Chapter 62 Compilation of Section 13 "The Essence of Mathematics and Physics"

The full name of "Shu Li Jing Yun" is "Yu Ding Shu Li Jing Yun", which was compiled from 1690 to 1721 with the strong support of Emperor Kangxi.French missionaries Zhang Cheng and Bai Jin participated in the translation, Mei Wending’s grandson Mei Cheng [jue Jue] Cheng, Mongolian mathematician Ming Antu, etc. participated in the compilation. All compilation work was carried out in the palace. fasting.This is an encyclopedia that systematically introduces western mathematics knowledge, including geometry, trigonometry, algebra, arithmetic, etc.The whole book is divided into two volumes, the upper and lower volumes. The upper volume has five volumes "Li Gang Ming Ti", the second volume has 40 volumes "Sections and Applications", and there are four types of tables and eight volumes, totaling 53 volumes.

The book also lists many application problems in ancient Chinese arithmetic books, but the answers are solved by Western mathematical methods.Only in the first volume are the two sections "Origin of Mathematics and Science" and "Explanation of Zhou Bi Jing" used to explain the "origin" and long history of traditional Chinese mathematics. Juan 2 to Juan 4 is "Elements of Geometry", which is divided into 12 chapters.The first chapter gives the definitions of point, line, surface, body, circle, parallel line, and various angles; the second chapter gives several definitions and theorems about triangles; the third chapter discusses quadrilaterals; the fourth chapter discusses Circles and circular inscribed and circumscribed polygons; Chapter 5 on solid geometry; Chapters 6 and 7 on proportions of quantities; Chapter 8 on similar shapes; Chapter 9 on Pythagorean theorem and other propositions related to proportions; Chapter 10 is on the surface area and volume of cones, spheres, and ellipsoids; Chapters 11 and 12 are on geometric construction.In short, its content is roughly the same as Euclid's "Elementary Geometry", but the writing style is quite different.

Volume 5 is "Algorithm Original", which discusses the nature of natural numbers, including the properties of product of natural numbers, common divisor, common multiple, ratio, arithmetic series, geometric series, etc. Volumes 1 to 30 of the second volume are practical arithmetic, covering weights and measures, notation, four arithmetic operations on integers and fractions, proportions, solving equations, taking squares and strips from squares, Pythagorean problems, trigonometry, inscribed and circumscribed circles Regular polygons, areas of regular polygons, circles, segments and ellipses, cylinders, cones, spheres, truncated spheroids and ellipsoids, specific gravity, etc.

Volumes 31 to 36 introduce the knowledge of algebra introduced to China at that time. Volumes 37 and 38 introduce logarithms and logarithmic proportions. Volumes 39 and 40 introduce proportional solutions, including the method of drawing a sundial and the Western slide rule-the false number ruler. The mathematical tables attached to the book include prime factor tables, logarithmic tables, trigonometric function tables, and trigonometric function logarithmic tables. After its publication, "The Essence of Mathematics and Physics" was widely circulated, and became an important classic for people to study and study Western mathematics for a relatively long period of time, and had a great impact on the later development of mathematics.