The architectural form of Yilun Hall is a single eave hanging on the top of a mountain, with a width of seven rooms. There is a throne in the middle where the emperor will sit. However, Zhu Yijun did not let anyone ascend the throne. Instead, he held a book and placed a large blackboard next to it. With a few pieces of chalk, he stood on the stage and looked at the people in the audience.
This was a very special class, a class where the emperor stood and the supervisors sat. This was against etiquette. The emperor stood while the students sat. However, the Minister of Rites did not raise any questions because it was requested by His Majesty. .
Students have to take notes and take quizzes, which cannot be done while standing.
Behind the students, more than a dozen courtiers sat and participated in the audience.
Zhu Yijun looked at the students in the audience. He knew clearly that the people below were almost certain to be Jinshi next year. In order to prevent the emperor's lectures from causing a loss of friendship between the emperor and his ministers, these were all the elites among the elites.
Zhu Yijun, who has participated in many court meetings and court discussions, did not show any stage fright when faced with the crowd of heads in the audience, but he is not too tall, after all, he is still young.
It doesn't matter if you are not tall. Fan Yingqi, a disciple of the Jin Party and Ge Shouli, has made the podium much taller.
"Guo Shoujing." Zhu Yijun wrote a few big characters on the blackboard, and then said: "Guo Shoujing and Zhu Shijie are the last glories of Chinese arithmetic. Many students are wondering, why should we learn arithmetic?"
"Arithmetic is a book of thousands of different principles, which can be reached through the method of connecting the original. Arithmetic is the general economics of the three talents and all things. Arithmetic is the language of infinite all things. It is the only way to let all things speak."
"But the development of this knowledge came to a standstill after the end of the Tang Dynasty, and the Song and Yuan Dynasties were its last glorious moment."
"Zhu Shijie's "Arithmetic Enlightenment" and "Four Yuan Jade Mirror" were only recently picked up by the emperor's uncle and fully explained."
"We are catching up to the glory of our ancestors in arithmetic."
The significance of degree bypass does not need to be elaborated. It penetrated into all aspects of the production and life of the Ming Dynasty. Even the courtiers who remonstrated did not talk about the art of demonism anymore. Most of them said that it was too difficult. Please give the emperor some time so that everyone can get used to arithmetic that has not been learned for more than two hundred years.
It is an undoubted fact that the Ming Dynasty was lagging behind in arithmetic. Due to the influence of various winds and public opinions, the scholars of the Ming Dynasty, or the group of Confucian students, did not pay much attention to arithmetic. For example, the Four Elements Technique taught by Zhu Yijun now consists of four An equation with an unknown number, let alone the Four Elements Technique, is the Tianyuan Technique. An equation with an unknown number is a difficult thing for Ming Dynasty to understand.
"Let's first look at this triangle. This is Yang Hui and Jia Xian's triangle. It comes from "Detailed Explanation of Nine Chapters of Arithmetic". It was proposed by Yang Hui three hundred years ago. This triangle was already used by Jia Xian in the Northern Song Dynasty about five hundred and twenty years ago. , is a typical combination of numbers and shapes.”
"We can easily see that both sides of this triangle are all 1, and each number in the triangle is equal to the sum of the two numbers above it."
"How to use this Yang Hui triangle specifically? In the expansion of (a+b)^n, each coefficient corresponds to each item in the (n+1)th row of Yang Hui's triangle."
Zhu Yijun unfolded (a+b+c+d)^2 and demonstrated the specific application of this Yang Hui triangle. He regarded a+b and c+d as a whole and then expanded them. This is called in the Four-Yuan Illustrated Book "Four Yuan Self-riding Duan Diagram".
He spoke very quickly, at a moderate speed, and soon explained several examples in the Siyuan Jade Mirror very clearly and thoroughly.
Zhu Yijun talked for nearly half an hour and found that none of the examples were difficult. He suddenly said: "Here is an example."
"Recruiting troops is based on cubes. The first recruitment is three feet, and the second recruitment is one more foot, and the number is soldiers. Today's recruitment lasts for fifteen days, and each person will be paid two hundred and fifty coins per day. How much is the recruitment and payment?"
If one person stands per foot and recruits soldiers in a cube, that is 3×3×3=27 people on the first day. On the second day, there is one more person on each side, which is 4×4×4=64 people. On the third day, it is 5^3=125. People, and so on.
Zhu Yijun asked the students to calculate. The students took out the abacus and started to calculate. They were all integers. This was nothing rare. The total number of recruits was 3^3+4^3+5^3+...+15^3. The final result was There are 23,400 people, and the total amount of copper coins is 23,462,000, which is 23,462 coins.
It took a quarter of an hour for ninety students to give their answers one after another, and Zhu Yijun said with a smile: "The calculation is too slow. Now we will interpolate four times to solve the problem."
"The upper difference is 27, the second difference is 37, the third difference is 24, and the fourth difference is 6. We only need to bring in such a song to find the result very quickly."
Zhu Yijun finally talked about the practical application of the fourth interpolation difference method. He tried his best to explain it clearly and clearly, clarifying the concept of four differences and how to simply sum it up.
After he finished speaking, he noticed the confusion on the faces of the ninety students, and then he gave several example questions in succession. These students began to use it stumblingly. By the end of get out of class, the four-time interpolation method was finally fully understood by the students. Mastered.
Zhu Yijun showed a heartfelt smile and said with a smile: "Today's class has been overtime for more than half an hour, but I see that most of the students have learned this method. I am very pleased. The teacher said to us, move The Dharma is too difficult, I’m afraid students won’t be able to learn it, but today I saw that it’s not the case.”
"After class, students can use this interpolation method more. It's not difficult. If you don't know how, don't be shy. You can ask each other for advice."
"I'm here. If you have any questions, you can ask."
"Your Majesty, students have questions." Zhang Siwen was overjoyed when he heard that he could ask questions and raised his hand.
"Say." Zhu Yijun nodded, indicating that Zhang Siwen could ask questions.
"Your Majesty, students are studying "Taiwanese Algorithm" in Byantong Hall. Today's arithmetic methods are all Thai-Western algorithms. Is this a comprehensive Thai-Westernization of arithmetic?" Zhang Siwen's question was sharp, and it got to the core issue. , the distinction between Huayi and Huayi.
This question made Zhang Juzheng, who was sitting in the audience, immediately darken his face. This question had actually been lingering in the minds of the officials for a long time. The arithmetic of the Ming Dynasty had many references from Western arithmetic. Symbols, algebra, etc., seemed to be fully European and Western.
Zhu Yijun said with a smile: "It is great to be open to all rivers. The Central Plains dynasties have always been open and tolerant, allowing the leaders of hundreds of families to use themselves. Taking Buddhism as an example, I learned from Southeast Haishang and Hongmao Fan that India has been conquered by the Mughals. The empire has replaced it, the Buddhist kingdom has been destroyed, and the Taoism has been lost. However, Ming Buddhism is still prosperous, and I even built a pagoda."
"Just like the Weaver Girl is better at weaving. If you ask the Weaver Girl to fish for wool, the Zhinang will not be able to catch it. And the dyer who is good at dyeing is not good at mining coal, right? The reason for the division of labor is that everyone has their own strengths. This The same is true in the world, all living beings in the universe have their own strengths."
"The Master also said: When three people travel together, there must be one who is my teacher."
"Back to arithmetic, we can learn from Thai and Western arithmetic, but it is not a comprehensive Westernization. For example, the original text of "Taiwan Algorithm" is indeed Thai, but it is a treasure trove of arithmetic obtained after a long period of translation by the Minister of Rites, and then corrected by the emperor's uncle and me. This kind of arithmetic suitable for the Ming Dynasty is not entirely the Taixi algorithm, but the emperor's algorithm."
"As for those symbols and algebraic expressions, they are just for the convenience of writing."
"A, B, C, D, addition, subtraction, multiplication and division are more troublesome than writing abcd+-×÷. It is for the convenience of calculation. The arithmetic is already very complicated."
"Actually, it's not exactly Taisi's algorithm. The sextant was invented by Ulugh Beg, the king of the Timurid Kingdom. The source of Taisi's algorithm is also Khwarazmo's "Algebra", and Khwarazmo also communicated with the Tang Dynasty. , the Arabic numerals we use were also invented by Indians and spread by Arabs.”
"Arabic numerals were already widely popular during the Song Dynasty."
Zhu Yijun answered this question from several aspects.
In the first aspect, the Central Plains Dynasty has not been a complacent culture since ancient times. Even in the Ming Dynasty, there were seven voyages to the West. During the Zhengde period, the Portuguese envoys Huo Zhe Yasan and Tomei Piles were resident in the capital and Longqing switch. In active external communication.
In the Datong calendar of the Ming Dynasty, Emperor Taizu Gao once said: The Western Regions are the most accurate in predicting celestial phenomena, and their five-star latitude is unparalleled in China. He ordered Hanlin Li Chong and Wu Bozong to translate his book together with Huihui master Ma Shayihei and others. The compilation of the Datong Lili was a model of incorporating the strengths of hundreds of schools of thought.
The second aspect is from the division of labor. It is not shameful to recognize the excellence and leadership of others. In terms of summary and induction, Taixi's algorithm also has advantages, just like division of labor. Since it is ahead, just use it. Anyway, it has to be translated and Chineseized. What I learned is indeed called the Taisei Algorithm, but it is not impossible to change the name to "Wang Zheng's Algorithm". Would it be more acceptable to change the name?
From the translation by the Ministry of Rites to the editing by Emperor Zhu Zaiyu, the Thai-Western algorithm was no longer entirely a Thai-Western algorithm.
The third aspect is the practical significance of mathematical symbolization and algebraization. For the sake of simplicity, we can write as few strokes as possible. The workload of arithmetic is really too great, such as the triangulation network distance measurement we are doing recently. According to the method, the 10-minute sine table has nine digits after the decimal point, which is really troublesome to write.
"Students understand." Zhang Siwen said very respectfully. He understood what His Majesty meant. The Tai-Western algorithm they learned was not entirely Tai-Westernization, but Tai-Western-Chinese.
"Your Majesty, students also have questions." Seeing that His Majesty answered Zhang Siwen's question, Wang Qian raised his hand to ask a question.
"You ask." Zhu Yijun asked still smiling.
"Your Majesty's students don't understand. Arithmetic is more like a highly complex intellectual game in which experts use their skills to solve difficult problems. Is it really so important? If it is important, why did Ming Dynasty not pay attention to it before, but now it pays attention to it? "Wang Qian expressed his doubts. He didn't quite understand degree bypass.
As soon as Wang Qian said this, Wang Chonggu directly raised his forehead. He also specifically told Wang Qian not to talk if nothing happened. As a result, Wang Qian directly asked a very strange question, questioning the importance of arithmetic or degree bypass.
"You asked a good question." Zhu Yijun said with a smile: "Yes, it is so important. Even if it is just a highly complex intellectual game, a lot of corrupt scholars with illogical logic can be screened out in the imperial examination. Just this point , is completely worthy of promotion.”
"The Ming Dynasty did not pay attention to it before but now it does. In fact, it is the same as the law of development of things."
"The law of development of all things is roughly like sawing wood. Sometimes it goes forward, sometimes it goes backward, but overall it develops in depth."
"For example, before the Ming Dynasty, the trend of promoting civil and military affairs was very rampant. From the time when Wang Ji was ordered to kill military generals, this trend spread to the Tumubao Incident, and then from the Hongzhi period to the 29th year of Jiajing, when I joined the invaders. "
"When you are beaten in pain, you have to strengthen your martial arts. Because you don't pay attention to arithmetic, people in the Ming Dynasty can no longer even measure acres, so you have to pay attention to it again."
As for the meaning of arithmetic, if Zhu Yijun really wanted to explain it clearly, it would take more than ten chapters. In summary, it is the three talents and the general economics of all things.
When Wang Qian heard this, he found that His Majesty answered with a completely contradictory negative, and immediately expressed that he understood clearly.
In addition to the monstrous art of arithmetic, the Ming Dynasty opposed arithmetic. In fact, there was another problem, that is, utilitarianism. Arithmetic and business are highly and closely integrated. The low status of merchants is because merchants are very utilitarian. .
But if the imperial court is not utilitarian now, it will perish.
Zhu Yijun has been reading the historical records of the country recently. The weakness of the Ming Dynasty at this time was definitely not achieved overnight, but a downward cycle. The speed of this downward cycle was not constant. There were also Emperors Yingzong and Xiaozong who stood up and stepped on the accelerator to the end to accelerate the Ming Dynasty. Slide down.
Jiajing did not go to court, and Emperor Longqing did not see his ministers and ministers, but they still approved the memorial.
Thirty years after Emperor Wanli arrived, Emperor Wanli stepped on the accelerator directly into the fuel tank, causing the Ming Dynasty on the downhill road to dive all the way into the abyss.
No matter what, the memorial still needs to be approved.
"Can the difference method only be used in the summation of high-order power operations?" Another student began to ask.
Zhu Yijun talked about several application cases of the recruitment method with a smile on his face. The recruitment method is a fitting method that can be used in all aspects of life, such as building construction, recruiting soldiers, recruiting troops, freight, smelting, astronomy, etc. , For example, in ironmaking, it is necessary to determine the amount of a certain material to be added, etc.
Zhu Yijun used the recruitment method to explain how to calculate the visual degrees of the sun, moon and five stars. He only gave a brief taste of it. Calculating the actual degrees of the sun, moon and five stars is still too difficult for students. If you want to enter Qintian Prison, you can continue to learn. .
Zhu Yijun answered the students' questions. It was not until sunset that Zhu Yijun ended the first class of the day.
Overall, his first class was extremely successful.
"Your Majesty, thank you for your hard work. Your Majesty's lectures were really thunderous, and the listeners were all enlightened." Feng Bao saw that everyone had dispersed, and he came up with a compliment. After giving a lecture, he stood for an hour and a half. This is really Extremely hard work.
"Flattery, prepare your horses and go to the capital camp." Zhu Yijun did not let Feng Bao continue to flatter him, but chose to go to the capital camp to parade the military horses. Emperor Cheng Zuwen once said that even if there is a knife in the sky, he must go to the capital with a steel umbrella. The battalion parades military horses.
The soldiers must know who the emperor is.
"Your Majesty, let's take a day off." Yu Dayou was old, but he still insisted on finishing the class. He was a rough man, but he actually learned the recruiting method. Before coming, Zhang Juzheng asked the young emperor to teach the Four Elements Art. His Majesty said After finishing the Four Elements Technique, he talked about the Zhaochai Method, and Yu Dayou understood both the Four Yuan Technique and the Zhaochai Method.
Of course, during the teaching process, no students asked the teacher to drag the class.
After all, there are twenty correction officers. Standing on both sides of the Yi Lun Hall, any student who dares to say this will definitely be corrected by physics.
"I have a rest today, and I want to rest tomorrow. I am too young to rest. I will go to the capital camp first. Everyone, please go back." Zhu Yijun waved his little hands, got on his horse, and ran towards Beitucheng outside Deshengmen.
Ge Shouli looked at His Majesty's leaving figure and said with a smile: "You are young in bright clothes and angry horses."
The sun was rising, and Ge Shouli was extremely pleased. He was also incredible at Zhang Juzheng's power to transform decay into miraculous power.
Zhang Juzheng held his hands and said: "Your Majesty lectures in simple and easy-to-understand terms, and uses all possible methods to make students understand. Zhongshu Sheren recorded the daily notes and excerpted them. This class, Very well said.”
"Zhang Huangbang announced the content of this class. The monthly exam will test the recruitment method. Those who get eight points out of ten will go to the Woolen Official Factory to collect wool for three days and worship wine. I will leave this matter to you."
"Yes." Fan Yingqi immediately accepted the order. He did not think that the request was very high. His Majesty's lectures were extremely lively and logical. For the students of the Imperial College, they would not be able to learn this without finding a rope to hang themselves on. Get up, I am so sorry for His Majesty's preparation.
The emperor gave lectures in person, and the lectures were so good that they exceeded everyone's expectations.
Zhang Juzheng was afraid that the students would not understand the recruitment method and asked the emperor to teach the Four Elements Art. He probably underestimated the emperor's teaching ability. Judging from the students' reactions after the class and Yu Dayou's reaction, this class was very successful. .
The monthly exam of the Imperial College depends on this content, can you learn it? If you can't learn it, go to labor reform and experience the hard work of poor coolies. After three days of manual labor, you will know that today's life is hard-earned, and you will definitely learn it next month.
The Imperial College was immediately filled with mourning, but after Jiao Hong read the yellow list, he had fully understood the application of the recruitment method, which was really not difficult.
Zhu Yijun came to the Beitucheng camp again. He did not torment the soldiers. The training was over. He just walked around. The soldiers thought that the emperor would not come today. But before the sun set, they saw the emperor's chariot and carriage. Longqi Dazhao and the emperor himself were talking with Qi Shuai.
This made the soldiers in the Beijing camp feel particularly at ease.
The dragon flag flying in the capital camp for one day proves that the Ming Dynasty's Zhenwu will not end.
After the news that Zhu Yijun killed Chen Youren, a cheap scholar, last time spread in the Beijing camp, Zhu Yijun entered the military camp, and the soldiers supported him from the bottom of their hearts.
Zhu Yijun and Qi Jiguang talked about the Northeast War. The Daning Guards and the Tuman Khans fought against each other for more than 20 rounds in a small area, with each winning or losing. However, relying on the advantage of the camp, the Ming Dynasty completely repelled the Tuman Khan and won the victory. Daning Wei's attempt.
Wang Rulong is not Tang Kekuan. Wang Rulong is a direct descendant of Qi Jiguang. He obeys the general's orders and does not take the initiative to go out to fight in the forts. Qinglong Fort, Xingshu Fort, and Taotushan Fort are the horns of each other. When the Tuman Khan has no artillery, he wants to Capturing it is just a fool's dream.
The fifth battalion of Khalkha also encountered Li Chengliang. Li Chengliang used his troops very strangely. If the Khalkha Ten Thousand Households hadn't run so fast, Li Chengliang would have almost had his butt removed. At that time, he fell off his horse and broke an arm. In a short period of time, he was unable to form an effective offensive against Zhang Wu.
"Subahai is very desperate, because even if the Zhangwu garrison is defeated, there are earthen forts everywhere from Zhangwu to Pinglu Fort. They must be destroyed, otherwise if they invade Liaodong, there will be no return." Zhu Yijun's He had zero military talent, but he also knew that if Su Bahai dared to play with him, he would be dead.
Once the enemy rushes in, it's like infantry entering a mine array. Nowhere in all directions is safe.
Hou Yuzhao's farming in Liaodong caused great trouble to his direct opponent Su Banghai.
"I am more worried about the reconciliation between the left and right wings." Qi Jiguang said worriedly: "Although Sanniang Zi seems to be respectful, she has been seeking reconciliation between the left and right wings. Last time she went from Qinglong Fort to the Tuman Khan Golden Summit. Account, discussed the matter."
For politicians, gender is secondary and political identity is crucial.
"Qi Shuai's worries are also my worries. Qi Shuai is too capable of fighting. I thought Beilu was weak, but the death of Tang Kekuan has clearly told me that even Dong Fox, who was fooled around by Qi Shuai, I can kill Tang Kekuan." Zhu Yijun was also worried about this issue.
"You have to poke the inside out so that the left and right wings cannot be reconciled. Let me think for a moment, eh, I have it!" Zhu Yijun raised his eyebrows with his left fist and right palm and said: "Let Wang Rulong take advantage of the winter to collect the fleece of the right wing. After being nagged so many times by Man Khan’s envoy, he was extra merciful and purchased it at a price lower than one-third of the price of the left wing.”
"This man is not worried about scarcity, but about inequality."
Qi Jiguang felt a chill run down his spine when he heard this. He looked at His Majesty blankly. Your Majesty may not know how to fight, but his ability to conquer fire was first-rate. With a turn of his eyes, he had an idea.
It's okay if the wool is not collected, but it ends up being purchased at a reduced price based on the left-wing price.
The right wing of Tuman Khan was originally not qualified to participate in the wool business. If he couldn't eat, he wouldn't be jealous. But if he did, but he ate less than others, he would immediately become jealous.
As for Anda Khan's left wing, it was originally a separate business, but a piece of it was poached by Tuman Khan at a low price. What would Anda Khan think? He was ready to kill Tuman Khan.
"Being your Majesty's enemy is really a sad thing." Qi Jiguang said sincerely. His Majesty's ability to use the power in his hands correctly is what Qi Jiguang is most gratified about. He can provide his Majesty with an invincible army. Use it, but His Majesty doesn't use it, so there's nothing he can do.
"Then Qi Shuai still has to win the battle before I can torment them like this." Zhu Yijun said with a bright smile.
It is an undisputed fact that military victory brings more initiative. All of this is based on winning the battle. If the battle cannot be won, no matter how many clever ideas are used, it will be useless.
The backs of Zhu Yijun and Qi Jiguang were stretched very long by the setting sun.
After Zhu Yijun returned to Beijing, the first thing he did was to read today's miscellaneous newspapers. The Jin miscellaneous newspapers comprehensively sorted out the various technological innovations of the woolen official factory and praised the craftsmen's diligent spirit. Many of them The inconspicuous small technology saves a lot of costs, manpower and material resources, and the Jin Party shows their respect for the craftsmen.
The main content reported by the Quanchu Miscellaneous News was the serialization of Qi Jiguang's Eastern Expedition and the nonsense about Ping Japanese, which made Zhang Juzheng very, very angry. The Ming Dynasty only had such an army. They would rather starve themselves than reach out to the people. Mi Vat, The Eastern Expedition, is a series of practical reports, serializing all of Qi Jiguang's achievements from military training to the pacification of Japan, focusing on the comparison of people's lives before and after the pacification of Japan.
Zhejiang's miscellaneous newspapers published some progress of Qingzhang, as well as Song Yiwang's flood control in Nanya.
In addition to the three major party periodicals, many miscellaneous newspapers have sprung up like mushrooms after a spring rain. For example, the People's Daily likes to report on various matters closely related to the people and has become the most popular newspaper outside the party periodicals. This People's Daily was founded by What Geng Dingxiang organized in Beijing was mainly about eating, drinking and having fun, such as Zhu Zaiyu's Twelve Rhymes, various novel musical instruments, and some ways to eat kelp.
The Jiegu Institute's research on large neck disease was also published in the People's Daily.
The miscellaneous newspaper that Zhu Yijun dislikes the most is the Fushe Newspaper founded by Sun Jigao and other retro Confucian scholars. It is all about retroism, and also likes the yin and yang of the government. Chen Youren's bones are not cold, and Sun Jigao does not dare to talk nonsense, but he still advocates Retro.
Zhu Yijun sneered and said: "This Sun Jigao, who is scolded by children every day, still writes newspapers and sells them well. You see, after a while, he won't even be able to pay the rent!"
Newspapers that cannot be sold will naturally be eliminated. Sun Jigao's Social Newspaper has a large market, but those old-fashioned things will no longer be listened to after a long time.
"The Ministry of Rites reported that the special envoy of Franz Ligasi wants to start a Thai-Spanish newspaper to publish some interesting overseas stories. Please report to Your Majesty." Zhang Hong took out a memorial, and Ligasi also wanted to join in the fun of publishing a miscellaneous newspaper. Let’s introduce things overseas.
After Zhu Yijun took the memorial and read it, Zhu approved the memorial. He approved Ligas' request, but specifically issued a chapter to the Ministry of Rites not to allow Ligasi to preach. If he found out, he would immediately ban it.
It is absolutely impossible to allow preaching, and most of the Dalongxing Temple was taken away to build the Royal Gemological Garden.
"Has Antonio left?" Zhu Yijun asked about the captain's whereabouts. He was an investor, so he naturally had to pay attention to the progress of the project.
"I borrowed 500,000 yuan and left the capital. I went to Tianjin and took a hydrofoil sailing boat to Songjiang Prefecture, ready to return to the West." Zhang Hong took out a memo, found Legas' entry, and reported Antonio's whereabouts. .
Antonio bought a total of four boats, bought two boats' firearms, bought some gunpowder, and hired a group of sailors and boatmen from the Ming Dynasty. These sailors and boatmen were for a five-year term. The contract was terminated when it expired, and the contract was renewed. , or change ships, it all depends on the decision of the captain and sailors.
The ships of the Ming Dynasty can carry bows, armor and knives, cannons and muskets, but they are not allowed to use bows and refills when entering the harbor. This must be done after coastal defense inspection and supervision. Zhu Yijun gave Antonio the treatment of the ships of the Ming Dynasty. After all, Antonio was professed to be a vassal when he came to the port.
Antonio spent all his profits on buying ships, and he also owed a lot of debt.
Da Ming makes money, Da Ming spends it, and one wants to take it home.
Please give me a monthly ticket, wow! ! ! ! ! ! !
(End of chapter)
