"Since fate, power, and potential are the same, accumulation cannot be different." Zhu Zaiyu took out a sentence and said solemnly: "It is very difficult to understand the meaning of this sentence."
This sentence means that if the horizontal cross-sectional areas of two solid bodies of equal height are equal at any height, then the volumes of the two solid bodies are equal.
Zhu Zaiyu took out two cubes. The first one was a regular cube and the other was a ball. The side length of this regular cube was the diameter of the ball. He handed the two small balls to Zhang Hong for His Majesty to check before he spoke. : "It started with a mistake."
"In the Nine Chapters of Arithmetic, it is said: A square inch of gold weighs sixteen taels, and a golden pill with a diameter weighs ninety taels. This is because it has never been tested. That is to say, a metal ball with a side length of one inch weighs sixteen taels, and a metal ball with a diameter of one inch weighs sixteen taels. The sphere is nine taels.”
"Then we got a spherical formula, which is V=9/16d."
"This formula has been used since the Zhou Dynasty. "Zhou Guan Kao Gong Ji": "Xu" is the measure. If it is changed to frying gold and tin, it will not be consumed. If it is not consumed, then use it. After it is used, it will be accurate. After it is accurate, it will be measured. .”
After hearing this, Zhu Yijun asked doubtfully: "How much error is there in the sphere formula calculated using actual measurement methods?"
Zhang Juzheng took the abacus and slapped it down, and answered: "9/16-π/6≈0.038901. Obviously, the difference is not very big, but that is the case in arithmetic. If it is wrong, it is wrong."
Zhu Zaiyu continued: "Based on the ratio of nine to sixteen, it is close to reality, but the pill is still hurtful. When calculating the volume of the ball and the circumscribed cube based on the ratio of 9/16, the volume of the ball is more realistic. More, how much more? About 0.038 times more."
"We have talked about it before when cutting a circle. If you cut it very finely, you will lose very little. If you cut it again and again until it cannot be cut, it will fit into the circle and nothing will be lost."
"That is to say, points constitute lines, and lines constitute surfaces. This is also the basic principle for obtaining the area formula."
"We know that the area of a circle is equal to π/4 of the area of the circumscribed square. 1,300 years ago, Liu Hui wondered whether he could find a cube so that no matter where it was cut, its cross-section would be a circle and circumscribed What about cutting into squares?”
"Liu Hui designed a cube like this. It's called Mou He Square Cover. Mou Tong is the same as the cover, square. That is to say, the cross section of each face of this cube is a square. Covering an umbrella, its shape is two squares. The umbrellas, clasped together, are exactly tangent to the ball.”
"Liu Hui intersected two cylinders with the same base radius, and then cut out the common part to obtain this cube."
"At this time, just find the volume of the cube and multiply it by π/4 to get the volume of the ball."
"Unfortunately, Liu Hui has never been able to find the volume of this cube. He said: If you use a crude form to measure the meaning, you are afraid of losing the truth. Those who dare not to doubt and wait until they can speak can look forward to the wisdom of future generations."
Zhu Yijun got the Mouhe square cover, which was a teaching aid made by Zhu Zaiyu. Thanks to the skillful hands of the Ming Dynasty craftsmen, the Mouhe square cover was cut out from the intersection of two cylinders. The volume of this thing is indeed difficult to find because it is irregular.
Zhu Zaiyucai continued: "More than 1,000 years ago, Zu Chongzhi's son Zu Xun solved this problem."
"It cuts the multi-square lid into eight small multi-square lids, and then cuts them. Using the Pythagorean theorem and other calculations, the small multi-square lid is reduced by 1/8 of the volume of the ball, and converted into the volume of a square pyramid, and the volume of the square cone is obtained. , we can get that the volume of the small square lid is 2r/3, the volume of the large square lid is 16r/3, and the volume of the ball is equal to 4πr/3, which solves this problem."
"If two solids of equal height have equal horizontal cross-sectional areas at any height, then the volumes of the two solids will be equal. Zu Xun used this method to solve the formula for the volume of a cone. It is difficult for Your Majesty to understand this."
Zhu Yijun said with a smile: "Since the fate, power and potential are the same, they cannot be different. It is not difficult to understand."
The little emperor thought for a moment, took out a pencil, drew a few words, and asked Zhang Hong to go down and prepare. After a while, Zhang Hong brought over a cylinder and a pile of silver coins.
"This is a silver coin from Taixi. This is a cylinder with the same radius as the base of the silver coin." Zhu Yijun stacked the silver coins randomly and said with a smile: "They have the same volume. To find the volume of the cylinder is to find the sum of the volumes of the silver coins."
Zhang Juzheng and Zhu Zaiyu glanced at each other, and then looked at the silver coins and cylinders stacked together. They could only say that mathematics has never been a problem for His Majesty. His Majesty can always understand these contents accurately. .
What is Zhu Zaiyu talking about? It's about integrals and infinite sums.
Differentiation is infinite cutting, integral is infinite summation, and the reciprocal operation of differential and integral is calculus.
In the field of mathematics, Ming Dynasty is fully qualified to conduct archaeological scientific research. If it can understand the mathematical principles of more than a thousand years ago, Ming Dynasty's arithmetic is completely at the top of the world.
"Uncle Emperor, is that true?" Zhu Yijun said with a smile.
Zhu Zaiyu bowed his head and said: "That's it, your Majesty is wise."
"Is this all? Can't we go further?" Zhu Yijun continued.
Going further? Zhu Zaiyu fell into some confusion, how can he go further? He lacked a mathematical tool to go further.
"Just take your time." Zhu Yijun stood up and said with a smile: "Uncle, if you study well, you will be rewarded!"
Archaeological scientific research is not unacceptable. The concept of infinite summation can solve many practical problems, such as the raging Qing Dynasty and the problem of measuring the area of irregular shapes. This idea can be used.
Cut an irregular figure into a small rectangle with the width of the step. Create a small rectangle on the left side of the step and a small rectangle on the right side of the step. The sum of the areas of the rectangles on the left and right sides of the step is divided by Second, get the area of irregular fields. This method is used very well in actual practice.
"Your Majesty, Mr. Cheng has a measuring cart to offer." Zhu Zaiyu actually didn't value rewards very much. He never cared much about these external things, otherwise he wouldn't be able to live in the earthen house outside the palace. More than ten years.
Zhu Zaiyu is more concerned that his ambition can be achieved, and is being achieved step by step. His Majesty's support for his scientific research work can only be given in three words, with no upper limit, and he will give him whatever he wants.
"Measuring scooter?" Zhu Yijun originally thought that today's calculations were over, but he didn't expect that there was still a big product waiting for him. He said with a smile: "Hurry up and bring it up."
Cheng Dawei pushed up a measuring scooter and handed a book to Zhang Hong.
This book contains detailed records about the measuring stepper, complete parts drawings, assembly drawings, design instructions and modification instructions. This is the result of accurate records and degree bypass. In other words, you only need to send this book In the future, various regions in the Ming Dynasty can use the designs in this book to mass-produce measuring carts to measure the number of acres of land in the Ming Dynasty.
This thing looks complicated indeed. It consists of a wooden coat, a cross, a bamboo ruler, an iron rotating center, a drill foot and a ring, but it is actually a tape measure used by later generations.
Cheng Dawei introduced his measuring cart and said: "In the ancient times, the fields were wider and longer, and they were all measured by ropes and rulers. This required a lot of manpower, and the errors were huge, so it was not accurate. The ruler body was retracted through rotation. Put it on the ruler and write inch by inch. Each inch is two centimeters; five inches is one cent; five feet is one step. Increase in order until it reaches more than thirty steps or less than forty steps. Use clear oil on the bamboo strips. With oil, the words won’t fall off easily and it’s easy to clean.”
Five feet is a step, two hundred and forty steps is an acre, and a hundred acres is an hectare.
"Good thing, good thing." Zhu Yijun looked at the tape measure in front of him, nodded and said: "Sir, after engraving, can you send it to Nanya Qingzhang for use?"
"I obey the decree." Zhang Juzheng bowed his head and said.
The application of the tape measure will greatly speed up the Qing Dynasty during the Ming Dynasty, clarify the specific number of acres in the world, and make a clear calculation of the fish scale book that has not been touched for nearly two hundred years.
In the twenty-sixth year of Hongwu's reign, a total of 8.5 million hectares of land, approximately 850 million acres, were discovered across the country. Later, the fish scale album and the atlas were disordered and inaccurate. Fifteen years after Emperor Xiaozong of the Ming Dynasty, the entire country was registered There are only 4.22 million hectares of land, which has been reduced by half in 109 years.
After Xiaozong, the seriously distorted number of acres of 4.22 million hectares has always been the standard land register of the Ming Dynasty. What Zhang Juzheng has to do is to find out how many acres of land there are in the world, and to figure out who owns the land and who owns the land. In hand, ask who collects taxes.
In the original historical line, Zhang Juzheng cleared all the land in the world except Henan in the ninth year of Wanli, totaling 7,013,976 hectares, and it became the later tax collection book. This was also the confidence that Emperor Wanli could do whatever he wanted.
It would be strange if Zhang Juzheng was not liquidated after his death.
When Zhu Yijun left the side hall of the Cultural Hall, he whispered to Zhang Juzheng beside him: "Sir, please protect yourself."
Zhang Juzheng bowed his head again and walked towards Wenyuan Pavilion. Zhang Juzheng was thinking about the problem as he walked. He had to consider the loopholes of the name-blinding system in the imperial examination, the various appeasements in the process of clearing the abbot, the imminent moves of the barbarian tribes, and the Thinking about whether the Northwest Nationality Party and Anda Khan will really come together... He has many, many things to consider. The late emperor handed over the empire and the young emperor into his hands. On the day when he returned to power, he wanted to bring a prosperous Ming Dynasty into his hands. Return it to His Majesty.
But he didn't notice that the little emperor was looking at him.
Zhu Yijun looked at the different black glazed tiles of Wenyuan Pavilion and watched Zhang Juzheng walk into Wenyuan Pavilion. The little emperor tilted his head and said to Zhang Hong: "Zhang Daban, what do you think Mr. is planning?"
Zhang Hong shook his head and said: "Your Majesty, this question is probably also a question that lingers in the minds of courtiers, courtiers, powerful people, and powerful gentry. What do you want, sir?"
"After thinking about it, I only got one answer, and that is: to repay the late emperor and be loyal to His Majesty's duty."
Zhu Yijun said calmly: "Sir, he wants to do Zhuge Kongming, but some people don't want him to do it. It's okay. Monsters and monsters can come, but at worst, the world will be burned to the ground."
Zhang Juzheng, who was handling imperial government affairs in Wenyuan Pavilion, trembled violently and looked in the direction of Wenhua Hall, feeling that he had just felt a palpitation in his heart.
"The war in the Northeast has resumed, and ethnic groups are still in danger in the Northwest." Lu Tiaoyang affixed a memorial to a blank stamp.
This is another memorial to impeach Zhang Juzheng. The content of the impeachment is still the old tune about Zhang Juzheng's power. However, Lu Tiaoyang, who participated in the court meeting, knew very well that these people had no idea at all and really wanted to impeach Zhang Juzheng. If it falls and the little emperor comes to power, the situation will only get worse.
Look at Lu Shusheng, the Minister of Rites, who was appointed to the official position. The little emperor did not say a word to Lu Shusheng. Today, as soon as Zhang Han mentioned that he was appointed to the official position, His Majesty immediately agreed. If Zhang Juzheng was not trying to manipulate him, I am afraid that Zhang Han would have gone home by now.
Zhang Juzheng said playfully: "If Wang Chonggu is in charge, Zhang Siwei can't cause any trouble."
"Oh? What Yuan Fu means is that this time Zhang Siwei was killed, it was Wang Chonggu who did it?" Lu Tiaoyang thought about Zhang Juzheng's words for a while, and immediately found something different. Regarding who Zhang Siwei was poisoned, who was it? There are different opinions on who committed the crime, and Gao Gong is the most suspected.
What surprised Lu Tiaoyang was that no one suspected Zhang Juzheng's hand. This was the most terrifying thing about Zhang Juzheng. Zhang Juzheng could win a complete victory without any conspiracy.
"This is what you said, not me." Zhang Juzheng did not respond directly, but he knew that it was Wang Chonggu who attacked Zhang Siwei.
You Qi's connections are so wide that he knows who did these things. You Qi also roughly knows about the chef in Zhang's house who fled to Sichuan, but he has no idea where he fled to.
When Lu Tiaoyang heard this, he also sneered and said, "It's true, it's really unsightly to see a dog biting a dog, and a villain quarreling with each other."
"He's not a villain, I think it was some of Zhang Siwei's actions that angered Wang Sikou. Otherwise, Wang Sikou wouldn't have attacked his relatives. He was his nephew. Wasn't he forced to do anything? ?" Zhang Juzheng knew what exactly provoked Wang Chonggu to take action.
Zhang Siwei bribed his cook and his majesty's cook. One of these two cooks was the bait thrown by Zhang Juzheng, and the other was the bait thrown by his majesty. When Zhang Juzheng found out, everyone went numb.
The disciples who are really taught by themselves use exactly the same methods.
Zhang Juzheng was on duty at Wenyuan Pavilion and sent an invitation to Wang Chonggu, asking Wang Chonggu to come to the palace and have a good talk with him.
When Wang Chonggu received the invitation, he knew what Zhang Juzheng was looking for: the Northeast War.
When Zhang Juzheng returned to the Quanchu Guild Hall, Wang Chonggu had already arrived at the Quanchu Guild Hall to wait. After Zhang Juzheng and Wang Chonggu exchanged greetings, Zhang Juzheng stopped going around and talked about business: "There is a big battle in the Northeast. I Is it possible to avoid border provocations in the northwest?"
"Wang Sikou knows how much profit the official wool factory can make. It's not that the imperial court prohibits making money and getting rich. Money is indeed a good thing, but a gentleman loves money and gets it in the right way. Since Wang Sikou and Northwest We have close relations with the northern captives, and if this matter is done properly, the imperial court will only be kind and generous."
The official wool factory is located in Gyeonggi, not the northwest. This is a dog chain held by the imperial court in the northwest. If the dog is disobedient, it can be tightened to let the northern captives know who is the master and who is the servant.
Wang Chonggu did not hesitate and said immediately: "Since Yuan Fu has spoken so thoroughly, I will also speak more clearly. If I can do it, there will be no problems for at least two years. After two years, I don't know. Zhang A four-dimensional idiot."
Now that Wu Dui is in charge of the northwest, how can Wang Chonggu guarantee what the situation will be like in two years? He can now guarantee that he still has absolute influence and decision-making power in the northwest. That's why Wang Chonggu called Zhang Siwei stupid and brought him to the capital. It was the stupidest move.
This is the first consensus. The restored vitality of Ming Dynasty is not enough to support Ming Dynasty's two-front war. The northeast and northwest are fighting at the same time. For Ming Dynasty, the burden is too great. Wang Chonggu and Zhang Juzheng reached the first consensus.
Zhang Juzheng said with a smile: "In two years, the Beijing Camp will be completed. It is best for the Beibei to be honest. No matter what the situation is, the official wool factory of the Ming Dynasty will need wool, right?"
"Yes, what's the result? The Ming Dynasty needs wool, and I will only make more and more." Wang Chonggu could fully understand what Zhang Juzhengli said.
This is the second consensus. Wang Chonggu does not threaten the imperial court by threatening his own dignity. Wang Chonggu can continue to make money from buying wool from the northwest.
On the premise of these two consensuses, we can continue to talk about the rest.
"But where is your Majesty?" Wang Chonggu asked a crucial question, what is the emperor's attitude? This is the key. Zhang Juzheng agreed. If His Majesty does not agree, it will not last long.
Zhang Juzheng said solemnly: "It depends on Wang Sikou. In the assassination of the king and the driving case, was Wang Sikou involved? If not, His Majesty will raise old scores and there will be no fuss. If Wang Sikou was involved, Then it depends on what Your Majesty wants. Your Majesty will always get married and be in charge."
"Between kings and ministers, there is mutuality. If Wang Sikou does not want to be your majesty's minister, the Ming Dynasty's minister, your majesty will certainly punish him, but having said that, your majesty will never hurt the minister of vitality for no reason. Today's court discussion, Wang Xiyuan has clearly mastered Zhang Zhang Han’s conclusive evidence, if Zhang Han hadn’t been so shameless, would Your Majesty have allowed me to continue the pursuit?”
The reason why Zhang Han was so embarrassed at the court meeting was not because Zhang Juzheng was too intimidating, nor was it because the young emperor was cold and ungrateful. He had already given Zhang Han a lot of face, and Zhang Han repeatedly disagreed with the method of anonymizing his name. They were pursued by name from behind.
Faces are given to each other. Wang Chonggu gave face to His Majesty. How could Your Majesty hurt his ministers for no reason?
"I was not involved in the assassination of the king, but I was among the nine clans of Zhang Siwei. Alas." Wang Chonggu leaned on the back of his chair and said in despair: "Zhang Siwei can do these things, not me." Can he do it only if his uncle supports him?"
"Whoever's problem is his problem, Wang Sikou is worrying too much." Zhang Juzheng said with relief.
Zhang Juzheng saw that Wang Chonggu was still extremely worried. After thinking about it, he finally said: "Your Majesty is actually not a complicated person. He can see through it at a glance. For the Ming Dynasty, if the benefits outweigh the disadvantages, Your Majesty will reward you; if the disadvantages outweigh the benefits, Your Majesty will punish you." . This is the standard by which Your Majesty judges whether a minister can be retained."
"The reason why His Majesty agreed to Wang Sikou's return to the imperial court was for the same reason. Wang Sikou blocked the holes in the Great Wall in the northwest and resettled 190,000 people. His Majesty saw these achievements. As for making profits, it is indeed There are disadvantages, but Wang Sikou’s advantages outweigh the disadvantages, so His Majesty will naturally agree to Wang Sikou’s return to the court.”
Some things should be said clearly in person, so as not to cause the villain to talk and talk at odds between the emperor and his ministers. In the two years since Wang Chonggu returned to the northwest, he has indeed made peace for the herdsmen. His majesty will reward ministers who do more good than harm.
The stone in Wang Chonggu's heart finally fell to the ground. He bowed his head and said, "Xie Yuanfu gave me some advice. The villain is always worried. I, the villain, am the most worried."
Zhang Juzheng said with a smile: "Wang Sikou is serious. Your Majesty knows clearly that people are driven by the situation. At that time, there was war in the northwest, Japanese invasion in the southeast, and the world was exhausted. Negotiating peace and tribute was the best way to stop losses. Some Wang Sikou has no control over the matter, right? Since His Majesty came to the throne, Wang Sikou's actions have done more good than harm, and that's enough."
The little emperor's clear sense of reason is the biggest reason why Zhang Juzheng has been relaxed in the past few years. There is no problem in the world that can't be difficult for him.
The only one who can make things difficult for him is His Majesty. There are only two dark clouds hanging over Zhang Juzheng's heart: the little emperor is not doing his job properly and the little emperor is too good at studying.
The faces of these two dark clouds are getting more and more ferocious.
Zhang Juzheng and Wang Chonggu had an in-depth exchange of views on border issues in the northwest, and the two sides reached a general consensus on border security issues.
When Wang Chonggu left the Quanchu Guild Hall, he was in a much better mood. The court did not want much, and Wang Chonggu was completely satisfied. As he walked, Wang Chonggu thought of Zhang Siwei, and his mood immediately became very bad.
Zhang Juzheng had a pile of silver coins and a cylinder in his hand. He kept dropping the silver coins. He was thinking about a problem, whether infinite cutting and infinite summation can be converted into each other. If this problem is solved, Many engineering problems can be solved easily.
Find the instant speed, find the tangent of the curve, find the length of the curve, the area enclosed by the curve, the volume enclosed by the curved surface, and the center of gravity of the object.
These are very clear practical issues with universal practical significance.
Zhang Juzheng doesn't trust anyone. Baoqisi grows sweet potatoes. He wants to grow them himself for fear of being deceived. The prism decomposes light and he wants to verify it himself. He even wants to try the preparation of sweet potato starch. He also doesn't trust Zhu Zai. Yu, a feudal prince who had no worries about food and clothing, did not have enough motivation to solve real problems.
Of course, Zhu Zaiyu has repeatedly proved that as an imperial uncle, he did not just eat and not work when he returned to the court. Archaeological arithmetic research was also the result of research.
Zhang Juzheng was wandering in the infinite truth of all things, slowly deducing bit by bit, and slowly returned to reality. He looked at You Qi and asked, "Why are you so panicked?"
"Your Majesty asked Feng Daxuan to send news from the palace. He Xinyin must be traced and brought to justice without delay. He must be captured from all corners of the world. If necessary, Tiqi can be arrested and searched in the sea."
Zhang Juzheng asked with some surprise: "What did He Xinyin do to make His Majesty so angry?"
You Qi said with a sigh on his face: "He Xinyin slandered Sir, Your Majesty is furious."
"Slander?" Zhang Juzheng took the note from You Qi and read it for a long time. The expression on his face was really complicated.
He Xinyin slandered Zhang Juzheng, the evil prime minister, and arranged the relationship between Zhang Juzheng and the Queen Mother Li. There were many disputes at the widow's door, and the royal family was no exception. When Zhang Juzheng was young, he was also a handsome young man from all over the country. As a matchmaker, he was able to break through the threshold of Zhang Juzheng's family. In addition, after having been pampered for so many years, Zhang Juzheng did have the capital to be a leading actor.
When Empress Dowager Li reprimanded the young emperor before, she liked to say: If Mr. Zhang knew about it, how could he get away with it?
Looking at it from another angle, when mothers at home reprimand their children, they like to threaten their fathers, as if to say: Don't be naughty, or I will punish you!
He Xinyin underestimated the words "strict etiquette". The emperor would have to be reminded of "strict etiquette" even if he didn't walk in all directions.
You Qi said inexplicably: "Why do these cheap Confucian scholars like to go down three directions so much when arranging people? If they do it, others must be the same as them? A bunch of cheap idiots! They should be sent to Jiegui In the hospital, dissect out the heart, liver, spleen and stomach and take a look!"
Zhang Juzheng said with a smile: "I can't find any other slander. He Xinyin can't say that I, Zhang Juzheng, did not do well in the country, or whether I did well or not, isn't that obvious to all?"
The purpose of the imperial court's existence is to adjust the main contradictions in society. The main contradictions in Ming Dynasty's society are that the country is poor and the soldiers are not strong, and the people are trapped in annexations. Zhang Juzheng effectively adjusted the main contradictions and did a good job in the country. Officials The impeachment mainly focused on Zhang Juzheng's personal moral issues.
For a politician, impeaching his personal morality cannot bring Zhang Juzheng down.
"This is what a lowly and despicable Confucian would do. Look, you can't refute this kind of bad thing. The words "treacherous" are getting darker and darker. Wang Daokun was impeached before for raping a common woman. Wang Daokun That's something ten thousand mouths can't explain." Zhang Juzheng also shook his head. There is a certain reason why cheap Confucians like to go to the lower world when they slander others.
The most critical question in this matter is whether the little emperor believes it or not.
Zhu Yijun has only one attitude towards this matter, that is, if he is caught, he will be sent to Jieguan!
Luo Bingliang, a tax collector from thousands of households, received strict orders from the capital to capture He Xinyin back to the capital.
After receiving the edict, Luo Bingliang directly led Tiqi to surround Nanya Chongzheng Academy and called out the inspectors Geng Dingxiang and Jiao Hong. As long as Geng Dingxiang did not tell the truth, Luo Bingliang would set the entire Chongzheng Academy on fire. Well, anyway, people in Nanya now call Luo Bingliang the soul seducer of King Yama. No matter how bad his reputation is, how bad can it be?
Luo Bingliang didn't care either. His son Luo Sigong beat the emperor every day in the palace. He had done such treasonous things, so what else was he afraid of?
Tiqi, a half-inside and half-outside yamen, mainly depends on the closeness with His Majesty. As long as His Majesty orders, Luo Bingliang will resolutely implement them.
"Don't make any mistakes. The pain of the five poisons is definitely not something Geng Yushi can bear. If you offend His Majesty, students from Chongzheng Academy will not be allowed to take part in the imperial examination, and your disciples will also be affected." Luo Bingliang looked at Geng Dingdi. , said threatening words in a calm tone.
Everyone in Nanya said that Jiao Hong had the qualifications to be the top scholar. If he could not participate in the imperial examination, it would be better for Geng Dingxiang to kill him.
Geng Dingxiang and He Xinyin are indeed related. They are both members of the Taizhou School.
Geng Dingxiang trembled when he heard this, and said directly without hesitation: "At the home of Cheng Xuebo's younger brother, Xiaogan, Huguang."
In the previous meeting at Chongzheng Academy, Geng Dingxiang showed his weakness and repeatedly told Lu Guangzu that it was better to pay taxes. After hearing Tiqi's threat, he immediately confessed without hesitation.
Tiqi knew where He Xinyin was going, and it only took him three days to catch He Xinyin, take him to Songjiang Mansion by speedboat, throw him on a hydrofoil sailboat, and send him directly to the capital.
I wrote this chapter twice today. I wanted to explain Zu Xun's theorem clearly. I wrote more than 4,000 words about the content of Zu Xun's [gèng] theorem, including the area formulas of cones, spheres, and spheres. Zu Xun was more than a thousand words ahead. It was not until the seventeenth century that Cavalieri figured out this problem. But after I finished writing it, I found that it was really obscure and difficult to understand. Finally, after repeated consideration, most of them were deleted. So the update is a bit late, please vote for me, Wow! ! ! ! !
(End of chapter)
