Bazhou, on the outskirts of Xiyang City, Sima Yangji of Bazhou sneezed several times one after another, he rubbed his nose, looked at the north with palpitations, and a wave of uneasy emotions surged into his heart. Pen × fun × Pavilion www. ｂｉｑｕｇｅ。 ｉｎｆｏ

Yang Ji felt that he was being remembered, and there was only one person who would 'worry' about him in this era, and that was Yu Wenwen, who was now far away in Yecheng, who was changing his ways to squeeze his knowledge every day.

"I'm going to be fine..."Yang Ji thought, this time Yuwenwen went to Yecheng, he stayed in Xiyang to lead the state soldiers, and together with the soldiers of the Hulin Army, he was not afraid of Xiao Xiaozuo, the only thing he was worried about was that something happened to him.

Kowtow at the court meeting can knock unconscious, there is no one in this world!

The news from Yecheng showed that the Shannan envoy Yuwenwen had a small accident, of course, there was no big problem, that is, he fainted a little, and when Yang Ji heard the news, his first reaction was that someone wanted to harm Yuwenwen.

For some reason, Yuwen Wen gave outsiders the feeling that he was out of tune, and Yang Ji knew about the reason, so he didn't think that Yu Wenwen would really be dizzy in the main hall, but he and the others were out of reach of the whip chief in Bazhou, and he could only hope that this one would return safely.

"Sima Yang, it's ready."

The voice pulled Yang Ji out of his distracted state, he looked at the group of people around him and nodded, "Then let's start." ”

Most of the people present were people from the workshop under the public name of Xiyang County, don't drive Xu Shao, Hao Wubo in Zhizhong was an exception, Changshi Ren Chong was originally going to be there, but he couldn't come for a while, and what they came to watch was a newly made device in the workshop.

"Observation begins!"

Lin Youdi stood in front of a triangular wooden shelf, on which was mounted a strange device, which was a horizontal metal pipe, about five feet long, with a bulge in the middle and two round holes inside.

The bulge was roughly the same height as the human face, and the two round holes were close to the interpupillary distance of the person, so Lin Youdi stepped forward and looked inside with his eyes.

"Red card, watch red card!"

In the wilderness ahead, a large wooden board draped in red cloth was suddenly erected, the color was bright and very conspicuous, but the distance was quite far and it looked a little difficult, Lin Youdi kept his eyes close to the two round holes, and at the same time twisted a small disc under the metal pipe with his right hand.

At the other end of the metal pipe, facing the side facing the wilderness, there is a small round mirror at the left and right ends, the left round mirror is fixed, while the right round mirror is rotating slightly, as if it is turning the small disc with Lin Youdi, and is slightly turning to the left.

After a while, the round mirror on the right side stopped turning, and Lin Youdi retracted his head, rubbed his eyes, leaned back again, and looked at the round hole for a moment before retracting his head again.

He looked at the small disc that he had just twisted, and its outer ring was densely engraved with many short lines, and there were many tadpole-like symbols engraved in correspondence, and after looking at it carefully, Lin Youdi took a deep breath and reported a number.

A young man standing next to Lin Youdi held a wooden board with a blank piece of paper in his hand, and when he heard Lin Youdi report the number, he wrote it on the white paper with charcoal.

Another man, also holding a wooden board in his left hand, on which was a white piece of paper, on which was densely packed with tadpole texts, he glanced at the numbers he had written down, and then stretched out his right hand and pressed his index finger on the paper to move slowly, as if to confirm the content line by line.

"Found it, here." He whispered, and the young man who was drinking white paper with a charcoal pen leaned over and wrote down a string of tadpole texts that he knew with his fingers on his white paper, and then wrote quickly with charcoal.

After a while, he finished writing, and drew an underline at the last string of tadpole texts, and the two looked at these 'ghost drawing talismans' and muttered for a moment, and finally came to Yang Ji's side to report: "Yang Sima, the distance is five hundred and thirty-three steps." ”

"Have you checked it?" Yang Ji asked.

"It's been checked!"

Yang Ji nodded, turned to Xu Shao on the side and said, "Xu don't drive, the measured distance is five hundred and thirty-three steps." ”

"The distance of the red cloth plank is five hundred and fifty steps," Xu Shao gave a result, and when Lin Youdi and the two young men heard it, they couldn't help but clench their fists and show excitement.

"Go on!"

The test continued, as the first time, various shields were erected in the distant wilderness, and Lin Youdi, who was observing with a strange device, reported the corresponding numbers, and the two young men kept calculating according to the numbers, and finally reported the distance and checked it with the real distance value in Xu Shao's hand.

Those planks were arranged by Xu Shao, and the distance was naturally kept secret from Lin Youdi and others, and the test was carried out many times, and each time the results were satisfactory and nodded silently.

"The actual distance is 1,160 steps, and 1,228 steps are measured, and there is an error of 68 steps, which is good." Xu Shao said that this was the tenth and last test, and the results still satisfied him.

Yang Ji patted Lin Youdi's shoulder, and several young people cheered excitedly in a low voice, while Hao Wubo, who was watching quietly, said with admiration on his face: "Pythagorean measurement, I finally saw it with my own eyes today." ”

He looked at the strange device and asked Yang Ji, "This test... Rangefinder, could it be that the farther the distance, the greater the error? ”

"Yes, as the saying goes, the steering mechanism of the lens is not precise enough, and if the distance is long, the subtle angle difference will lead to a large deviation in the calculation result."

"One degree equals sixty minutes, one minute equals sixty seconds... The division of angles in the Western triangular theory is very different from that of the Central Plains. Hao Wubo groaned, "I read "Zhou Ji" and learned about the Pythagorean measurement, and now I see it, it is really an eye-opener. ”

"Chengye, used by Yang Sima, is a trigonometric function of Western trigonometry." Xu Shao corrected, but after thinking about it, he asked Yang Ji: "Different paths lead to the same end, could it be that this geometric trigonometric function is similar to the Pythagorean technique of the Central Plains?" ”

"Exactly, Yang got several volumes of strange books by chance in the past, so he learned this Western arithmetic, one of which is called "The Great Measurement", and another is called "The Law of Measurement"..."

"According to the "Big Test", there are 'three methods' and 'two simple methods' for calculating trigonometric functions..."

Yang Ji talked eloquently and shared what he had learned with Xu Shao and Hao Wubo, who had read "Zhou Ji" and "Nine Chapters of Arithmetic", so the basic arithmetic ability is still there, and the most important thing is to know the Pythagorean technique, which is much easier to communicate.

The art of Pythagorean was first seen in "Zhou Ji", the hooker, the short right-angled side of the right-angled triangle, the strand, the long right-angled side of the right-angled triangle, and the 'string', which is the hypotenuse of the right-angled triangle.

"Zhou Ji" proposed "Hook three strands, four strings and five", and Zhao Shuang, a scholar of Wu State in the Three Kingdoms of the late Han Dynasty, annotated "Zhou Ji", expressing it as "Pythagorean multiplies each other, and merges it, which is a string." Divide the square by the string. ”

On this basis, the "Pythagorean method" was proposed in the "Zhou Ji", and the Pythagorean method was also proposed in the similar "Nine Chapters of Arithmetic", and the principle of proportion using the Pythagorean theorem was mentioned in the "Pythagorean" chapter.

Among them, it is mentioned that the distance measurement of the standing table, the height measurement of the standing wood, and the depth measurement of the standing wood, and "Zhou Ji" directly came to a "measuring the height of the sun".

In Western geometric trigonometry, there is a concept of trigonometric function, so there is a new application for Pythagorean measurement, that is, the use of included angles, and then bring in the sine, cosine and tangent functions in the trigonometric function to extrapolate.

The principle of this measurement method is to use two telescopes separated by a known distance to observe object A at the same time, and the distance of object A can be calculated according to the trigonometric function at different azimuth angles between the two telescopes.

The specific application is to fix two telescopes on a crossbar, one of which is horizontally perpendicular to the crossbar and fixed (the left end), and the other telescope can rotate horizontally (the right end), and the crossbar itself rotates horizontally.

When observing object A, first aim the front sight in the field of view of the left telescope at object A, then fix the crossbar, and then rotate the right telescope to align the front sight in the field of view with object A (the crosshairs of the two mirrors coincide).

At this time, a right-angled triangle is formed between the two telescopes and object A, and the distance B between the two telescopes can be regarded as the short right-angled side of the right-angled triangle, and the distance C between the left telescope and object A is the long right-angled side of the right-angled triangle.

The angle D between the right telescope and the crossbar is known, and its adjacent edge B is also known (the length of the crossbar), so according to the angle value of D, find out the corresponding trigonometric value, and then bring in its adjacent edge B, you can reverse the length of C, so that the ranging is completed.

According to this principle, the larger the rotation angle of the moving telescope, the more accurate the measurement result, so when the distance between the measured object is too far, the rotation angle of the active telescope is very small, which directly leads to a sharp increase in the measurement error.

Therefore, the distance between the two telescopes should be as long as possible to ensure that the measurement results are accurate.

Yang Ji said very carefully, and there were real objects to see, Xu Shao and Hao Wubo tossed for a while, and finally figured out the key to this 'optical measurement', that is, to calculate the comparison table of the corresponding trigonometric functions of each angle.

Then when measuring, the angle of the telescope is obtained, and the result can be calculated by substituting it with the distance between the two mirrors, that is, the distance, and the value on the trigonometric function comparison table is directly related to whether the calculation is correct or not.

"The Great Test, three methods, two simple methods... It's not easy to calculate, right? Xu Shao asked, and seeing Yang Ji nodded, he asked curiously, "How long has Yang Sima been counting this comparison table?" ”

"I almost forgot about this method, I recalled it for a long time, and I repeatedly checked and deduced it, and it took me four months to finally calculate it."

Hao Wubo was speechless when he heard this, Xu Shao looked at Yang Ji with sympathy, the origin of this Yang Sima really made him curious, he really couldn't understand which school the other party was learning.

Proficient in architecture、Arithmetic,It is said that there is a study of Buddhism but practiced a murderous knife method.,If you want to say that you are a general, the level of riding combat is not very good.,If you want to say that you are a scholar, you haven't seen his poetry.。

There is also this unheard of Western geometric trigonometry, what sine, cosine, tangent, and when applied to Pythagorean measurements, can be used to calculate the sides of unknown lengths and unknown angles in triangles.

Xu Shao thinks that this so-called Western geometric trigonometry is the same as the 'Western Treasure Glass Mirror', which is under the pretense of 'Western Ocean', but it is actually someone's own knowledge.

There were many merchants and monks in the Western Regions who traveled between the Western Regions and the Central Plains, and they had never heard of these wonderful arithmetic methods, and the various terms in them had never been seen in the hand-me-down books.

Yang Ji gave him a very strange feeling, Xu Shao only felt it in another person, that is, Gongyu Wenwen of Xiyang County, the feeling these two people gave him can't be described in words, anyway, he just feels that some times it is weird.

"Sima Yang, what is the use of making this rangefinder? It looks quite sophisticated, and it comes at a high price. Hao Wubo asked, he felt that Yuwen Wen tossing this thing would never be out of boredom, and it must have an important use, "Could it be used to measure the acres of land?" ”。

"Exactly, not only that, but this rangefinder can be improved to measure height."

"Distance measurement and height measurement, I think it is used for the survey when building water conservancy? Could it be to build a river embankment in the future? Xu Shao asked, he felt that this thing was similar to chicken ribs, it was indeed exquisitely conceived, but it was not very useful.

Whether there is such a thing, the field is the same measurement, and the construction of water conservancy facilities dozens of miles long has long been a mature survey method, and this thing is made as a novelty, and it is not in the way.

"There are many uses, and you will know about it later." Yang Ji sold a pass, Xu Shao didn't ask when he saw this, and went to try the rangefinder with Hao Wubo.

'What's the use of this thing... Now you can't make a cannon. Yang Ji sighed in his heart, and his thoughts flew to another era.

During the Wanli period of the Ming Dynasty, people of insight led by Xu Guangqi cooperated with Western missionaries Matteo Ricci and others to introduce Western academic works for translation, including the "Measurement Law" on Pythagorean measurement.

In the fourth year of Chongzhen, Xu Guangqi and Western missionaries Tang Ruowang, Deng Yuhan and others co-edited the "Great Test", which was presented to the imperial court as part of the almanac, which was the first time that trigonometry entered the Central Plains.

The calculation method of trigonometric functions is recorded in the "Great Measurement", and it is this trigonometric function that can be used for ranging measurement, which has aroused the interest of many people, because if it can accurately measure the range, it can give full play to the power of artillery.

At this time, the Ming Dynasty was stormy, and the Tatar chieftain Huang Taiji led the crowd to attack and harass Gyeonggi, and there were hungry people inside.

Xu Guangqi's manuscripts of Western works dedicated to the imperial court circulated among the people, "The Great Measurement" and "Measurement Law" are the second, Yang Ji has also learned and is proficient in this way, but the building will fall, it is beyond the power of manpower to recover.

In the fifteenth year of Chongzhen, the Qing army entered the eastern part of Koushan to besiege Yizhou, and the Ming army defending the city relied on the artillery to shoot at the Qing army's artillery.

Yang Ji, who was measuring the range of the artillery on the side, was shocked and injured internally, his hearing was impaired, his mouth and nose were bleeding, and when the Qing army broke through the city, he was no longer able to kill the enemy, so he had to die and die for the country.

"Cannons, Hongyi cannons... When will I see you majestic..."

(ps: There have been a lot of things recently, and there is a daily update these days, mainly at night) (To be continued.) )