The design of good notation is a cause that was dear to Charles Babbage’s heart throughout his career. He was convinced of the “immense power of signs” (1864, 364), both to rigorously express complex ideas and to facilitate the discovery of new ones. As a young man, he promoted the Leibnizian notation for the calculus in England, and later he developed a Mechanical Notation for designing his computational engines. In addition, he reflected on the principles that underlie the design of good mathematical notations. In this paper, we discuss these reflections, which can be found somewhat scattered in Babbage’s writings, for the first time in a systematic way. Babbage’s desiderata for mathematical notations are presented as ten guidelines pertinent to notational design and its application to both individual symbols and complex expressions. To illustrate the applicability of these guidelines in non-mathematical domains, some aspects of his Mechanical Notation are also discussed.

良好符号的设计是查尔斯·巴贝奇整个职业生涯中一直珍视的事业。他深信“符号的巨大力量”（1864, 364），既可以严格表达复杂的思想，又可以促进新思想的发现。作为一个年轻人，他在英国推广了莱布尼茨的微积分符号，后来他开发了一种机械符号来设计他的计算引擎。此外，他还反思了构成良好数学符号设计的原则。在本文中，我们第一次以系统的方式讨论了这些在巴贝奇著作中散布的思考。巴贝奇对数学符号的需求被呈现为与符号设计及其在单个符号和复杂表达式中的应用相关的十个指南。