100 must-read books for college students

Chapter 42 The Masterpiece of Superman Wisdom
Chapter 41 A masterpiece of superhuman wisdom: "Mathematical Principles of Natural Philosophy"

Newton, known as the "Superman in Genius", summed up the achievements of celestial mechanics and terrestrial mechanics, and made a contribution to the rules of classical mechanics.
Fan Yi
A set of basic concepts, proposed the three laws of motion and the law of universal gravitation, thus establishing a grand system of classical mechanics;
Invented calculus, introduced new mathematical analysis tools into the proof and derivation of mechanics, and built the whole mechanics on the basis of rigorous derivation
On the basis of deduction, mechanics has become a real science.These brilliant achievements are recorded in the "Natural Philosophy" written by Newton himself.
Mathematical Principles of Learning.

Engage in natural science research and create a classical mechanics system

Newton (1642-1727) was born in a small village in Walsthorpe, England.In the first half of the seventeenth century, when he was born, naturally
Science has begun to make great strides forward, and astronomy, mechanics, and mathematics have all made great progress.terrestrial mechanics

The time is ripe for a comprehensive synthesis of the research results of mechanics and the establishment of a classical mechanics system. At this time, the European capitalist economy
There has been considerable development, and there is an urgent need for natural science to provide more explanations and more guidance for social production.take cattle

It is in this situation that the classical mechanics represented by Ton developed rapidly. Newton entered Trinity College, Cambridge in 1661
, During his time at Cambridge University, Newton seriously studied Euclid's "Elements of Geometry", Kepler's Optics, Descartes'

Geometry etc. When Newton returned to the country to avoid the plague in 1665, he began to explore the problem of gravity, trying to rely on the force on the earth
Principles of science to explain the motion of planets.At the same time, he initially conceived the basic framework of the "flow number method" (calculus method), and also carried out

A scientific experiment to break down sunlight. In 1667, Newton returned to Cambridge University and became a researcher at Trinity College, where he continued to study mechanics
, the study of optics and mathematics. In 1684, Newton studied the theory of gravity again, and the result was a great success, which aroused the high praise of his colleagues.
sigh.At the urging of his friend Halley and others, Newton began to write the book "Mathematical Principles of Natural Philosophy" in 1686, which comprehensively
Summarized the scientific results of his research in mechanics and mathematics.Published in 1687, second edition in 1713, 1725

, Two years before Newton's death, the third edition was revised and issued.

Newton said in the preface of "Principles": "Our research is not in technology but in science, not in the power of human hands but in the power of nature.
", "Our research is the mathematical principle of the theory of nature", "Mathematically deduced as much as possible within the scope of physics", "put
Natural phenomena are attributed to mathematical theorems. "It can be seen that Newton's intention is very ambitious. His fundamental purpose is to
Establish a new system of natural philosophy (natural theory) with the content of physics and mathematical methods, and provide a clear and accurate explanation for all natural phenomena.
Establish a new framework for mechanical interpretation.

Three Laws of Classical Mechanics

The main body of "Principles" consists of three parts.There are two introductory sections before the main text, the length of which only accounts for about [-]% of the whole book, but they are particularly
important.

The introduction of the first section is "Description and Remarks".Here, Newton first introduced some basic concepts of mechanics such as mass, momentum and force
Defined, and described the nature, function and measurement of centripetal force.Then Newton introduced absolute space and absolute time
The new concept of time established his absolute space-time view.Although Newton's view of time and space has great limitations in today's view, but
Its normative effect on Newtonian mechanics is not dispensable.

The introduction of the second section is "Fundamental Theorems and Laws of Motion".That is, Newton's three laws of motion, which are our
Now called the three basic laws of classical mechanics.

Law [-]: Every object remains at rest or is equal to its original state if there is no external influence to change its state.
State of fast linear motion.

Newton believed that this is a basic universal fact of nature, an indisputable law of nature.According to this
Law, Newton further proposed that external force is the cause of changing the state of motion of things, not the cause of maintaining the original state.ox
Dunton cited a lot of facts in the book to prove this law, for example, if there is no air resistance and the influence of gravity,

Cannonballs will not stop and fall; and planets and other celestial bodies can maintain their motion state for a long time because they are in a medium with weak resistance.

state.

Law [-]: The change in motion is proportional to the force applied and occurs in the direction of the force.

What Newton is talking about here is the momentum problem we are talking about now. Momentum is equal to the product of the mass and velocity of an object. For this
, Newton's explanatory part has been defined.The change of momentum is the change of the product of mass and velocity, and the change of velocity is the addition

Speed, this is the common expression of the second law in modern times, the written formula is f=ma, f represents the force exerted, a is the force exerted by the cause

The acceleration produced by the force has a direction and is called a vector, and m is the mass of the force-bearing object, which is not in Newton's system
changing.Then the second law can be expressed as: For the same object, the applied force is proportional to the resulting acceleration.
Compare.

Law [-]: For every action force, there is always an equal and opposite reaction force against it; or in other words, two objects

The interaction forces exerted by each other are equal and opposite in direction.According to this law, Newton believed that two interacting objects

Regardless of whether there is a change in the state of motion on the surface of the body, the action force and reaction force between them always appear in pairs and

exist at the same time.The horse-drawn stone only sees that the horse acts on the stone, but does not see the influence of the stone on the horse, that is because of the existence of friction

Reason, if there is ice under the horse's hoof, the slipping of the horse's hoof shows the effect of the stone on the horse.When Newton explained the third law, he said:

This law also applies to attraction.Attraction is what usually creates centripetal force in circular motion, opposite to it

, the centrifugal force exerted on the object exerting the centripetal force by an object in circular motion of equal size, that is, the centripetal force
Centrifugal force and reaction force play a great role in the calculation of the motion of planets and satellites in the solar system, even in artificial

This relationship is still used in the calculation of satellite motion.The law of action and reaction was first proposed by Newton

of.With these three basic laws, the description of motion in classical mechanics is complete.After the three laws, there are 6
inference.Powerful composition and decomposition principles, motion superposition and relativity principles, and important momentum conservation principles, etc.

Now let's talk about the content of the main text. The general title of the first part of the main text is "On the Motion of Bodies", which is divided into 14 chapters.main

Study the relationship between the trajectory of an object's motion and the force under the action of gravity.One of the key points is to put forward the key points of calculus to determine

The ratio of the limited amount.The second point is to explain the true meaning of Kepler's three laws by using the limit method and using infinitesimal quantities.

For example, the relationship between the effect of gravity and Kepler's area law is proved, and the relationship between gravity and the square of the distance is deduced
.In this chapter, Newton also proposed the mechanical nature of optics, but he came to a wrong conclusion: "Light is in the optical dense medium
The velocity in the medium is greater than the velocity in the optically sparse medium. "

Newton also took the general title of the second volume as "On the Motion of Bodies", but in fact he mainly discussed the motion of objects in a medium with resistance.
the movement.It is divided into 9 chapters.The first thing to discuss is the situation that when the object is moving, it is subjected to a resistance proportional to the speed or the square of the speed.
Then some theorems and conjectures of hydrostatics and dynamics are discussed.The last chapter studies vortex motion in liquids, stating that

It is impossible for the vortex motion to make the planet follow Kepler's three laws, thus negating Descartes' ether vortex hypothesis on the planetary motion.

"On the Cosmic System" is the title of the third volume, using the basic principles and laws of mechanics to explain various phenomena in the universe.

The most important part of it is Newton's accurate formulation of the law of universal gravitation, and the use of this law to successfully explain the planets and their
Motion of satellites, motion of comets, tidal phenomena, and the slightly flattened ellipse of the Earth's poles.

In the third volume, Newton also solemnly put forward the "law of reasoning of natural philosophy" which is still of great significance today.

The core of Newton's four laws of reasoning is to emphasize the objectivity of research, that is, to insist on a materialistic attitude towards natural research.

Rule one is essentially the principle of simplicity; rule two is the principle of unity.Rule [-] and Rule [-] are also from the perspective of methodology and cognition
The theoretical point of view has given correct guidance to scientific research.

Newton's "Mathematical Principles of Natural Philosophy" is a great work in the history of human science and thought.

Human beings have studied natural science for hundreds of years, and it has also had a very important impact on human thinking. It can be said that cattle

Dayton's book research goes far beyond the boundaries of disciplines, becoming a masterpiece affecting many aspects of human development.

The mechanical system established by Newton in this book is of great significance, it marks the beginning of Copernicus to Aristotle's world

The final stage of the transformation of the world image.Therefore, it is a symbol of the beginning of the formation of modern science, and a reflection of nature in the history of human cognition.

The generalization and synthesis of the first theory of natural law.It summarizes the achievements of modern celestial mechanics and mechanics on the ground, and provides classical force

It stipulates a set of basic concepts, puts forward the three laws of mechanics and the law of universal gravitation, thus making classical mechanics a

complete theoretical system.Newton's book marked the maturity of classical mechanics.The theoretical body of classical mechanics presented in this book

The system has become the standard measure of modern science, so this book is a monument in the history of science.

In Newton's time, there was no separation between science and philosophy. The word "philosophy" means science and philosophy. "Principles" book

, mainly contributed to the natural sciences, but also has outstanding insights in philosophy, it is not only a place in the history of science

A milestone and a beacon for scientific research. When "Principia" was published, it was praised by scientists and philosophers. 18th century

The astronomer Laplace of the [-]th century believed that "Principles" "reached the highest possible state of physical science" and "beyond the

The masterpiece of all products of human wisdom". In the 20th century, Einstein reviewed Newton's achievements and said: "Before and after him
, no one has determined the direction of Western thought, research, and practice as he did. "

(End of this chapter)