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, 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.