How should I read The Elements of Geometry?
Reading geometry is not reading propositions, but reading his methods, his system and his logic. You said that you didn't get anything after reading two chapters, so look at how each proposition in the second chapter is proved. It is nothing more than drawing a picture, then rambling, and finally saying that the proposition is valid, but the method is inside, and he uses a picture to help prove it. And if you carefully observe every character, you will find that his paintings are so reasonable and obvious. If you do it once, you will find it interesting. Similarly, in the first chapter, how many kinds of argumentation methods and skills are there? To be honest, I am not a very smart person, or an idiot, whatever you say. I'm just stupid anyway. I need to read what others have read once, but since I am interested in mathematics, I will stick to it no matter how hard it is. That's far, hehe! Hmm. . In the Elements of Geometry, the best reading is actually the first chapter, because we have been in contact with it since junior high school (I don't know if you have finished reading it in junior high school), but because of this, we ignore the author's argument means for the proposition. For example, in the proposition 16, he uses the congruence of triangles to judge. When I first saw this proposition, I directly thought of using parallelism to prove it, but the theory of parallel lines appeared later. In fact, this also reflects the importance of triangles to some extent. In the west, trigonometry has matured for a long time, and farmers in ancient Egypt even used trigonometric functions to measure land. I think, when you were in junior high school, you often heard the teacher say that you should draw auxiliary lines to prove the application problems. Then, in this proposition, the author directly applied a number to assist in the proof, which is not very enlightening. By the way, if you go to high school, you can add auxiliary lines or graphics to your arms and fingers. What's wrong with trying to solve geometry problems in high school? Of course, in the first chapter, the most important argument method is the reduction to absurdity, which is taught by high school teachers, but it is only a passing. However, in the original work, there are many reduction to absurdity, which is a good place to practice reduction to absurdity. When reading the original work, we might as well see how the author proved it, and since it is geometric proof, it is very important to see how the graph changes when the author uses reduction to absurdity. A book on geometry originally created European geometry, but it also inspired the birth of non-European geometry. It can only be said that everything is not absolute, everything is invisible, and it becomes sound only when the eyes touch it and hear it.