Dai Yan suddenly found that he couldn't convince others, and he didn't know how to persuade himself, because what he took for granted others couldn't understand at all.

In desperation, he had to say: "Since you can't understand, then let's do it, I'll wait to measure one of the fields first, and I'll still make up for it according to the method of Fangcai, what do you think?" ”

For this, everyone present had no objection. Pen? Interesting? Pavilion wWw. ｂiquge。 So he extended one of the triangular fields step by step to make it a parallelogram, and concluded that the area size of this triangular field is still the calculation method of multiplying the positive and subordinate fields, and the area size of this field is 9 acres and 72 square steps. Then he calculated the area of the remaining three trapezoids according to the same method, and this time because the first two completed shapes were parallelograms, there were slightly more people who understood, and then easily calculated the area of the remaining three fields. In the end, he came up with a total area of 45 acres and 25 steps for the five fields, which was divided into 135 acres and 15 square steps for the children of Le, and 90 acres and 10 square steps for the children of the Mu family.

Then he asked the Le's disciple who was seeking justice, "Can the field I give you a fair share?" Are you convinced? ”

That Le's child has the unique "axis" character of the Song people, and one is one. He immediately knelt down and said: "The division of the field of the prince is really fair, and the exact size of the land has been measured, and it is divided into five equal parts, and the villain takes the third, and the villain has no complaints. ”

Dai Yan looked at the patriarchs of the Le and Mu families again, and neither of them said anything, and left after saying goodbye to Dai Yan.

In the Fengyi Mansion, Dai Yan warmly received everyone from the Mo family.

However, the Mo family giant didn't pay any attention to the things outside his body, and as soon as Fang sat down, Tian Jiu asked Dai Yan: "Childe, I see that the method of earth surveying and land measurement that you used by the river just now seems to be an extremely clever knowledge, dare to ask Gongzi if he can teach me?" ”

"The giant is too humble, you are a first-class scholar in the whole world, how dare the kid teach Mr. However, if the gentleman wants to know about this knowledge, the boy is willing to answer the question to the gentleman. Dai Yan said briskly.

"Then thank you Childe, I want to ask why the size of the triangle field that Childe said is exactly the same as the size calculation method of Guitian?" Tian Jiu asked directly.

"This question is actually easy to answer, because in the boy's opinion, Gui is actually a triangle, but it is a more special kind of triangle, since the size of the triangle is calculated by half a wide to multiply the positive from, then the calculation method of the Gui shape is also applicable, dare to ask Mr. understand?" Dai Yan asked.

"I just can't understand at this point, Childe said that all triangles can adapt to this rule, so dare to ask Childe how to know? What if you really find one that doesn't fit into this rule? Tian Jiu asked.

How can it not be applicable, this is a formula that all third-grade elementary school students understand, Dai Yan said in his heart. However, he finally found out what the problem was, because there is no geometry at all in this era, and geometry is a systematic discipline at all, and it is meaningless to take a formula alone, so he decided to start from scratch.

So he said, "To answer this question, let's start at the beginning." Mr. first imagines a plane, which has no thickness, and there are dots and lines on the plane. The relationship between lines is intersecting and parallel. Dai Yan began to talk about the giant from the initial geometry.

Then he began to explain the basic axioms and axioms of geometry, and when Juzi asked what was the difference between the axioms and the axioms, Dai Yan replied: "The hypothesis is the initial proposition I set; For example, this one: any straight line can be extended indefinitely, this is the most basic proposition. Axioms, on the other hand, are propositions and principles that have been repeatedly tested by practice to be true and do not need to be proved by other judgments; For example, this one: the line between two points is the shortest. Sir, imagine that if you have a dog next to you, and you have a piece of meat in your hand, and you throw the meat in one direction, then the dog must rush over and eat the meat, and it will definitely not spare a few laps before passing over, right? Even dogs know this truth, let alone people? ”

Dai Yan compared the axiom of line segments to a truth that dogs can know, and for a while, everyone in the hall burst into laughter.

Then Dai Yan began to talk about the theorem again, which is actually the core of geometry. When he talked about the famous donkey bridge theorem, although there were many top scholars in the audience, there were indeed people who could not understand why the two bottom angles of the Gui shape (isosceles triangle) must be equal. This made the giant furious and scolded these guys for being stupid, because in his opinion, it was so simple to prove that the young boy had pointed it out step by step, but they still couldn't understand it, which was that the brain was not open.

Then Dai Yan saw the cruel side of the Mo family. Those who couldn't pass the "Donkey Bridge" were all punished by the giant to face the wall, and the giant said bluntly: When can you understand when you can rest. And those who were physically punished all did not say a word and immediately obeyed.

"Giant, you're too strict, aren't you?" Dai Yan asked directly.

Tian Jiu instructed his entourage to take out a roll of bamboo slips and handed it to Dai Yan. Dai Yan took a look, but it was a famous article in the Mo family: big and small. Later, Tian Jiu instructed his disciple to hand Dai Yan a bamboo book, but it was the ink scripture of the Mo family.

"The big and the small here are exactly what is done below, and what is done below is for the sake of argument. The Book of Ink is written by my predecessors after Mozi, and the meaning of it is mostly debated with other families, but also seeks the truth of the world. However, I learned this method of earth surveying from Childe, and found that the essence of it is actually the logical proof of what Childe said. The logical proof is so simple and clear, but it is the truth of the world, which makes people indisputable. Therefore, there is a logical proof of the son, my size is taken, and the ink scripture of my Mo family can be discarded. Tian Jiu said with a sad expression.

"Giants, never." Dai Yan hurriedly stopped. Just kidding, the big and small and even the ink scripture are all treasures of Chinese civilization. In Chinese civilization, the knowledge of logic in addition to the Mo family is only available to famous masters, not to mention that he still has something to ask the Mo family, where can he dare to let the giant abandon his knowledge?

As you can see, although this logical proof is simple and straightforward, it also needs to be supported by words. As the giant said, the knowledge that the kid said before I call it geometry, and logic is the basis of geometry, at present, these studies are just a little idea in the kid's heart, where can it compare to the wisdom of the predecessors of the Mo family for many years? Dai Yan said modestly.

"Childe is too modest." Tian Jiu said bluntly. Then he asked: "Childe's knowledge is so broad and profound, I don't know if Childe is self-taught or learned from others?" ”

Where does this knowledge come from? Dai Yan didn't know what to say. After he came to the Warring States Period, he found that the people of this era were still far more simple than those of later generations, and people did not seem to be like the China of later generations, and everyone needed to wear masks to survive.

"If Childe doesn't want to say it, forget it. However, Childe's knowledge is so broad, although I have not been able to fully see through this knowledge, but in my mind, starting from the logical proof of this knowledge, if it can be extended to various studies, then one day the world will become transparent because of this knowledge, everything in the world can be explained, and Childe, as the starting point of this knowledge, will also be famous in the world from now on, or can be passed on forever, is Childe not moved? Tian Jiu asked.

Forever? As for the starting point of logic, Dai Yan still knows. He knew that logic originated with Thales, who was later known as the "father of science and philosophy" in Europe. It was from this logic that the West took this logic as its starting point, and finally built the entire edifice of science through the unremitting efforts of generations. But can you be like that? Dai Yan still knows himself very well, he is just an otaku who has been poor for many years, where can he become a person like Thales in the West and Kong Mo in the East?

So he said: "Sir's words are right, logic can certainly be extended to all kinds of learning, but because this knowledge is too basic, the subsequent addition of this knowledge must be cautious, you must know that any carelessness may cause the collapse of the entire knowledge edifice, so it will inevitably take a lot of energy, and the boy thinks that he may not have so much energy to spend on it." ”

Tian Jiu said "It's a pity" in his mouth. Then he asked, "I don't know what Gongzi thinks of my Mohist learning?" ”

Mohism? To be honest, if it was the former otaku, of course Dai Yan would like the Mo family very much. Because the Mo family is a school that really speaks for the people at the bottom. For example, the Mohists advocated economizing, believing that everything that must be rich in the people is useful, otherwise it is useless or harmful. All its value is determined by this. In fact, this kind of study is very similar to the doctrine of later generations that represents the advanced productive forces of human society. But who is Dai Yan today? He is the lord of Fengyi, if he really does what the Mo family says, such as the Mo family's non-music, it is not allowed to listen to a song and a song, and he must personally participate in labor, which is obviously against the tradition of the nobility at this time.

So Dai Yan had to be cautious and said: "The learning of the Mohist family is a great knowledge, and Mozi is worthy of being my Chinese sage." He gently avoided his views on Mohist learning.

Tian Jiu smiled at this and said nothing. Of course, he understood what Dai Yan meant, since this son did not answer his opinion on the Mo family positively, he must have a lot of opinions about the Mo family. However, isn't this exactly what the nobles thought of the Mo family at this time? Since the rise of the Mo family as the three major scholars of Confucianism, Mo and Yang in the world, the Mo family has always been despised as the study of villains, but so what? In his view, as a giant, the truth does not need to care about the opinions of others, and one day everyone in the world will recognize the knowledge of the Mo family.