Chapter 135: "A Treasure of Arithmetic Learning", "Algorithm Unification" and "Taiwan Arithmetic"

Style: Historical Author: Who will I return to?Words: 7303Update Time: 24/02/20 13:32:15
False accusations are usually dealt with by sitting back.

In the Han Dynasty, the "Book of Han" equated false accusations with killing or wounding people, and clearly stipulated: Tuo should not sit down if he is over eighty years old and does not make false accusations or kill or wound people.

False accusation is the same as slander with words and injury with weapons.

In the Tang Dynasty, "Tang Lv Shu Yi· Litigation 3" states: Those who falsely accuse others will sit down. Sitting back means imposing the punishment that the false accusation deserves on the person who made the false accusation.

The Ming Dynasty inherited the system of the Tang Dynasty, and the Ming Dynasty law was more stringent in the case of false accusation and rebellion, adding three levels to the crime. It is clearly stated: false accusations will be added to the second level of the false accusation; false accusations of abortion and cane crimes will be added to the false accusations of the third level. Each crime will stop the rod from flowing for one hundred miles and travel three thousand miles. It is a crime to falsely accuse someone of death. If the person falsely accused has already been killed, he will sit down and die. For those who are still undecided, the staff will travel three thousand miles with a hundred sticks and three years of additional service.

In the "Gangxianshi Lei" and the Metropolitan Procuratorate Chapter of the Ming Dynasty Huidian, officials are also required not to stay in prostitution, not to take prostitutes to play, not to sneak into the theater and wander around, etc. They are also not allowed to make false accusations, and the false accusations will be increased if they are found guilty. Third class.

The Kechen Yanguan is an extremely important part of the Ming Dynasty's error-correction mechanism. If the Kechen Yanguan is weaponized and turned into a tool, and becomes a tool to eliminate dissidents and create trouble, the Ming Dynasty's official administration will immediately collapse completely.

Judging from the actual supervision situation in the Ming Dynasty, the role played by Yanguan showed a downward trend. It was fine in the early and middle periods. In the middle and late period, Yanguan changed from a decontamination agent in officialdom to a catalyst for corruption and degeneration in officialdom. .

In fact, Zhang Juzheng had no good solution to Ke Dao Yan Guan. He could not attack Ke Dao Yan Guan, otherwise all Fu Yingzhen's accusations against Zhang Juzheng would be confirmed.

It doesn't matter if it's not convenient for Zhang Juzheng to take action, as long as Zhu Yijun takes action.

Tishuai Zhao Mengyou was sharpening his sword and was waiting. After pulling the four people on the ground onto the bench, he raised the imperial staff and struck it hard. The officials kept beating the imperial staff one after another. Weeping and wailing.

Zhu Yijun, on the other hand, watched with cold eyes. It was not until the execution was over that Zhu Yijun stood up. Without even looking at them, he left the Huangji Gate and returned to the Wenhua Hall to continue to listen to the government affairs.

The treatment of these four people is not over yet. After receiving the imperial cane, they still have to remove their official status and return to their hometowns to live idle and are not allowed to sign official documents. This eliminates the possibility of these people to resurrect. The four people resurrected because of the impeachment of Lu Guangzu. , and finally ended up like this, it can only be said that he is to blame.

Soon an imperial edict was announced to the world. If the officials and officials still felt that the emperor had harmed the ministers and the upright people, they could continue to report. As a result, Zhu Yijun did not wait for the officials to continue to report. The little emperor was The chain of traps is really tricky. If you create cards out of thin air and then use the stick to punish them, and then play them one after another, I'm afraid it won't be over with just one stroke of the imperial stick.

At this point, Zhu Yijun took advantage of the conflict between Duoqing and Ding You to deal a heavy blow to the arrogance of the humble Confucianism, and to a certain extent corrected the trapping style of Ke Dao Yan Guan, politics, and the righteousness of people. .

Zhu Zaiyu has been busy with a big thing recently, which is about the official compilation of arithmetic, that is, the compilation of textbooks. Originally, Zhu Zaiyu thought it was a very simple thing, but he was repeatedly rejected by the Ming Emperor. The emperor criticized his compilation. I just gave one evaluation of the textbook, and I was not satisfied with it.

It wasn't that there was something wrong with Zhu Zaiyu's arithmetic skills, it was really that the little emperor's requirements were too high.

"Uncle Emperor, what is arithmetic and mathematics?" Zhu Yijun looked at the textbook submitted by Zhu Zaiyu in the side hall of the Wenhua Palace, rejected it again, and said with a little helplessness: "Borrowing from Yan Gong's "Tongyuan Algorithm" in the early days of the Republic of China "One sentence in "It is: a book of ten thousand different principles, which can be expressed as a method to understand the original principles."

"This is arithmetic and mathematics."

"During the Jingtai period, Wu Jing wrote "The Encyclopedia of Arithmetic Algorithms with Detailed Annotations in Nine Chapters", which can be regarded as the most complete collection of arithmetic in the Ming Dynasty. But what is the "Arithmetic Enlightenment" written by the emperor's uncle? Divination methods, pregnancy prediction, arithmetic Can you solve the problem of whether you will get sick or whether you will have a boy or a girl?"

"What is arithmetic? Arithmetic is the language of infinite things. It is the only way to make all things speak. If this kind of official arithmetic is spread all over the world, what is the difference between it and the art of witchcraft? Wouldn't it make people laugh?"

Zhu Zaiyu was silent for a moment, bowed his head and said: "No, your majesty is wise."

In fact, Zhu Zaiyu was not satisfied with his arithmetic enlightenment. He had tried his best.

As the emperor's arithmetic teacher, he really had nothing to teach him. The little emperor was really good at arithmetic.

Zhu Yijun still said with a serious face: "Arithmetic is an expression of the principles of infinite things. It should be as concise and concise as possible. It should have a complete set of rigorous and well-organized argumentation processes. It should boldly make conjectures about practical problems and be careful. Demonstrate, carefully summarize, and verify repeatedly.”

"Arithmetic is the solid foundation for the development of all things. Arithmetic is the general economics of the three talents and all things."

"The arithmetic enlightenment written by the emperor's uncle is like folk wizards dancing a dance that they don't even know about in front of the sun. They pray to gods and worship Buddha in front of clay statues, then burn a charm and drink it in one gulp. Steamed buns made with blood can cure tuberculosis."

"Uncle Emperor, this is not the arithmetic that I want, nor is it the arithmetic that Ming Dynasty should have."

"Uncle Emperor?"

Zhu Zaiyu said quickly: "I am here."

Zhu Yijun continued: "The emperor's arithmetic enlightenment is not only unenlightening, but can easily lead people astray. It just teaches people to calculate like this, rather than teaching the world's scholars how to calculate, let alone why to calculate like this. It’s just like the rotten scholars shouting about the methods of the ancestors, they are teaching people how to do it, but they don’t teach people how to do it, let alone why they do it.”

"To put it more clearly, it means knowing what it is, knowing why it is so, and knowing why it is inevitable. The emperor's arithmetic enlightenment only knows what it is, but does not know why it is so."

"I'm very disappointed."

"Even a twelve-year-old like me can complete the arithmetic taught by the emperor's uncle. Is this considered a subject?"

Zhu Zaiyu screamed crazily in his heart, little emperor, can you be like ordinary people? You have already mastered arithmetic, do you still need someone to teach you?

In the six-month arithmetic class, Zhu Zaiyu was completely numb. Rather than saying that he was teaching the little emperor, it was better to say that the little emperor was teaching him. For many questions, the emperor did not need him to teach him at all. The little emperor could use the Winter Solstice Guidance The shadow length of the watch can measure the winter time to the accuracy of the minute. Like Zhu Zaiyu and Zhang Juzheng, they are both prodigies.

"Your Majesty, is there a possibility that the arithmetic compiled by me is just acceptable to our Ming students?" Zhu Zaiyu thought for a while and put forward a hypothesis. It was not that there was something wrong with his compilation, but that there was something wrong with his compilation. Is the emperor too demanding? I overestimated the acceptance ability of Ming students.

Except for the Four Books and Five Classics, the students of the Ming Dynasty did not read anything else, not even the Code of Ming Dynasty, let alone arithmetic. The reason why the students of the Ming Dynasty did not study arithmetic was because the imperial examinations of the Ming Dynasty did not take Ming arithmetic. Not only did the Ming Dynasty not take the exam, but also The Song Dynasty didn’t even take the exam. The subject of arithmetic was just a flash in the pan in the early Tang Dynasty. By the end of the Tang Dynasty and the Five Dynasties and Ten Kingdoms, arithmetic was no longer tested at all.

It can be said that the development speed of arithmetic in the Central Plains Dynasty almost stagnated after arithmetic was not included in the imperial examination.

"What the emperor said makes sense." Zhu Yijun also nodded helplessly. His requirements were indeed a bit high. What he wanted was arithmetic, but what Zhu Zaiyu gave was arithmetic. This gap between expectations and reality was the reason why the emperor and the emperor The main conflict between uncles.

"Your Majesty, should we let the students accept arithmetic first? It is also very good to be able to do arithmetic." Feng Bao also said something fair for the emperor's uncle. Not everyone is a child prodigy born with knowledge, and not everyone is a child prodigy. Be able to accept the concept of arithmetic as the overall economics of the three talents and all things.

Walk the road step by step and eat the food one bite at a time.

Zhu Yijun thought for a while and said: "Uncle Huang's arithmetic is not mathematical, so it would be better to revise it."

"Your Majesty, Ge Shouli is requesting an audience outside the palace." A small yellow doorman hurried in and said.

"What is he here for?" Zhu Yijun asked a little strangely: "Xuan Lai."

Ge Shouli walked into the Wenhua Hall step by step holding fifty-five volumes of books, placed the books he brought on the ground, respectfully bowed five times and kowtowed three times, and said loudly: "Greetings to your Majesty, long live your Majesty, Long live."

Zhu Yijun looked at Ge Shouli and asked, "Ge Ping is here, why are you here?"

Ge Shouli said with a smile: "I am here to relieve your majesty's worries. I saw that Yuan Fu Shen's old chapter ordered the study of politics to revitalize talents. The great Situ Du made a bypass to pay national taxes and arithmetic. Your majesty also collects taxes and seeks talents in arithmetic. I have a treasure book fifty-five Volume, the book is called: "Xinji Tongzheng Ancient and Modern Arithmetic Learning"."

"Oh? Submit it for reading." Zhu Yijun picked it up and looked at it for a long time before putting it down and saying, "Where did the book come from?"

Ge Shouli hurriedly replied: "Arithmetic is indispensable in the world, both public and private. This book was written by Wang Wensu, a Shanxi merchant during the Chenghua period. It was mostly circulated among Shanxi merchants' homes to facilitate business. In the family of Yang Dazai There is a copy, and I find it novel. At that time, I was the Minister of the Ministry of Household Affairs, in charge of the national tax accounting system, so I copied a copy for my own use. Now I heard that Your Majesty and Prince Zheng are confused by the enlightenment of arithmetic, so I dedicated the book."

Zhu Yijun looked at the arithmetic treasure book in his hand, then looked at Ge Shouli and said with a smile: "It turns out that I got it from Dazai Yang. It's very good. Ge Gong contributed a lot by presenting the book. What kind of reward do you want?"

"I solve your Majesty's problems without asking for favors. I am the censor of the left capital of the country. I am in charge of admonishment, but I can't restrain you. Today, four crazy students have caused an unprovoked provocation in front of the emperor's door, causing the emperor to bully him. The heart is to be close to the ministers, and the ministers are guilty of deceiving their superiors in order to serve the master."

"If there is suspicion and fear between the ministers and ministers, there will be estrangement between them, and there will be too much discussion, the blessings of tranquility and peace will not be enjoyed forever. I deeply regret what I have done."

Zhu Yijun understood that Ge Shouli wanted to remove himself from the previous incident of Huangji Sect Fugu.

Wu Zhongxing, Zhao Yongxian and others were all censors. As the head of the censors, it was hard not to misunderstand that Ge Shouli was working together in the middle. Ge Shouli was really unjust, so when he saw the emperor, his uncle, and Yuan Fu, they all felt for him. When he was troubled by arithmetic, Ge Shouli came with his "Baojian of Arithmetic".

Zhu Yijun thought about it again and said: "Gong Ge is wrong. I have always known the respectful heart of Mr. Ge. As the leader of the Jin Party, Mr. Ge respects the authority of the Lord. Today I present a treasure book to Prince Shaobao, and Yin Yizi is the secretary of the Central Committee." I am an exception, and I will give you a python robe and a fighting bull each, a hundred taels of silver, four strands of silk, five thousand guan of banknotes, and five bottles of wine. It is a small token of favor and no need to say goodbye."

The wine was sweet potato roasted by Zhu Yijun himself. The wine was given out five bottles at a time, which meant that Zhu Yijun was really happy.

Prince Shaobao, from now on Ge Shouli will be Ge Shaobao in the court, even though his Shaobao title is just a promotion.

"I thank you for Your Majesty's kindness." After hearing this, Ge Shouli thanked His Majesty again, fell to the ground, and whispered: "Your Majesty, I... am already old and can no longer solve your Majesty's worries."

"Huh? Is Mr. Ge going to become an official? If Mr. Ge is worried that his official position will be implicated, there is no need to worry. I am not an ignorant person. Let alone Mr. Ge, it is Yuan Fu, the late emperor, and Shizong. Who can control it? Got the official position of Ke Dao? A group of people wanted to be famous for a while, and they dared to resist the imperial decree, just for the sake of the family." Zhu Yijun thought that Ge Shouli was afraid of being implicated by Ke Chen Fugu, so he simply became an official and went into hiding.

"Your Majesty, I am already seventy this year, which is a rare age." Ge Shouli said, "I am really old."

"Gong Ge, please get up and talk. Ge Gong is already seventy this year?! I look like he is only in his fifties. Ge Gong is really well-kept." Zhu Yijun looked at Ge Shouli with wide eyes. He looked at it for a long time. , I really didn’t see that Ge Shouli looked seventy years old.

"Your Majesty." Ge Shouli said with a smile: "At this age, if you continue to occupy the position and refuse to leave, you will be disgusted by people and despised by dogs, and you will be greedy for position and slander your ministers."

"Is Mr. Ge suffering from an old illness?" Zhu Yijun asked doubtfully.

Ge Shouli shook his head and said, "No."

"Then it's over? I want to see who dares to make a fuss about Ge Gong's age." Zhu Yijun heard that Ge Shouli was not ill and said with a smile: "Ge Gong, there is no need to say anything more about becoming an official. mentioned."

Ge Shouli can be used, and the Jin Party has taken on a new look in Ge Shouli's hands. At this time, Ge Shouli retreated, and Zhang Siwei and Wang Chonggu immediately lost the competition within the party. How could Zhu Yijun make Zhang Siwei happy?

As Ge Shouli said, "A Book of Arithmetic Learning" was published in the second year of Jiajing and was widely circulated among Shanxi merchants. Didn't Zhang Siwei know about it? As long as he was a little reverent, why didn't he submit the "Baojian of Arithmetic Learning" to the emperor to solve the most urgent tasks of the Ming Dynasty? Zhang Siwei didn't have it, so Ge ​​Shouli came.

"Then I will continue to solve your Majesty's problems?" Ge Shouli thought for a while and said.

"Excellent, excellent, sweet potato roasting, no... Guojiao's wine has a high alcohol content. It's better for Mr. Ge to drink it lightly." Zhu Yijun nodded with a bright smile on his face.

This was Ge Shouli's test. By presenting a book, he could test whether he was a sycophant in the emperor's mind, and whether he should go away to protect himself.

But it was obvious that the little emperor was still very satisfied with Ge Shouli. Ge Shouli had the sour and rotten temperament typical of some scholars, but he was neither a cheap scholar nor a rotten scholar. Now he had directly turned into a fun-loving person, watching fun all day long.

As for the rebellious group of Ke Dao Yan Guan, Ge Shouli couldn't control it. It wasn't that Ge Shouli had a problem, it was that Ke Dao Yan Guan's roots were rotten.

"Your Majesty, Mr. Yuan Fu is outside the palace asking for an audience." Another person from the small yellow door hurried in to report the news.

"Xuan."

Zhang Juzheng also held a stack of books and walked in step by step. He put the books on the ground, waved his sleeves and said, "I pay homage to your majesty. Is your majesty paying homage to you?"

"Excuse me, sir, you are here to present a book too? What book did you bring?" Zhu Yijun looked at the dozen volumes of books that Zhang Juzheng was holding and asked curiously.

Zhang Juzheng bowed his head and said: "Reporting to your majesty, "Zhizhi Algorithm Tongzong" written by Cheng Dawei, a businessman in Huizhou Prefecture, South Zhili, has a total of seventeen volumes. Since Gui E advocated a compilation method, I have been paying attention to mental arithmetic talents. Please report Shen Jiuzhang ordered us to study politics. I heard that His Majesty and Prince Zheng were trapped here, so I specially presented a treasure book."

Zhu Yijun read the book carefully. It was not surprising that Zhang Juzheng presented the book. It was Zhang Juzheng who proposed the academic policy of Shen Jiuzhang, and he also added arithmetic. As a result, he wanted to promote arithmetic. Without textbooks, Zhang Juzheng naturally could not allow himself to implement the policies. It is the flower in the mirror and the moon in the water, so I presented the book.

"My Ming Dynasty is really full of talents." Zhu Yijun said with emotion after briefly reading through it.

Zhu Yijun smiled and asked, "What reward do you want, sir?"

"I will naturally implement the executive order when I propose it. I would like to kowtow and lead you. I am deeply grateful for the kindness of Heaven." Zhang Juzheng did not want the reward because His Majesty had already given it. He issued an edict to his parents to come to Beijing to be loyal and filial. From Liang Menglong's unrequited love to Zhao Mengyou's extravagant efforts to fabricate Lu Guangzu's love affair out of thin air, this series of struggles were all decided by the little emperor, who solved the political problems that Zhang Juzheng's parents would face in the future. Huge passive on.

What kind of reward does Zhang Juzheng need for this kind of support? Being a good first assistant and implementing the New Deal is Zhang Juzheng's greatest gratitude to God.

Zhu Yijun shook his head and said: "Sir, you don't want it. I have to give it. I have merit but no reward. If the world sees it, wouldn't it mean that I am ungrateful? You have merit in dedicating the book and I will increase my salary by one grade. Please don't refuse, sir."

"I kowtow to express my gratitude to Heaven." Zhang Juzheng thought over and over again and refused to express his gratitude. He did a good job in presiding over the new policy.

Zhu Yijun looked at the two piles of arithmetic and said, "Where is Cheng Dawei, the author of Algorithm Tongzong?"

"Nanya Huizhou does business." Zhang Juzheng answered honestly. This book was sent to the capital by Song Yangshan, the governor of Yingtian, in order to cooperate with Zhang Juzheng in rectifying academic affairs.

After Zhu Yijun heard this, he thought for a while and said seriously: "The virtuous people are in the wild. It's because I don't practice benevolence. Sir, with such a great talent, is it appropriate to recommend him back to the capital?"

There are virtuous people in the opposition and not in the court. This is the result of the emperor not practicing morality. This is the only way for the humble Confucians. Since such a mathematician is still alive, he naturally gets it to serve the country in the capital.

"I obey the order." Zhang Juzheng obeyed the leader's order.

Zhang Juzheng looked at another pile of books and asked, "Is Mr. Ge also here to present books?"

"What a coincidence, is Yuan Fu also here to present a book?" Ge Shouli said with a smile. In this matter, Ge Shouli was one step ahead of others in the matter of assuming the authority of the Lord and presented the arithmetic treasure earlier than Zhang Juzheng. Learn.

"Your Majesty, Wan Shihe, Minister of Rites, is asking for an audience outside the palace." Another small yellow door hurried in.

"What day is it today? Are you all together?" Zhu Yijun was also delighted when he heard this and said, "Xuan."

Wan Shihe walked in with a few books in his hands, kowtowed five times and said: "I pay homage to Your Majesty. Is Your Majesty doing your best to bow down?"

"Well, no gift, what book does Wan Shangshu want to present?" Zhu Yijun asked, looking at the books Wan Shihe brought.

"The Minister of Honglu Temple, Chen Xuexue, compiled and compiled "Taishi Arithmetic" in six volumes." Wan Shihe handed the book to Zhang Hong and said with great respect.

In Haojing and Luzon, the Ming Dynasty obtained a large number of books. Among these books, Chen Xuexue picked and picked out all the scriptures. After selecting all the scriptures, he selected the whole set of arithmetic and made a compilation, compilation and translation.

Zhu Yijun opened it and looked at it for a long time, nodding his head and saying: "Very good, Wan Shangshu has contributed a lot to the book presentation, Yin Yizi is a member of Zhongshushe, Chen Xuexue has been promoted to an official level, and for special exceptions, each person will be given an additional hundred taels of silver." , four pieces of silk on the inside and outside, five thousand guan of banknotes, and five bottles of wine, in recognition of the merits of translation, compilation and compilation."

"Not bad." Zhu Yijun looked through so many masterpieces in his hands. It all starts with making a telescope. As the language of all things, arithmetic has become more and more important. If the emperor wants to learn arithmetic, the officials of the empire must learn arithmetic. He would do his best to take out arithmetic works and let the emperor check them.

Zhu Yijun smiled and said: "Uncle Emperor, make a copy and start compiling "Arithmetic Enlightenment"."

Zhu Yijun is holding the "Baojian of Mathematics" in his hand. It is a pity that this masterpiece of mathematics compiled by Wang Wensu is only circulated in the hands of Shanxi merchants. It is used as a tool for business.

There is a kind of thinking in the book of arithmetic: Tongzheng New Collection.

The general certificate is to eliminate the false and retain the true, fill in the gaps and correct the source. It is a review and demonstration of past mathematics, and it talks about why it is calculated in this way. The new set is to put forward your own conjectures on some issues, and to be cautious through the general certificate. Argument, summarize.

In line with Zhu Yijun's requirements for arithmetic, make bold assumptions, carefully demonstrate, and summarize.

Zhu Yijun saw the "Baojian of Arithmetic Studies" which studies the numerical solution of higher-order equations of one variable. In this book, arithmetic is like a heavenly book, with concepts such as Mr. A, Yu Shi, Yi Lian Zeng Multiply, Mr. B, and Party B. It's really not easy to understand.

The emperor had a copy of "Taishi Arithmetic" on hand, which introduced the "Algebra" published by Milan in the 29th year of Jiajing. It summarized the symbols of addition, subtraction, multiplication and division, and if the unknown numbers are replaced by parent-child algebra, it will become easier to understand.

After Zhu Yijun read the six volumes of "Algebra", he realized that there was still no concept of decimal in Thai and Western arithmetic at this time. Decimal fractions, decimal decimals, calculation methods and representations were lacking. (It was not until 1585 that the Dutch mathematician Stephen systematically introduced decimal fractions.)

However, in Zhu Yijun's mathematics textbook, "Nine Chapters of Arithmetic" from the Wei, Jin, Southern and Northern Dynasties states: The unnamed ones are regarded as molecules. When one retreats, ten is its mother, and when it retreats, it is hundreds. thin. When calculating compound interest in "Nine Chapters of the Book of Numbers" of the Southern Song Dynasty, the great mathematician Qin Jiushao calculated the compound interest as: seventy-nine cents, three points, four centimeters, eight cents, four silks, six suddens, seven micros, seven sands, three wilds, one light, two clear, five smokes.

In fact, there is no actual unit below the text, and every cent is just a calculation of interest.

Wang Wensu's numerical solution to higher-order equations of one variable is very interesting.

For example, to find the approximate root of x-3x+1=0, the method given by Wang Wensu is simple and crude. Just cut off x and get a formula -3x+1=0, x=1/3. Put this approximate root into , the left side = 1/27≈0.03, obviously, 0.03≠0, there is an error.

Obviously this approximate root is not approximate and accurate enough. Why make a further approximation? Let the error be u, that is to say, x=1/3+u. Put this approximate root into the original formula to get, (1/3+u)-3 (1/3+u)+1=0, this equation is still a higher-order equation, how to solve it? Cut off the higher order terms again and get an equation 1/27+1/3u-1-3u+1=0. The solution is: u=1/72, x=1/3+1/72=25/72 .

Bringing in the approximate root of x=25/72, the left side ≈ 0.00025. Obviously, 0.00025≠0, there is still an error.

Why make a further approximation? Let the error be i, x=25/72+i, then bring in this approximate root, and repeat the same process again, and you will get a more approximate value.

On this basis, Wang Wensu adopted a valuation method, first roughly finding the approximate root a, and then setting the error b, making it more accurate step by step.

Find an approximate solution for f(x)=0. Suppose x=a+b. Substitute it to get: f(a+b)=f(a)+kb+o(b). f(a) can be solved. The constant term, o(b), is a high-order term that is difficult to calculate. We can directly cut it off to obtain a linear equation of one variable. We only need to find the coefficient K of the linear term, and we can iteratively obtain an approximate solution to the equation, regardless of the order of the equation. No matter how high it is, it can be approximated infinitely.

This K was called differential in later generations. This method of iteratively solving higher-order equations is actually more of an application-oriented approach to finding approximate solutions, but it is indeed an infinite cut of differential.

What happens after that? After that it was gone.

Even the results of Wang Wensu's decades of sitting as a master of classics are just reference books for businessmen to settle accounts and have not been widely circulated. However, Ge Shouli presented these fifty-five volumes of books to solve some problems without teaching materials. It's just an urgent matter.

Compared with the Song and Yuan Dynasties, the mathematics of the Ming Dynasty was improved, but this progress was sporadic and unsystematic.

Zhu Yijun looked at his pile of arithmetic masterpieces and knew that he was very busy.

Zhu Zaiyu deleted some contents about fortune-telling and pregnancy prediction, and re-edited the "Arithmetic Enlightenment". Enlightenment is enlightenment, adding, subtracting, multiplying, dividing and solving equations. The level is roughly equivalent to that of later elementary school to junior high school textbooks. Mathematics is further improved. Simplified, the six-volume "Taishi Arithmetic" is easy to understand for Zhu Zaiyu. Various mathematical symbols and algebraic thinking make mathematics simpler and more concise.

As for higher-level arithmetic textbooks, Zhu Zaiyu had to study and understand the three masterpieces in his hand before he could continue to compile them.

Zhu Yijun is only twelve years old, he can afford to wait.

After Chen Lin watched the little emperor angrily reprimanding his ministers in the capital, Chen Lin took his trimaran hydrofoil sailboat south again, heading towards Songjiang Mansion.

Chen Lin, who returned to Songjiang Prefecture, needed to perform another ocean test mission. This time, she went to Yuegang, to the Penghu Inspection Department, and to Luzon. This time, a total of seven hydrofoil sailboats went to the Luzon Governor-General of the Ming Dynasty. Yin Zhengmao has been officially appointed governor of Luzon.

This was not the first time that the Ming Dynasty appointed a governor of Luzon. In the third year of Yongle, Xu Chailao took the seal of the Ming Dynasty and became the governor of Luzon, taking charge of military, political, financial and cultural powers.

In Yu Dayou's coastal defense plan, Luzon Manila will also set up an inspection department to be responsible for anti-smuggling.

The reason why Chen Lin wanted to go to Luzon was, firstly, to continue testing the hydrofoil sailboat, and secondly, to confirm whether the red-haired sailboat would arrive as scheduled this year.

The Ming Dynasty needed silver, and a massive inflow of silver was needed to activate the Ming Dynasty's commodity economy, increase the circulation of Ming Dynasty commodities, and complete the national tax reform. However, the Ming Dynasty stretched out a paw and brought the Spanish Viceroyalty of Luzon back under the Ming Dynasty.

And Spain needs the massive commodities provided by Ming Dynasty to alleviate the intensifying domestic contradictions of soaring prices.

War or peace, that is the question.

There is still debate about whether the concept of 'Part B' in the "Baojian of Arithmetic Science" is a derivative. Party B is indeed equal to the first derivative of A times A. From this point of view, we can indeed find out in Wang Wensu's The shadow of "derivative" is found in the method, but it is just a shadow. The solution of one-dimensional higher-order equations in "Arithmetic Treasure Book" is still a numerical solution method in which difference approximates differential. I am still a little embarrassed and regretful when I write this. Please give me a monthly ticket, wow! ! ! ! !

(End of chapter)