After Zhuge Liang wrote a reply, he came to the back room and handed over the eldest brother's first volume of family letters to the eldest sister Zhuge Yun and the second sister Zhuge Yu, who had just finished washing the dishes and clothes.

Zhuge Yun is already nineteen years old, if he hadn't been displaced and couldn't settle down, he would be an older leftover girl if he hadn't married at this age.

Zhuge Yu is seventeen years old, and the pressure is not much less.

A few months ago, they also secretly observed Kuai Qi and Pang Shanmin and others who came to visit.

But Kuai Qi is really a straw bag, just a nobleman, who made the Kuai family now the number one Wenchen family in Jingzhou. Zhuge Yun was very dissatisfied with the other party, but he also had a faint consciousness of self-sacrifice in his heart.

As for that Pang Shanmin, his academic character is a little better than Kuai Qi, after all, he is Pang Tong's cousin. But the appearance is more and more clumsy, and it is really unsightly. After all, Zhuge Yu has the eldest sister to protect him, and sometimes he thinks: If the eldest sister sacrifices, will he not have to sacrifice again...... One Kuai family is enough to cover the Zhuge family, right?

Therefore, before dinner just now, I heard the third brother quietly play treasure and say: The eldest brother suddenly made a fortune in Guangling, was treated as a teacher by General Zhendong, and brought countless belongings, and the melancholy Zhuge Yun and Zhuge Yu instantly breathed a sigh of relief.

"Big brother is suddenly so powerful? Then don't we have to send people under the fence and rely on marriage to gain status? The first reaction of the sisters was the same, fantasizing that if the eldest brother's situation could be better than that of the uncle, then they would decisively go to the eldest brother!

Even if you want to marry someone in the future, you have to marry someone who is handsome, and you don't have to sacrifice your character and appearance for money, power, and status.

Now that the second brother finally finished reading the letter and wrote a reply, they came up to read it together.

Zhuge Jin's confident writing also made them feel unfamiliar.

"The eldest brother used to be humble in even writing family letters, but now he has the domineering spirit of Master Meng. The changes are so great, it can be seen that it is really soaring. Zhuge Yun is the closest to Zhuge Jin, and he knows him best, so he can't help but praise.

Zhuge Yu looked at it for a while, and then pushed the second brother: "Ah Liang! If the eldest brother can really protect us, my eldest sister and I will go to the company first, and you will stay in Jingzhou and mediate with the little lady of the Huang family.

Anyway, you men should be regarded as marrying a wife and virtue, and if you are not satisfied with beauty, you will have the opportunity to take a concubine in the future. We only have one chance, and we won't be accompanied. ”

Zhuge Yu had also seen that Huang Yueying, and knew that the second brother could talk to each other quite well - of course, just as an ordinary friend.

The little lady's character and knowledge are not bad, but she is not fair and beautiful enough, and her hair is not black and shiny.

Zhuge Yu felt that compared to what happened to her and her eldest sister, the second brother's situation was acceptable, after all, they had similar interests, and it was not too late to find a beauty in the future.

Zhuge Liang originally wanted to analyze the changes in the eldest brother with the eldest sister and the second sister, but Zhuge Yu was so anxious that he dropped the family letter and turned his head to leave, and went back to the house to figure out the secret scroll given by the eldest brother.

……

Zhuge Liang is only sixteen years old after all, and boys are often not as precocious as girls of his age, so the second sister laughed at his friendship with Huang Yueying, and he couldn't hold his face.

At this time, brushing questions is the best way to divert attention! So he took open the second scroll of his eldest brother and began to study it.

"I want to see what progress my eldest brother has made in the past two years, and I think he can teach me, it can't be that he has found some secluded learning......

Zhuge Liang quickly glanced and found that the first half of the second volume was mainly a table of contents, and the respective contents of the subsequent dozen volumes were outlined and indexed.

The second half is an experience of persuasion, mainly talking about the heart of learning.

Zhuge Liang pouted, what he needed now was a challenge! It's to brush the questions to relieve the embarrassment! I don't want to see the cliché for the time being!

As for the learning method, can the eldest brother's learning method be better than his own? If he had to have this ability, he wouldn't have been crushed by himself back then.

So Zhuge Liang dropped the second volume, skipped it directly, and just jumped to open all the fifth to eighth volumes according to the table of contents.

The table of contents says that these four volumes are all arithmetic! It is something more profound and integrated than "Zhou Ji" and "Nine Chapters".

Zhuge Liang knew very well that when he left his hometown two years ago, his arithmetic was definitely beating his eldest brother.

Let's take a look at how many catties and taels there are in these things that are treated as good things by the eldest brother.

……

"Huh? What the hell is this? ”

Not to mention, as soon as he opened the fifth volume, Zhuge Liang was really shocked by the preemptive sound.

Because he didn't know all the ghost drawings in the volume.

Fortunately, his desire to explore was very steady, he took a deep breath, and looked at it carefully without fear, and sure enough, every symbol was explained before it was called.

"Hah! It turned out that it was just the numbers and symbols of the poisonous country, and the purpose was to omit the words 'ten hundred thousand', and directly represent ten hundred million with the number of digits, which saved a lot of effort...... This also facilitates the use of symbolic formulas directly, which is much less labor-saving than using words to describe the algorithm. ”

Zhuge Liang spent a lot of time on tea, first accepted the Arabic numerals 0 to 9, spent another cup of tea, accepted the "+-×÷/=" sign, and also took a piece of wood, and used a gray pen to contact each other dozens of times to write, and then realized the labor-saving beauty of this thing.

After mastering the numbers and symbols, and then looking at the first few questions listed by the eldest brother that made him adapt, Zhuge Liang quickly regained his confidence.

"Isn't this just a reexpression of the nine chapters of chickens and rabbits in the same cage with body poison numbers and formulas, how can there be X and Y...... Well, it seems that these two runes mean A, B, and C, and in this question, they represent the number of chickens and rabbits......"

"This is a way to express the hook three strands, four strings and five with the body poison formula, and there is nothing new, but this idea of substituting a symbol into the equation is a lot more simplified, and you don't have to think about the meaning every time, as long as you deal with numbers......"

In just two questions, Zhuge Liang summed up the main benefits of using numbers and symbols, and he was faintly lit up a flame of "mathematical abstraction" in his heart.

The traditional "Zhou Ji" and "Nine Chapters" are too application-oriented, and the generalized abstraction of mathematics is certainly not as good as that of later generations. Zhuge Jin just combed it through and restated it, which made the second brother's way of thinking have a new improvement.

The ancients finished learning "Zhou Ji", which was roughly equivalent to the level of the fourth and fifth grades of primary school in later generations. That is, the calculation of the perimeter area of the four operations, fractions, negative numbers, and simple graphs.

After the completion of the "Nine Chapters", it can be roughly improved to the first mathematics of the later generations, including the Pythagorean theorem and various multivariate systems of equations. It's just that there are fewer contents such as circular geometry, open root numbers, and irrational numbers than later generations.

Zhuge Liang only took half an hour to re-understand the mathematics from the later generations to the first year of junior high school, which was very easy.

"Big brother also underestimates my foundation too much! However, he can also understand this, and it seems that he has made a lot of progress in the past two years. Zhuge Liang thought proudly.

He continued to look down with courage and diligence, and the second half of the fifth volume was a thing called the "Circle Cutting Method", as well as the derivation of the principle of the area algorithm for other complex geometric figures.

Zhuge Jin's writing process is very detailed, and the conclusion is given at the end, and it is not a proof process that lacks basic formulas like later textbooks, and directly asks students to memorize.

Such a simple and logical lesson plan, if you are not a gold medal lecturer yourself, it is difficult for others to write it on their own.

"Huh? It's kind of interesting. Why didn't I think that the circle was infinitely widened, and it was countless triangles with the circumference as the total bottom length...... There is also this kind of strange pattern, which can also be used to derive the area algorithm after cutting and conversion, and it is absolutely easy to use when measuring acres in the future, without going step by step in every line. ”

Zhuge Liang's mood finally changed from the surprise at the beginning to a little dignified.

This time, it took him more than an hour to get a preliminary understanding.

After doing all this, when he recovered from his intoxication, he realized that the simple leak on the desk had already been dripped off.

The night at the beginning of the month was dark, and I don't know what time it was, maybe it was the hour? Everything around was silent, and the sisters and third brothers were already asleep.

Zhuge Liang still couldn't stop his excitement and went to get the sixth volume again.

The beginning of this volume is the principle of the opening number, as well as trigonometric functions, as well as the irrational numbers derived from it—of course, Zhuge Jin uses experimental methods to demonstrate, not purely mathematical methods.

I won't go into details, anyway, it is very gradual and very suitable for Zhuge Liang's current knowledge structure.

Trigonometric functions and root numbers are still inspired step by step by the extension of the integer solution to the Pythagorean theorem in Volume 5, and the context is very clear.

By making up for these two shortcomings, Zhuge Liang can be regarded as completely surpassing the mathematics level of the first year of junior high school students in later generations, and began to get a glimpse of the "trigonometric function" in the upper grades.

But this time Zhuge Liang finally suffered.

He looked at it for another quarter of an hour, still not knowing how to count.

He was eager to do an experiment by cutting so many triangular planks at a specific angle according to the method shown by his big brother, and then using a ruler to measure the length of the specific hypotenuse to get the function value and the number of the open root.

But it was already dark at night, and it was difficult to make too much noise, and I couldn't find tools and materials, so I had to give up.

At this moment, Zhuge Liang was in the field of arithmetic and put away his contempt.

"In the past two years, big brother will have adventures!" Looking at the completely incomprehensible content on the sixth volume, as well as the seventh and eighth volumes like the Book of Heaven, he finally recognized his position.

"Volumes 3 and 4 are the basics of logic and common sense of thinking, Volumes 9 to 11, Common Sense of Heaven and Earth, and Laws of Agriculture and Animal Husbandry Life from 12 to 14. Fifteen and sixteen, the experience of ingenious application...... It's so wide-ranging. Did I underestimate what my eldest brother learned at first? You shouldn't have jumped to see it just now. ”

After looking through all the catalogs, Zhuge Liang finally got his attitude right and decided to take back his eldest brother's original "Persuasion of Learning" and read it carefully from the beginning. Maybe that way you can get twice the result with half the effort, and avoid being too quick to achieve it.

He reopened the second volume, which he had discarded, and read it without a hint of arrogance.

Perhaps, this is also a rare time in Zhuge Liang's life to put away the heart of "looking at its strategy" and take it seriously to "be pure".

——

PS: The new book issue seeks votes, collects, and chasing.

Tomorrow will end Zhuge Liang's first experience of reading, and the follow-up growth is all "practice", learning while encountering problems over and over again, interspersed with writing, which will not slow down the plot.

Thank you all for your patience and thank you.