rods and thought to himself: "If there were vertical calculations for Arabic numerals and abacus, the calculation of these engineering quantities should be much faster."

However, Heifu did not rashly offer his treasures. In fact, he only had the math level of a junior high school student. It was not very useful to teach ordinary people. He thought that when he arrived in Xianyang in the future, he would find an opportunity to reveal it to Zhang Cang. I wonder if it can bring a mathematical revolution to this era?

…

After calculating the amount of work, Zhang Han assigned work to the 10,000 Nanjun laborers assigned to him. They were responsible for the construction of three miles of fortifications. So throughout the early October, the outskirts of Shangcai became a large construction site, with loess all over the sky and thousands of laborers carrying soil...

The wall was built using the same method that Heifu had participated in in Anlu County. Thousands of other laborers skillfully used tools to cut down the trees in the forest near Shangcai, sawed them into pieces after removing the branches, and finally nailed them into pieces of wood. When the board was filled with soil, the laborers swung the heavy pestle and smashed the loose soil! The enthusiastic calls shook the fields, and basically one layer of board was built every day.

Heifu and other leaders, also with soldiers, were waiting outside the construction site fully armed to deal with the harassment of the Chu army that might come at any time.

"Isn't this a way to lure the enemy?"

On the border between Qin and Chu, tens of thousands of Qin troops protected tens of thousands of civilians. They were preparing for battle and preparing for battle at all times, fearing that the Chu army would not come.

The cavalry scouts of Chu were also watching this scene from afar, but the main army never dared to attack rashly, because Xiang Yan knew that this might also be a trap set by Wang Jian for him.

A few days later, a thick earth wall more than ten feet high appeared out of thin air in the eastern suburbs of Shangcai, rising from the ground. At the location where the benchmark was inserted every hundred steps before, Zhang Han was also urging the civilians to build a taller and stronger corner tower.

It was at this time that an accident happened...

A corner tower that had just been rammed was tested by Zhang Han and his men for its strength, but after more than ten people carried wooden stakes and hit it hard a few times, it showed signs of cracking! And a large number of soil blocks fell off!

"If the Chu army attacks, how can this corner tower defend against the enemy? It will definitely become a gap for the enemy to break through, and a thousand-mile embankment will be destroyed by an ant hole!"

"The people who built this corner tower will be whipped ten times, and then torn down and rebuilt!"

Zhang Han glared at the Sikong Xiaoli in charge of this section, saying that if it happened again, the person in charge would be beheaded, and the rest of the people would also die!

Sikong's petty official was timid, and Zhang Han said to Heifu with some distress: "The Supervisor of the Imperial Censor requires that the corner tower must be as hard as the walls of Guanzhong, and it must be indestructible, but it took a long time to tamp it out. Now the construction period is only more than ten days, and it may be difficult to tamp it in a hurry. Moreover, the quality of the soil is directly related to the solidity of the corner tower of the rampart. The soil is fine but not loose, oily but not dry, and bright but not dark. But the soil in Shangcai is really average, far less useful than the loess in Guanzhong..."

These days, the forest coverage rate in Shangcai is relatively high, and there is a lot of humus in the soil. It is indeed difficult to guarantee the quality of the corner tower of the rampart with such soil nearby.

Zhang Han decided to ask people to dig dry and loose loess from afar to build the corner tower, so as to ensure the quality. Heifu rolled his eyes and gave Zhang Han an idea.

"Shao Rong, in Anlu Village, Nanjun, there is a folk method used to repair houses. After drying, it is extremely hard. Not only does it not change after being soaked in water, but even iron nails are difficult to drive into it! It has been intact after hundreds of years of wind and rain!"

After saying this, he was afraid that Zhang Han would not believe it, so he took out his brother-in-law to take the blame: "My brother-in-law is not only proficient in carpentry, but also used this method to repair houses for others."

"There is such a method?" Zhang Han was immediately very interested and asked Hei Fu to explain in detail.

Hei Fu smiled. This was a common method for repairing houses in rural hometowns in the previous life. It was not popular in this era. He pointed to the tributary of the Ru River flowing not far away and said: "It's very simple, and the materials are not difficult. It is called Sanhetu with common loess, plus the fired mirage ash and river sand mixed and rammed!"