In the way of writing, Newton followed the axiom model of ancient Greece and deduced propositions from definitions and laws (axioms). For specific problems (such as the movement of the moon), he compared the results of theoretical deduction with those of observation.
The book is divided into five parts, the first is "definition", which gives the definitions of material quantity, time, space and centripetal force. The second part is "axiom or law of motion", including three famous laws of motion. The following contents are divided into three volumes. The titles of the first two volumes are the same, both of which are On the Motion of Objects. The first book studies the motion of objects in free space without resistance. Many propositions involve solving the motion state (orbit, speed, motion time, etc.). ) and the force determined by the motion state of the object. The second volume studies the motion, fluid mechanics and wave theory of objects with given resistance. The third volume of this book is entitled On the System of the Universe. Newton deduced the law of gravity from the first volume and the results of astronomical observation, and studied the shape of the earth, explained the tides of the ocean, explored the movement of the moon, and determined the orbit of the comet. The "rules of studying philosophy" and "general explanation" in this volume have great influence on philosophy and theology.
At that time, the Royal Society wanted to publish this book, but it couldn't come up with the right money. Hooke, director of the Royal Society, claimed that inverse square law, that is, gravity, was his first discovery. Out of anger, edmund halley suggested that Newton write this book, and he published Newton's book at his own expense. 1687 In July, the Latin version of Mathematical Principles of Natural Philosophy came out. The second edition was published in 17 13, and the third edition was published in 1725.
Mott translated it into English on 1729, which is the popular English version now. Each edition was updated by Newton himself with a preface. There are many later versions, and the Chinese version is published in 193 1. The purpose of this book is to explore the natural forces from various moving phenomena, and then use these forces to explain various natural phenomena.
This book is divided into four parts. The opening and the first article introduce the three basic laws of motion and basic mechanical quantities of mechanics; The concept of mass was first put forward and defined by Newton, but Newton called it "the quantity of matter" at that time, and this name was later used by another physical quantity. In the second chapter, the motion of an object in a damping medium is discussed, and the formula that the resistance is proportional to the first and second squares of the velocity of the object is put forward. The elasticity and compressibility of gas and the speed of sound in air were also studied, which provided Newton with a stage to show his mathematical skills. The third topic is the cosmic system, which discusses the operation of planets, satellites and comets in the solar system and the generation of ocean tides, involving perturbation in many-body problems.
Newton did not claim to have built a system. Newton pointed out at the beginning of the preface to the first edition of Mathematical Principles of Natural Philosophy that he would "devote himself to the development of mathematics related to philosophy". This book is a combination of geometry and mechanics, a kind of "rational mechanics", and a kind of "science of accurately asking questions and demonstrating them", aiming at studying the movement produced by a certain force and the force needed for a certain movement. His task is to "study natural forces from dynamic phenomena, and then deduce other motion phenomena from these forces."
However, Newton actually built the most magnificent system in human history. What he said is mainly gravity, which is what we call gravity today, and the friction, resistance and tidal force of the ocean derived from gravity. Motion includes falling body, throwing body, rolling ball, simple pendulum and compound pendulum, fluid, planetary rotation and revolution, return point, orbital nutation and so on. In short, it includes, in other words, Newton explained all movements and phenomena from ground objects to celestial bodies with unified mechanical reasons.
Structurally, the mathematical principle of natural philosophy is a standard axiomatic system. Starting from the most basic definitions and axioms, it "deduces some general propositions in the first part and the second part". The first part, entitled "Motion of Objects", prepares the discussion of the whole book with mathematical tools, classifies various forms of motion, and examines the relationship between each form of motion and force in detail. The second part discusses "the motion of an object (in a blocked medium)", and further investigates the influence of various forms of resistance on the motion, and discusses various actual forces and motions on the ground. The third part "demonstrates their application to the cosmic system, deduces the gravitational force that makes objects tend to the sun and planets from astronomical phenomena with the propositions proved by the first two parts, and then calculates the movements of planets, comets, moons and oceans from these forces with other mathematical propositions". At the end of the book, Newton wrote a famous General Explanation, which focused on Newton's views on the fundamental reason of everything in the universe-gravity and the general reason why our universe is such a beautiful system, and his views on the existence and essence of God.
In terms of writing skills, Newton is a very attentive person. Although he established his own system according to Euclid's Elements of Geometry, he never forgot that his mission was to explain natural phenomena, and he was not lost in pure formal reasoning. He is an excellent mathematician and has a series of first-class inventions in mathematics, but he strictly regards mathematics as a tool and only leads readers to do a little math hiking when necessary.
On the other hand, Newton was not addicted to pure philosophical thinking at all. All the propositions in Mathematical Principles of Natural Philosophy come from the real world, either mathematics, astronomy or physics, that is, Newton understood natural philosophy. All the expositions in Mathematical Principles of Natural Philosophy are given in the form of propositions, and each proposition is proved or solved. All proofs and solutions are completely mathematical, and inferences will be added when necessary, and each inference has a proof or solution. Only when Newton thinks that a problem has special significance in philosophy, does he add notes to explain it or further popularize it.
Calculus, a mathematical method independently invented by Newton and Leibniz, runs through the book, but Newton called it "flow number", which is one of Newton's achievements. It occupies a very important position in the history of science, because it marks the establishment of the classical mechanical system.
Newton published three editions of Mathematical Principles of Natural Philosophy in 1687, 17 13 and 1726 respectively, all in Latin. The first English translation after Newton's death was translated from the third edition published in 1729 by Andrew Mott. 1802, the English version based on the first edition of Mathematical Principles of Natural Philosophy appeared. From 65438 to 0930, florian Kaio, an American scholar and historian of science, revised and published Mott's English version in modern English, which became the standard edition of Mathematical Principles of Natural Philosophy with the largest readership in the 20th century. In the early 1960s, Cohen, an American historian of science, cooperated with A 1exander Koyré, a French historian of science, and published a modern English version of Mathematical Principles of Natural Philosophy on the basis of the first English version translated by Mott.
In the history of science, Mathematical Principles of Natural Philosophy is the first classic work of classical mechanics, an epoch-making masterpiece, and the first complete scientific cosmology and scientific theoretical system mastered by human beings. Its influence covers all fields of classical natural science, and it has achieved fruitful results again and again in the next 300 years. As far as the history of human civilization is concerned, it has achieved the industrial revolution in Britain, induced the Enlightenment and the Great Revolution in France, and made direct and rich achievements in both social productive forces and social basic systems. So far, there is no second important scientific and academic theory that has made such great achievements.
The mathematical principle of natural philosophy has reached a theoretical height that is unprecedented and unprecedented. Einstein said: "it is impossible to replace Newton's concept of universal unity with an equally all-encompassing concept of unity." Without Newton's clear system, the gains we have made so far will be impossible. " In fact, the problems discussed by Newton in Mathematical Principles of Natural Philosophy and the methods to deal with these problems are still taught in mathematics and physics majors in universities, while the knowledge of physics, mathematics and astronomy learned by students of other majors has not reached the level of mathematical principles of natural philosophy in depth and breadth.
All these determine the eternal value of the book Mathematical Principles of Natural Philosophy.
The mathematical principle of natural philosophy puts forward three basic laws of classical mechanics and the law of universal gravitation, which are based on objective research. Newton attached great importance to the methods and attitudes of scientific research, and he pointed out four basic rules for studying nature. The core of these four rules is to emphasize the objectivity of research, that is, to adhere to the materialistic attitude towards natural research. His own research is based on long-term practical observation.
At the same time, his explanation of natural phenomena through laws is based on a lot of mathematical analysis. In the first chapter of the first part of this book, Newton talked about calculus and geometry. These contents are actually the mathematical basis of this book. Newton was originally one of the inventors of calculus, but in order to make it easier for readers to accept it, he tried to avoid using more difficult calculus methods in this book. The mathematical tools he uses are strictly limited to geometry.
There is a long "explanation" at the beginning of the book, which explains the basic definitions of some concepts used in the book, such as force, celestial body, mechanics and motion. After the "explanation", Newton introduced the "basic theorem or law of motion" in detail, that is, Newton's three theorems and laws about the motion of objects.
The first law: if there is no external influence to change the state of each object, then the object still maintains its original static or uniform linear motion state. Newton thought that this was a basic universal fact in nature, and it was indisputable. According to this law, external force is the reason to change the motion state of an object, not to maintain the original state. For example, the shell will stop falling because of air resistance and gravity. If there is no such external force, the shell will keep moving at a constant speed.
The second law: the change of motion is directly proportional to the applied force and occurs in the direction of the force. This is actually what we are talking about today. Momentum is equal to the product of the mass and velocity of an object, and the change of velocity is acceleration. For the same object, the applied force is directly proportional to the generated acceleration.
The third law: for every action, there is always an equal reaction; In other words, the interaction force exerted by two substances is constant and the direction is just the opposite. According to this law, Newton pointed out that the force and reaction between two interacting objects appear in pairs or exist at the same time, regardless of whether the motion state changes on the surface. For example, when people paddle forward, the ship can move forward because there is a force on the water when people paddle into the water, and the aquatic products produce an equal reaction to push the ship forward. The third law also applies to centripetal force and centrifugal force in circular motion.
The main content of the mathematical principle of natural philosophy is the establishment and application of the law of universal gravitation. The second chapter of the first part of Mathematical Principles of Natural Philosophy is "On the method of centripetal force". Newton started from this chapter, and through the careful study of various special forms of motion involving centripetal force, he gradually expanded to the third part of the discussion on the cosmic system. In the first chapter of the third part, he discussed the causes of the cosmic system, and explained with three theorems that "the force that keeps the satellite away from the straight line and stays in its orbit", "the force that keeps the planet away from the straight line and stays in its orbit" and "the force that keeps the moon from leaving its orbit" are centripetal forces (the centers are Jupiter, the sun and the earth respectively), and these centripetal forces are inversely proportional to the square of the distance between their centers. After distinguishing the difference between gravity and magnetic force, he came to the conclusion that all objects have gravity (that is, gravity) and are directly proportional to the quantity (that is, mass) of the substances contained. Newton put forward a relatively complete and classic account of the law of universal gravitation:
Theorem: The matter of two balls has mutual weight, that is, they attract each other. If matter is uniform at equal distance from the center, the weight of one ball relative to other balls, that is, the attraction between them, is inversely proportional to the square of the distance between centers.
After the classical expression of the law of gravity, Newton immediately used it to explain a large number of practical problems, that is, to explain the existence of gravity from a large number of natural facts. The natural facts he cited include the deviation of the moon's motion, the change of tides, the length of precession and so on.