Newton said in the preface of Principles: "Our research is not in technology but in science, not in human hands, but in the power of nature", "Our research is the mathematical principle of natural theory", "We should try our best to deduce it mathematically within the physical scope" and "all natural phenomena should be attributed to mathematical theorems" It can be seen that Newton's idea is very grand. His fundamental purpose is to establish a new system of natural philosophy (natural theory) with physics and mathematical methods as the content, and to establish a new framework for mechanical explanation of all natural phenomena.
The text of the Principles is divided into three parts. There are two introductory chapters before the text, which only account for about 4% of the book, but its content is very important.
The introduction 1 is "explanation and postscript". Here, Newton first defined some basic concepts of mechanics such as mass, momentum and force, and described the nature, function and measurement of centripetal force. Then, Newton introduced the new concepts of absolute space and absolute time, and established his absolute view of time and space. Newton's concept of time and space has great limitations today, but it is indispensable to the normative role of Newtonian mechanics.
The second introduction is "Basic Theorem and Law of Motion". Here, Newton expounded the famous three laws of motion. The first law, that is, the law of inertia: "Unless it changes its state under the influence of external forces, any object will remain at rest or move in a straight line at a constant speed." The second law is the law of motion: "The change of motion is directly proportional to the applied force and occurs along the direction of the force." These two laws were discovered or touched by Galileo, and Newton gave a clearer and more general expression. The third law is the law of action and reaction, which was first put forward by Newton. With these three basic laws, the description of motion in classical mechanics is complete. After the three laws, there are six inferences. Powerful principles of synthesis and decomposition, superposition and relativity of motion, and important principles of momentum conservation.
The first part of the text is entitled "On the Motion of Objects", which is divided into 14 chapters. This paper mainly studies the relationship between the orbit of an object and the force under the action of gravity. One of the key points is to put forward the main points of calculus to determine the ratio of infinitesimal. The second point is to explain the true meaning of Kepler's three laws with limit method and infinitesimal. For example, the relationship between gravity and Kepler's area law is proved, and the inverse relationship between gravity and the square of distance is deduced. In this series, Newton also put forward the mechanical nature of optics, but came to a wrong conclusion: "The speed of light in an optically dense medium is higher than that in an optically sparse medium."
The general title of the second part is also On the Motion of Objects, but it mainly discusses the motion of objects in resistive media. * * * is divided into 9 chapters. In this paper, firstly, the situation that an object is subjected to resistance proportional to the velocity or the square of the velocity is discussed, and then some theorems and conjectures of hydrostatics and dynamics are discussed. In the last chapter, the vortex motion in liquid is studied, and it is pointed out that vortex motion cannot make planets obey Kepler's three laws, thus denying Descartes' etheric vortex hypothesis of planetary motion.
The third part is entitled "On the Cosmic System", which uses the basic principles and laws of mechanics to explain various phenomena in the universe. The most important part is that Newton accurately expounded the law of gravity, and successfully explained the motion of planets and their satellites, the motion of comets, tidal phenomena and slightly flat ellipses at the poles of the earth by using this law.
In the third part, Newton also solemnly put forward the "natural philosophy reasoning law" which is still of great significance today. Rule 1: "There is no need to seek other reasons for natural things except those that are true enough to explain their phenomena ... because nature likes simplification and doesn't like to brag about itself with unnecessary reasons." Law 2: "Similar results in nature must be attributed to the same cause as far as possible." Rule 3: "The attribute of an object that can neither be enhanced nor weakened, but is possessed by all objects in our experimental range, should be regarded as the universal attribute of all objects." Law 4: "In experimental philosophy, we must regard the propositions derived from various phenomena by general induction as completely correct or very close to correct;" Although you can imagine any contrary hypothesis, you should treat it like this until there are other phenomena or exceptions that can make it more correct. "
Newton's first law is essentially the principle of simplicity; The second rule is the principle of unity. For natural science research, the principle of simplicity is reasonable and conforms to the aesthetics of science and technology. It is always one of the basic standards for people to evaluate scientific theories. The unified law sees the similarity and unity of nature, which effectively encourages and helps people to explore more natural laws. Law 3 and Law 4 also give correct guidance to scientific research from the perspective of methodology and epistemology. Rule 3 emphasizes the combination of experience and reason; Rule 4 affirms the scientific nature of induction and does not think that induction is omnipotent, thus avoiding skeptical agnosticism and metaphysical mechanical realism. In fact, these two laws have implied the dialectical relationship between relative truth and absolute truth and the law of truth testing and development.