I'm really not doing business

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

"Since the fate is the same, the accumulation cannot be different." Zhu Zaiyu took out a sentence and said with a serious face: "It is very difficult to understand the meaning of this sentence."

This sentence means that if two solids of equal height have the same horizontal cross-sectional area at any height, then the two solids have the same volume.

Zhu Zaiyu took out two cubes, the first one is a regular cube and the other is a ball. The side length of this regular cube is the diameter of the ball. He handed the two small balls to Zhang Hong for inspection by His Majesty before he spoke. : "It started with a mistake."

"In the Nine Chapters of Arithmetic, it is said that a square inch of gold weighs 16 taels, and a golden ball weighs nine taels in diameter. It has never been tested here. That is to say, a metal ball with a side length of one inch weighs 16 taels, and a sphere with a diameter of one inch, It's nine taels."

"Then we got a sphere formula, which is V=9/16d."

"This formula has been used since the Zhou Dynasty. "Zhou Guan · Kao Gong Ji": "Zhou's family is the measure. If it is changed to fry gold and tin, it will not be consumed. If it is not consumed, then it will be used. If it is the right, it will be approved. If it is approved, it will be measured." .”

After Zhu Yijun heard about it, he asked suspiciously: "How much error is there in the sphere formula calculated by the actual measurement method?"

Zhang Juzheng took the abacus and typed it cracklingly, and answered: "9/16-π/6≈0.038901, obviously, the difference is not very big, but arithmetic is like this, if it is wrong, it is wrong."

Zhu Zaiyu continued: "Using the ratio of nine to sixteen, it is even close to reality, but the pill still hurts the ears. According to the ratio of 9/16, when calculating the volume of the ball and the circumscribed cube, the volume of the ball is more realistic. A little more, how much more? About 0.038 times more."

"We mentioned it before when we cut the circle. If you cut it thinner, you will lose less. If you cut it again and again until it cannot be cut, it will fit into the circle without losing anything."

"That is to say, points form lines, and lines form surfaces. This is also the basic principle obtained from the area formula."

"We know that the area of ​​a circle is equal to π/4 of the area of ​​the circumscribed square. 1300 years ago, Liu Hui wondered if he could find a cube whose cross section would be a circle and the circumscribed area no matter where the cube was cut. What about cutting squares?"

"Liu Hui designed such a cube, named Mou He Fang Gai, which is the same as Mou He Fang Gai. The lid is square, which means that the cross section of each face of the cube is a square. The shape of the lid umbrella is two squares. The umbrella, snapped together, is exactly tangent to the ball."

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

"At this time, just ask for the volume of the cube and multiply it by π/4 to get the volume of the sphere."

"Unfortunately, Liu Hui has never been able to find out the volume of this cube. He said: "If you don't care about the shape, you are afraid of being wrong. Dare not to question, so that those who can speak can hope for the wisdom of future generations."

Zhu Yijun got the Mouhe square cover, which is a teaching aid made by Zhu Zaiyu. Thanks to the skillful hands of the craftsmen of the Ming Dynasty, the Mouhe square cover was cut out from the intersection of two cylinders.

Zhu Zaiyu then continued: "More than 1000 years ago, Zu Chongzhi's son Zu Bin solved this problem."

"It cuts the Mouhe square lid into eight small Mouhe square lids, and then cuts them apart. Using the Pythagorean theorem to calculate, the small Mouhe square lid is reduced by 1/8 of the volume of the sphere, and converted into the volume of a square cone to obtain the volume of the square cone. , it can be obtained that the volume of the small Mouhe square lid is 2r/3, the volume of the large Mouhe square lid is 16r/3, and the volume of the ball is equal to 4πr/3, which solves this problem.”

"For two solids of equal height, if the horizontal cross-sectional area at any height is equal, then the volumes of the two solids are equal. Zu Yi used this method to solve the formula for the volume of a cone, which is very difficult for Your Majesty to understand."

Zhu Yijun said with a smile: "Since the power and power are the same, the accumulation cannot be different. It is not difficult to understand."

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

"This is a silver coin from Taixi. It is a cylinder with the same radius as the bottom of the silver coin." Zhu Yijun stacked up the silver coins casually, and said with a smile, "They have the same volume. To find the volume of a 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 stacked silver coins and cylinders. It can only be said that Mathematics never seems to have troubled His Majesty. His Majesty can always understand these contents accurately. .

What is Zhu Zaiyu talking about?It's about integrals, infinite sums.

Differentiation is an infinite cut, integration is an infinite sum, and the reciprocal operation of differentiation and integration is calculus.

In the field of mathematics, Daming is fully qualified to conduct archaeological scientific research. If he can understand the mathematical principles of more than 1000 years ago, Daming's mathematics is already at the top of the world.

"Uncle Huang, is that so?" Zhu Yijun said with a smile.

Zhu Zaiyu bowed his head and said, "That's right, Your Majesty is wise."

"Is it just like this? Can't we go further?" Zhu Yijun continued.

further?Zhu Zaiyu fell into some confusion, how could he go any further?He lacked a mathematical tool to go any further.

"Just take your time." Zhu Yijun stood up, and said with a smile: "Uncle Huang is well-informed, and he will be rewarded a lot!"

Archaeological scientific research is not unacceptable. The concept of infinite summation can solve many practical problems, such as the problem of measuring the area of ​​irregular graphics in full swing. This kind of thinking can be used.

Cut an irregular figure into a small rectangle with the width of the step, build a small rectangle on the left side of the step, and build a small rectangle on the right side of the step, and divide the sum of the areas of the left and right rectangles by Second, to obtain the area of ​​irregular fields, this method is used with great proficiency in actual clearing.

"Your Majesty, Mr. Cheng has a walking cart to offer." Zhu Zaiyu actually doesn't value the reward very much. He has never paid much attention to these external things, otherwise he would not be able to live in the earthen house outside the palace. More than ten years.

Zhu Zaiyu cared more, his ambition can be achieved, and he is achieving it step by step. His Majesty's support for his scientific research work is only three words, no upper limit, and what he wants.

"Measuring a scooter?" Zhu Yijun originally thought that today's arithmetic was over, but he didn't expect that there were still big goods waiting for him, so he said with a smile: "Submit it quickly."

Cheng Dawei pushed up a measuring scooter and handed a book to Zhang Hong.

This book contains detailed records about the measurement of the step car, complete parts drawings, general assembly drawings, design instructions, and modification instructions. This is the result of accurate records and degree bypasses. Going forward, all parts of Daming can use the design in this book to manufacture a large number of measuring vehicles to measure the number of acres of Daming fields.

This thing is said to be complicated and it looks complicated. It is composed of wooden coat, cross, bamboo ruler, iron center, drill foot and ring, etc., but it is actually a tape measure used by later generations.

Cheng Dawei introduced his measuring walking cart and said: "The ancients measured the width and length of the field, and they all relied on the rope to pull the amount. It required a lot of manpower, and the error was huge, so it was not accurate. The ruler body was shortened by turning. Put it on the slender ruler, write inch by inch, each inch is [-] centimeters; It is oily, the characters are not easy to fall off, and it is easy to clean.”

Five feet is a step, a step is 240 mu, and a hundred mu is an hectare.

"Good thing, good thing." Zhu Yijun looked at the tape measure in front of him, nodded and said, "Sir, how about sending it to Nanya Qingzhang after it is printed?"

"I obey the order." Zhang Juzheng bowed his head and said.

The application of the tape measure will greatly speed up the clearing of 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 200 years.

In the 26th year of Hongwu, a total of 850 million hectares of land was verified across the country, about 5000 million mu of land. Later, this fish scale book and atlas were disordered and inaccurate. After 15 years of Emperor Xiaozong Hongzhi in the Ming Dynasty, the registered land in the country was only 422 million hectares. , reduced by half in one hundred and nine years.

After Emperor Xiaozong, 422 million hectares, a severely distorted number of acres, has always been the standard land book of the Ming Dynasty, and what Zhang Juzheng has to do is to find out how many acres of land in the world are, and to figure out who owns the acres in the world, and who owns the fields. hand, just ask who is taxed.

In the original historical line, in the ninth year of Wanli, Zhang Juzheng cleared all the land in the world except Henan, with a total of 7013976 hectares, and it became the tax collection book later.

Find out who owns the farmland. After Zhang Juzheng's death, it is strange that he is not liquidated.

When Zhu Yijun left the side hall of the Cultural Palace, 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 problems while walking. He had to consider the loopholes in the system of obfuscating names in the examination process, all kinds of appeasement in the process of clearing the head, and the eagerness of the barbarian tribes. Considering whether the Northwest Tribal Party will really come together with Altan Khan... He has to consider a lot. The first emperor handed over the empire and the little emperor to him. Return it to His Majesty.

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

And Zhu Yijun looked at the very 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's question is probably a question that haunts the minds of courtiers, courtiers, the world's powerful and powerful, powerful and wealthy gentry. What exactly is the master planning?"

"After thinking about it, I only got one answer, that is: report to the late emperor and be loyal to His Majesty's duty."

Zhu Yijun said calmly: "Mr. wants to be Zhuge Kongming, but some people don't want him to do it. It's all right. Goblins and snakes come here. At worst, the whole world will be burned."

Zhang Juzheng, who was dealing with the government affairs of the empire in Wenyuan Pavilion, shivered suddenly, and looked in the direction of Wenhua Palace, feeling a palpitation just now.

"The war in the Northeast has resumed, and the clan and party are still in danger in the Northwest." Lu Tiaoyang pasted a blank floating ticket on a memorial.

This is another memorial to the impeachment of Zhang Juzheng. The content of the impeachment is still the old-fashioned Zhang Juzheng, who is so powerful. But Lu Tiaoyang, who participated in the court meeting, is very clear. Falling down, the little emperor is in power, and the situation will only get worse.

Look at Lu Shusheng, Minister of the Ministry of Rites, who was appointed before, the little emperor did not say a word to Lu Shusheng. Today, when Zhang Han said that he would retire, His Majesty immediately agreed. Zhang Juzheng was not trying to deal with it, and Zhang Han might have gone home now.

Zhang Juzheng said playfully: "Wang Chonggu is in charge, so Zhang Siwei can't make any trouble."

"Oh? What Yuanfu means is that Wang Chonggu was responsible for the murder of Zhang Siwei this time?" Lu Tiaoyang considered Zhang Juzheng's words for a while, and immediately felt a little different. Regarding Zhang Siwei being poisoned, who was it? There are different opinions about who should do it, but Gao Gong is the most suspected.

To Lu Tiaoyang's surprise, no one doubted Zhang Juzheng's hands. This is the most terrifying thing about Zhang Juzheng. Zhang Juzheng can win a big victory without any tricks.

"That's what you said, not me." Zhang Juzheng didn't respond positively, but he knew that it was Wang Chonggu who attacked Zhang Siwei.

You Qi has a very wide network of contacts, so wide that he knows who is doing these things. You Qi also probably knows about the chef in Zhang's mansion and fled to Sichuan, but he has no idea where he fled to.

Lu Tiaoyang also sneered and said, "It's true, a dog bites a dog's mouth hair, and it's really unsightly to be bullied by a villain."

"It's not a villain, I think it's Zhang Siwei's behavior that annoyed Wang Sikou, otherwise Wang Sikou would not attack his relatives, but he is his own nephew, isn't he forced to do nothing?" ?” Zhang Juzheng knew exactly what behavior provoked Wang Chonggu to act.

Zhang Siwei bribed his chef and His Majesty's chef, and one of these two chefs was the bait thrown by Zhang Juzheng, and the other was the bait thrown by His Majesty. When Zhang Juzheng found out, he was numb.

It is really an apprentice taught by myself, and the methods are exactly the same.

Zhang Juzheng was on duty at Wenyuan Pavilion, so someone sent an invitation to Wang Chonggu, asking Wang Chonggu to come over to the mansion, and he wanted to have a good talk with Wang Chonggu.

When Wang Chonggu received the invitation, he knew what Zhang Juzheng was looking for him 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. I don’t want frontier quarrels in the northwest, can it be done?”

"Wang Sikou is very clear about how rich the profit of the official wool factory is. Isn't the court forbidden to make money and get rich? Silver is indeed a good thing, but a gentleman loves money in a proper way. Since Wang Sikou and Northwest The northern captives are closely related, and if this matter is done properly, the imperial court will only reward them generously."

The official wool factory is located in Gyeonggi, not in the northwest. This is a dog leash held by the court in the northwest.

Wang Chonggu didn't hesitate, and immediately said: "Since Yuanfu has spoken so thoroughly, I will also speak clearly. If I can do it, there will be no problems for at least two years. After two years, I won't know. A four-dimensional idiot."

Now that Wu Dui is in charge of the Northwest, how can Wang Chonggu guarantee the situation two years from now?He can now guarantee that he still has absolute influence and decision-making power in the northwest, so Wang Chonggu scolded Zhang Siwei for being stupid, and bringing him to the capital was the most stupid move.

This is the first consensus. Daming's current recovery of energy is not enough to support the two-front battle of Daming. The Northeast and Northwest are fighting at the same time. For Daming, the burden is still too great. Wang Chonggu and Zhang Juzheng reached the first consensus.

Zhang Juzheng said with a smile: "Two years later, the Beijing camp will be established. It is best for the northern captives to be honest. No matter what kind of beating, the official wool factory in Ming Dynasty needs wool, right?"

"That's right, no matter what the result is, Ming Dynasty needs wool, and I will only earn more and more." Wang Chonggu could fully understand Zhang Juzhengli's words.

This is the second consensus. Wang Chonggu does not threaten the imperial court with self-respect. Wang Chonggu can keep earning money from buying wool from the northwest.

On the premise of these two consensuses, we can continue to discuss the rest.

"But what about Your Majesty?" Wang Chonggu asked a crucial question, what is the emperor's attitude?This is the key, Zhang Juzheng agreed, but if His Majesty does not agree, it will not last long.

Zhang Ju said with a serious face: "It depends on Wang Sikou. Did Wang Sikou participate in the assassination of the king? If not, His Majesty will dig up the old account, and it will not be troublesome. If Wang Sikou is involved, Then it depends on what His Majesty wants. Your Majesty will always get married and take charge of the government."

"There is a mutual relationship between monarchs and ministers. If Wang Sikou doesn't want to be your Majesty's minister, or Ming's minister, His Majesty will of course punish you, but having said that, Your Majesty will never hurt the Minister of Vitality for no reason. In today's court meeting, Wang Xiyuan has clearly mastered Zhang. John's conclusive evidence, if Zhang Han hadn't shamed his face, would His Majesty let me continue to pursue it?"

The reason why Zhang Han was so embarrassed at the court meeting was not that Zhang Juzheng was overly intimidating, nor was it that the little emperor was cold and ungrateful. He had already given Zhang Han a lot of face. Followed by named after the pursuit.

Faces are given to each other, Wang Chonggu gave face to His Majesty, how could His Majesty hurt his subjects for no reason?
"I was not included in the assassination of the king, but I was included in Zhang Siwei's nine clans, alas." Wang Chonggu leaned back in his chair and said in despair: "It's not me who Zhang Siwei can do these things." Can he do it only if his uncle supports him?"

"Whoever's problem is whose problem, Wang Sikou didn't worry too much." Zhang Juzheng still gave a word of relief.

Zhang Juzheng saw that Wang Chonggu was still extremely worried. After thinking about it, he said: "Your Majesty is actually not complicated. You can see through it at a glance. For Da Ming, if the benefits outweigh the harm, your majesty will reward you; if the harm outweighs the benefits, your majesty will punish you." This is the standard in His Majesty's heart to measure whether a courtier can be retained."

"The reason why His Majesty agreed to Wang Sikou's return to the court is also the same. Wang Sikou blocked the hole built in the Great Wall in the northwest and resettled 19 people. His Majesty has seen all these credits. As for profit, it is indeed a disadvantage. , but Wang Sikou's advantages outweigh the disadvantages, so His Majesty will naturally agree with Wang Sikou's return to the court."

Some things should be clearly stated face to face, so that the villain will not shake his lips and tongue in the middle and separate the monarch and his ministers. Wang Chonggu has indeed done the work of Antu herdsmen in the past two years since he returned to the northwest.

The stone in Wang Chonggu's heart finally fell to the ground. He bowed his head and said, "Xie Yuanfu, point out the maze. The villain is a relative. I, the villain, are most worried."

Zhang Juzheng said with a smile: "Wang Sikou is serious. Your Majesty knows very well that people move according to the situation. At that time, there were wars in the northwest, Japanese infestation in the southeast, and the world was exhausted. The best way to stop losses was to negotiate a peace with Gongshi. As for the matter, Wang Sikou can't help himself, right? Since His Majesty ascended the throne, what Wang Sikou has done has done more good than harm, and that's enough."

The little emperor's understanding of things is the biggest reason why Zhang Juzheng has been relaxed in the past few years. There is no problem in the world that it is difficult to get him.

The only one who can make him difficult is His Majesty. There are only two dark clouds in 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 became more and more ferocious.

Zhang Juzheng and Wang Chonggu conducted in-depth exchanges on the issue of the northwest frontier, and the two sides reached a general consensus on the security of the frontier.

When Wang Chonggu left the Quanchu Guild Hall, he was in a much better mood. The court didn't want a lot, and Wang Chonggu was completely satisfied. As he walked, Wang Chonggu thought of Zhang Siwei, and his mood immediately became very bad.

Zhang Juzheng has a stack of silver coins and a cylinder in his hand. He keeps dropping the silver coins. He is thinking about a problem, whether infinite cutting and infinite sum can be converted into each other. If this problem is solved, Many engineering problems can be easily solved.

Find the instant speed, find the tangent of the curve, find the length of the curve, the area surrounded by the curve, the volume surrounded by the 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, and he wants to grow them himself, lest someone will deceive him; he wants to verify the light by himself when the prism is decomposed, and he even has to try the preparation of sweet potato starch. He also doesn't trust Zhu Zai. Yu, a son of a feudal prince who has no worries about food and clothing, does not have enough motivation to solve practical problems.

Of course, Zhu Zaiyu has repeatedly proved that, as the emperor's uncle, his return to the court is not just about eating and not working. Archaeological arithmetic research is also the result of research.

Zhang Juzheng was wandering in the infinite theory of all things, slowly deduced little by little, and slowly returned to reality, looked at You Qi and asked, "Why are you so panicked?"

"Your Majesty asked Feng Dadang to send the news from the palace. He Xinyin must be tracked down without delay. He must be arrested at every corner of the world. If necessary, he can be searched by Ti Qihai."

Zhang Juzheng asked in surprise: "What did He Xinyin do to make His Majesty so angry?"

You Qi sighed and said: "He Xinyin slandered Mr., His Majesty is furious."

"Slander?" Zhang Juzheng took the note from You Qi's hand, and after reading it for a long time, the expression on his face was really extremely complicated.

He Xinyin slandered Zhang Juzheng, the black-hearted prime minister, and arranged the relationship between Zhang Juzheng and Queen Mother Li.When Zhang Juzheng was young, he was also a handsome young man from all over the world. The matchmaker was able to break the threshold of Zhang Juzheng's family. Coupled with the fact that he has been pampered for so many years, Zhang Juzheng did have the capital of a leading actor.

When Empress Dowager Li reprimanded the little emperor before, she liked to say: If Mr. Zhang knows, how can he get it?
Looking at it from another angle, when the mother reprimands the child, she likes to threaten the father, as if saying: Don't be naughty, or I will beat you!

He Xinyin underestimated the words strict etiquette and strict etiquette. If the emperor walks in four square steps, he will be told by the officials that there is strict etiquette.

You Qi didn't know why and said: "These lowly Confucians, when they arrange people, why do they like to go down the third road so much? If they do what they do, do others have to be like them? A bunch of lowly embryos! They should be sent to Jiejie In the courtyard, dissect the heart, liver, spleen and stomach to see!"

Zhang Juzheng said with a smile: "I can't find any other slander. He Xinyin can't say that I, Zhang Juzheng, have done a good job in the country. Isn't that obvious to all?"

The purpose of the existence of the imperial court is to adjust the main contradictions in society. The main contradictions in the current Ming Dynasty are that the country is poor and the army is not strong, and the people are trapped in mergers. Zhang Juzheng has effectively adjusted the main contradictions, and the country has done a good job. The impeachment mainly focused on Zhang Juzheng's personal morality.

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

"The lowly Confucian who is abusive, will do this trick. You see, you can't refute this kind of bad thing. The word rape is getting darker and darker. Wang Daokun was impeached before and raped women. Wang Daokun That's [-] mouths can't tell." Zhang Juzheng also shook his head, there is a certain reason why lowly Confucians like to go to the lower three roads when they slander people.

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 Jieyuan!
Luo Bingliang, a thousand tax collectors, received a strict order from the capital to bring He Xinyin back to the capital.

After receiving the edict, Luo Bingliang took Tiqi directly, surrounded Nanya Chongzheng Academy, and called out Geng Dingxing and Jiao Hong, the inspectors and censors. As long as Geng Dingxiang didn't tell the truth, Luo Bingliang would set the entire Chongzheng Academy on fire. Well, anyway, Luo Bingliang is called the envoy of King Yama's soul, 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 did such rebellious things, why are he afraid of other things?

Tiqi's yamen, which is half inside and half outside, mainly depends on the closeness to His Majesty. As long as His Majesty orders, Luo Bingliang will resolutely carry out.

"Don't make mistakes, the pain of the five poisons is definitely not something Geng Yushi can bear. If His Majesty is offended, students from Chongzheng Academy will not be allowed to take the imperial examination, and your disciples will also be affected." Luo Bingliang looked at Geng. , said the threatening words in a calm tone.

On the ground in Nanya, it is said that Jiao Hong has the qualifications of the number one scholar. If he can't participate in the imperial examination, then for Geng Dingxiang, he might as well kill him.

Geng Dingxiang and He Xinyin are indeed related, they are both members of the Taizhou School.

Geng Dingzhi shuddered when he heard it, and said directly without ambiguity: "At the home of Cheng Xuebo's younger brother in Xiaogan, Huguang."

In the previous assembly of Chongzheng Academy, Geng Dingzhi showed his weakness, and repeatedly told Lu Guangzu that it is better to pay taxes, but he immediately confessed without hesitation after hearing Tiqi's threat.

Tiqi knew where He Xinyin was going, and within three days, he was directly arrested, sent to Songjiang Mansion by fast boat, thrown on a hydrofoil sailboat, and sent directly to the capital.

　I wrote this chapter twice today. I wanted to explain Zu’s theorem clearly. I wrote more than 4000 words of Zu’s [gèng] theorem, including the area formulas of cones, spheres, and spheres. It was not until the seventeenth century that Cavalieri figured out this problem.But after writing it, I found that it was really obscure.In the end, after repeated consideration, most of them were deleted.So the update is a bit late, ask for a monthly ticket, woo! ! ! ! !
　　
　
(End of this chapter)