Chapter 149 Since the power and potential are the same, the accumulation cannot be different.


Chapter 149 Since the fate and power potential are the same, the accumulation cannot be different

"The fate and power potential are the same, so the accumulation cannot be different." Zhu Zaiyu took out a sentence and said with a solemn expression: "To understand The meaning of this sentence is very difficult. "

The meaning of this sentence is that if the horizontal cross-sectional areas of two solid bodies of equal height are equal at any height, 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 to His Majesty. After checking, he said: "This started from a mistake."

"Nine chapters of arithmetic say: A square inch of gold weighs sixteen taels, and a golden pill weighs nine taels per inch. Shui was born here, and he has never Experiment. That is to say, a metal ball with a side length of one inch weighs sixteen taels, and a sphere with a diameter of one inch weighs nine taels. "

"Then we get a spherical formula, which is V=9. /16d. "

"This formula has been used since the Zhou Dynasty. "Zhou Guan Kao Gong Ji": "Xu's" is the measurement, if it is fried, it will not consume, and then it will be used. Then calibrate it, and then measure it."

After hearing this, Zhu Yijun asked doubtfully: "What is the error of the sphere formula calculated by actual measurement method?"

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 Zai Chu continued: "Using 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 larger than the actual volume. , 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 if he could find a cube so that no matter where it is cut, its cross-section would be a circle and a circumscribed square? "

"Liu Hui designed such a cube? , the name is Mou He Square Cover, Mou Tong, He Cover, square, that is to say, the cross section of each face of this cube is square, cover umbrella, its shape is two square umbrellas, buckled together, just like the ball Completely tangent."

"Liu Hui intersected two cylinders with the same base radius, and then cut out the common part to obtain this cube."

"At this time, only the requirements were met. Find the volume of the cube and multiply it by π/4 to get the volume of the sphere."

"Unfortunately, Liu Hui was never able to find the volume of the cube. . Dare not to doubt, and wait for 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. , a composite square cover cut out from the intersection of two cylinders. The volume of this thing is indeed difficult to find, as it is irregular.

Zhu Zaiyu continued: "More than 1,000 years ago, Zu Chongzhi's son Zu Xun solved this problem."

"It cut the Mouhe square lid into eight small Mouhe square lids, and then Cut it open, use the Pythagorean theorem and other calculations to subtract 1/8 of the volume of the ball from the small Mouhe square cover, and convert it into the volume of a square cone. After obtaining the volume of the square cone, we can get the volume of the small Mouhe square cover as 2r/3. The volume of the square lid is 16r/3, and the volume of the ball is equal to 4πr/3, which solves this problem. ”

"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. 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 are incompatible. It is not difficult to understand."

The little emperor thought for a moment, took out a pencil, and drew a few times, letting Zhang Hong went down to prepare. After a while, Zhang Hong brought over a cylinder and a pile of silver coins.

"This is a silver coin from Thailand. 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 silver coin. "

Zhang Juzheng and Zhu Zaiyu looked at each other, and then looked at the stacked silver coins and cylinders. They can only say that mathematics has never been difficult. Your Majesty, your 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, 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.

Go 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: "The emperor's research is well done, and he will be rewarded!"

Archaeological scientific research is not unacceptable. The thing is, the concept of infinite sum can solve many practical problems, such as the problem of Qingzhang in full swing 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 steps are left and right. Divide the sum of the rectangular areas by two to get the area of ​​the irregular acres. This method is used very well in actual practice.

"Your Majesty, Mr. Cheng has a measuring cart to offer." Zhu Zaiyu actually didn't attach much importance to rewards. He never cared much about these external things, otherwise he wouldn't be able to live in the land outside the palace. I have lived in this house for 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 large amount of goods waiting for him. He said with a smile: "Hurry up and bring it up."

Cheng Dawei pushed up a measuring cart 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, that is to say, only This book needs to be distributed so that various regions in the Ming Dynasty can use the designs in this book to mass-produce measuring carts and 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 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 and could not be accurate. Passed Rotate to realize the retraction and expansion of the ruler body. On the ruler, write inch by inch, each inch is two centimeters; five inches is one minute; five feet is one step, and the number increases in sequence until it reaches more than thirty steps or less than forty steps. , use clear oil on the bamboo strips, the words will not fall off easily, and it is easy to clean. "

Five feet is a step, two hundred and forty steps is an mu, 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, can you print it and send it to Nanya Qingzhang for use?"

"I obey the order. "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, 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. In the fifteenth year of Hongzhi's reign in the Ming Dynasty, Later, there were only 4.22 million hectares of registered land in the country, which was 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 who owns the acres of land in the world. Whoever has the field in his hand will ask whoever taxes it.

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 is why the Wanli Emperor was able to do whatever he wanted. Confidence.

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. When thinking about the problem, he had to consider the loopholes in the name-blinding system that became legal in the examination, the various appeasements in the process of clearing the father-in-law, the preparations of the barbarian tribes, and whether the Northwest ethnic party would really come to an end with An Da Khan. Together... He has a lot to consider. The late emperor handed over the empire and the young emperor into his hands. On the day when he returns to power, he will return a prosperous Ming Dynasty to His Majesty.

But he didn't notice that the little emperor was looking at him.

While 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. "What?"

Zhang Hong shook his head and said: "Your Majesty's question is probably 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 your Majesty's duty."

Zhu Yijun said calmly: "Sir, I want to be Zhuge Kongming. Some people don’t want him to do it. It’s okay. Monsters and monsters can come. The worst is, they will burn the world to pieces.” Shivering, I looked in the direction of Wenhua Palace, feeling like I had just felt a palpitation in my heart.

"The war in the Northeast has resumed, and there is still a danger of ethnic groups 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, but Lu Tiaoyang, who participated in the court meeting, knew very well that these people had no idea at all. Zhang Juzheng was really impeached and brought down. With the little emperor in 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: "Wang Chonggu is in charge, so Zhang Siwei can't cause any trouble."

"Oh? What Yuan Fu means is that Wang Chonggu was responsible for Zhang Siwei's murder this time. "?" Lu Tiaoyang thought about Zhang Juzheng's words for a while and immediately realized some differences. There were different opinions on who was responsible for Zhang Siwei's poisoning, and Gao Gong was 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 cook in Zhang's house who fled to Sichuan, but he has no idea where he fled to.

Lü Tiaoyang also sneered when he heard this and said: "It's true, a dog bites a dog, and it's really unsightly for villains to fight against each other."

"No, that's not true. You 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? Knowing what exactly provoked Wang Chonggu to take action.

Zhang Siwei bribed his cook and also 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, people All numb.

They are really disciples taught by themselves, and their methods are exactly the same.

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 walking around and talked about business: "Northeast China There is a big war happening, and I don’t want border quarrels to happen in the northwest. Can I do that?” , To make a fortune, money is indeed a good thing, but a gentleman loves money in a wise way. Since Wang Sikou has a close relationship with the Northwest Beibei, if this matter is done well, the court will only be generous and reward it. "

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 spoke 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 Siwei is an idiot.”

Now that Wu Dui is in charge of the northwest, how can Wang Chonggu guarantee the situation 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 current recovery 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 an agreement The first consensus.

Zhang Juzheng said with a smile: "In two years, the Beijing Camp will be established. 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?"< br>
"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 case of assassinating the king and killing the driver, was Wang Sikou involved? If not, your majesty will not let you go over old scores. If Wang Sikou is involved, it depends on your majesty’s intention.” Of course your Majesty will punish your ministers, but having said that, Your Majesty will never hurt the Minister of Vitality without any reason. During today’s court meeting, Wang Xiyuan has clearly obtained conclusive evidence about Zhang Han. If Zhang Han hadn’t been shameless, how would Your Majesty have allowed me to do so? Continue to pursue? "

The reason why Zhang Han was in such a mess at the court meeting was not because Zhang Juzheng was too intimidating, nor was it because the little emperor was cold and unkind. He had already given Zhang Han a lot of face, and Zhang Han repeatedly refused Agreeing to the anonymity method, only then began the pursuit of naming.

Face is given to each other. Wang Chonggu gave face to His Majesty. How could His 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. "Son, it's only because of my uncle's support that he can do it."

"Whose problem is his problem, Wang Sikou is overly worried," Zhang Juzheng said in relief.

Zhang Juzheng saw that Wang Chonggu was still extremely worried. After thinking about it, he said: "Your Majesty is actually not a complicated person. He can see through it at a glance. For the Ming Dynasty, the advantages outweigh the disadvantages, and your Majesty will reward you; the disadvantages outweigh the advantages." , Your Majesty will punish you. This is the standard in Your Majesty’s heart to measure 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 the advantages of Wang Sikou 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 to avoid the villain’s bluster in the middle to drive a wedge between the emperor and his ministers. Wang Chonggu. In the past two years since returning to the northwest, your majesty will reward those ministers who have truly made peace with the herdsmen and whose benefits outweighed the disadvantages.

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 has a long life, and I, the villain, am the most worried."

Zhang Juzheng said with a smile: "Wang Sikou's words are 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 tired. Negotiating peace and tribute was the best way to stop losses. There are some things that Wang Sikou has no control over, right? Since His Majesty came to the throne, Wang Sikou’s actions have done more good than harm. This is enough.” The biggest reason for being relaxed is that 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 question, whether infinite cutting and infinite summing 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 does not trust anyone. Baoqisi grows sweet potatoes. He wants to grow them himself for fear of being deceived by others. The prism decomposes light and he wants to verify it himself. He even wants to try the preparation of sweet potato starch. He also distrusted Zhu Zaiyu, a prince who had no worries about food and clothing and 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 is 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 Somewhat surprised, he asked: "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 was furious."
< br>"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 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. The matchmaker 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 scold 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" by the official even if he didn't walk in all directions.

You Qi said without knowing why: "Why do these cheap Confucians like to go down three directions when arranging people? If they do it, others must be the same as them? A bunch of cheap idiots! He should be sent to the Jiecu Hospital to have his heart, liver, spleen and stomach dissected out and have a look!"

Zhang Juzheng said with a smile: "I can't find any other slander. He Xinyin can't say that I, Zhang Juzheng, am in the country! Whether it’s done well or not, isn’t that obvious to all?”

The purpose of the imperial court is to regulate the main contradiction in society. The main contradiction in Ming Dynasty’s society is that the country is poor and the soldiers are not strong. The people were trapped in the annexation. Zhang Juzheng effectively adjusted the main contradictions and did a good job in governing the country. The officials' impeachment mainly focused on Zhang Juzheng's personal moral issues.

For a political figure, impeaching his personal morality cannot bring down Zhang Juzheng.

“This is what a lowly and despicable Confucian would do. You see, you can’t refute this kind of bad thing. The word “treacherous” gets worse and worse. Wang Daokun was impeached before. Wang Daokun can't explain it with ten thousand mouths. "Zhang Juzheng also shook his head. There is a certain reason why low-class Confucians like to go to the lower-class way when they slander others.

The most critical question in this matter is whether the little emperor believes it or not.

Zhu Yijun has one attitude towards this matter, that is, if he is caught, he will be sent to Jiecuyuan!

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 took Tiqi directly and surrounded Nanya Chongzheng Academy. He called out the inspectors Geng Dingxiang and Jiao Hong. As long as Geng Dingxiang did not tell the truth, Luo Bingliang would bring down the entire Chongzheng Academy. The academy was set on fire. Anyway, people in Nanya now called Luo Bingliang the soul seducer of King Yama. No matter how bad his reputation was, how could it be worse?

Luo Bingliang didn't care either. His son Luo Sigong beat the emperor every day in the palace. He had done such treacherous and unethical things. What else were 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 a mistake. The torture 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 participate in the imperial examination, and your disciples will also be affected. "Luo Bingliang looked at Geng Dingliang and 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 his brother Cheng Xuebo in Xiaogan, Huguang."

In the previous gathering at Chongzheng Academy, Geng Dingxiang showed that In view of his weakness, he repeatedly told Lu Guangzu that it was better to pay taxes. Upon hearing Tiqi's threat, he immediately confessed without hesitation.

Tiqi knew where He Xinyin was going, and it only took him three days to capture 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 this chapter)

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