Subject
Arithmetic -- Early works to 1900 Books
Best books
Augustus De Morgan
Elements of arithmetic
"Elements of Arithmetic" by Augustus De Morgan is a mathematical textbook written in the mid-19th century. The work serves as a foundational guide to arithmetic, focusing on principles and reasoning rather than rote calculations, making it suitable for both students and educators. The text aims to establish a solid understanding of arithmetic concepts, laying out the basic operations, such as addition, subtraction, multiplication, and division, while emphasizing the importance of reasoning in mathematics. The opening of the book includes a preface that outlines De Morgan's intent, stating that this edition contains significant appendixes aimed at aiding advanced students. It discusses the importance of teaching arithmetic through reasoning rather than mere routine and highlights the need for a rational approach to mathematics. Following the preface, the first section introduces numeration, illustrating how different counting methods were used throughout history with examples of simple counting techniques and their evolution into more complex systems, ultimately leading into structured numeral systems. This thoughtful approach sets a clear foundation for understanding arithmetic principles.
Unknown
The Earliest Arithmetics in English
"The Earliest Arithmetics in English" by Robert Steele is a scholarly work written in the early 20th century. This publication compiles and analyzes early arithmetic texts in the English language, focusing primarily on works from the 15th century. The book examines the evolution of arithmetic, the tools and methods used for calculations, and the importance of these texts in the historical context of mathematics. The opening of this volume presents an introductory exploration of the scarcity of English-language arithmetic texts prior to the 16th century, indicating that Latin dominated mathematical literature at the time. It outlines early mathematical practices, the significance of historical figures such as Sacro Bosco and Alexander de Villa Dei, and the various methodologies employed in arithmetic, such as the use of counting boards and the algorithmic approach to calculations. The introduction serves as a precursor to two main treatises that will be presented within the work, diving into the structure and principles of early arithmetic education.
approximately 5th century Sunzi
孫子算經
"孫子算經" by approximately 5th century Sunzi is a mathematical treatise written between the 3rd and 5th centuries CE. This ancient Chinese work explores arithmetic methods, Diophantine equations, astronomy, and calendar development. Divided into three chapters, it provides the first detailed description of counting rod rules and their manipulation in basic operations. The treatise also contains the earliest known example of the Chinese remainder theorem, a fundamental tool for solving complex mathematical problems.
Hui Liu
海島算經
"海島算經" by Liu Hui is a mathematical manual written during the Three Kingdoms era (220–280). Originally an extension of "The Nine Chapters on the Mathematical Art," it became a separate work during the Tang dynasty and was included in imperial mathematics examinations. The text presents practical surveying problems, demonstrating how to measure inaccessible distances and heights using poles and geometric principles. Nine problems cover scenarios like determining island heights, mountain elevations, and city dimensions through ingenious indirect measurement techniques.
Recently surfaced classics