(2004-02-06)

Brook Taylor, a British mathematician,1one of the most outstanding representatives of the British Newton School in the early 8th century, was born in Edmonton, middlesex on August/865 1685. After 1709, he moved to London and obtained a master's degree in law. 17 12 was elected as the royal family. Two years later, he received a doctorate in law. In the same year (i.e. 17 14), he became the secretary of the royal society. Four years later, he resigned for health reasons. 17 17 years, he solved the numerical equation by Taylor theorem. Finally in 173 12.

Taylor's main work is the Positive and Negative Increment Method published by 17 15. In the book, he stated the famous theorem-Taylor Theorem, which was first put forward in his letter to the teacher (mathematician and astronomer) in July of 17 12: where V is the increment of independent variable and the flow. It is a constant. The above formula is expressed in modern form as follows: This formula is developed from Gregory-Newton interpolation formula, and when x = 0, it is called Ma Kraulin theorem. 1In the 1920s, Lagrange emphasized the importance of this formula and called it the basic theorem of differential calculus, but Taylor did not consider the convergence of series in his proof, so the proof was not rigorous.

Taylor theorem initiated the finite difference theory, so that any univariate function can be expanded into a power series; Meanwhile, Taylor became the founder of finite difference theory. In his book, Taylor also discusses the application of calculus in a series of physical problems, among which the result of lateral vibration of strings is particularly important. He deduced the basic frequency formula by solving the equation, which initiated the study of string vibration. In addition, this book also includes his other creative work in mathematics, such as discussing the singular solutions of ordinary differential equations and the research on curvature problems.

17 15 years later, he published the famous linear perspective theory, and even the second edition of Principles of Linear Perspective (17 19). He developed his linear perspective system in a very strict form, among which the most outstanding contribution is to put forward and use the concept of "vanishing point", which is of great significance to photogrammetry.