THE MATHEMATICS OF EGYPT, MESOPOTAMIA, CHINA, INDIA, AND ISLAM: A SOURCEBOOK Edited by Victor J. Katz Princeton University Press, 2007, 685 pp. ISBN-13: 978-0-691-11485-9
The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook should be an essential addition to the college library and personal library of anyone teaching or studying the history of mathematics. This extensive book consists of five chapters, each written by a leading scholar in the field. The chapters include short histories of the development of mathematics in each of the five areas covered as well as numerous source texts in translation. Each chapter provides an extensive list of source texts and an essential reference list.
The first chapter, written by Annette Imhausen of Mainz University, covers Egyptian mathematics. Imhausen begins with a discussion of Egyptian writing systems and the nature of the extant Egyptian mathematical texts. She then provides complete translations and commentaries of several texts, including problem texts from the Rhind Mathematical Papyrus (problems 6, 23, 26, 27, 41, 48, 50, 52, 56, 58, 65, 69, and 76), the Moscow Mathematical Papyrus (problems 10, 14, 15), and the Lahun Mathematical Fragment (UC 32160). Also presented are table texts from the Lahun Mathematical Fragments (UC 32159), the Rhind 2/N table, and the Mathematical Leather Role. Imhausen also includes translations of several administrative texts (the Reisner papyri and the Ostraca from Deir el Medina) as well as problem and table texts from the Graeco-Roman period that are not usually included in comprehensive history of mathematics texts.
The second chapter, written by Eleanor Robson of Cambridge University, examines Mesopotamian mathematics. This chapter is an exciting treasure trove of cuneiform mathematical texts, including over sixty translations that have not been published elsewhere. Robson begins with a discussion of the source texts, including the authors and contexts of the texts, and how the texts presented were chosen and translated. The translated texts are presented by time period. In the section on texts dated between 3200 and 2000 BCE, Robson presents translations of me oldest known piece of recorded mathematics (W 19408,76), the earliest known mathematical diagram containing textual data (IM 58045), and eight other ancient mathematical texts. Next, from the Old Babylonian Period (200-1600 BCE), complete translations of eight arithmetical and metrological tables are presented, including 22 mathematical problem texts containing hundreds of problems in geometry, geometrical algebra, quantity surveying, and arithmetic progressions. Rough work (diagrams and calculations by students) and reference lists (used by Babylonian teachers to construct problems) from the Old Babylonian period complete this subsection. The chapter concludes with ten texts from the later Mesopotamian time period 1400-150 BCE.
The third chapter, by Joseph Dauben of Herbert Lehman College CUNY, focuses on the mathematics of China. This chapter is divided into nine sections. Two preliminary sections set the context for Chinese mathematics and outline the methods and procedures of counting rods as well as the "out-in" principle used in geometric proof. A translation of the earliest known Chinese mathematical text written on 200 bamboo strips is then presented. The discussion follows with sections on the Gou-go (Pythagorean Theorem), the famous Jiu Thang suan shu (Nine Chapters on the Mathematical Art) as given and commented upon by Liu Hui, and me Sea Island Mathematical Classic. These are probably the most famous ancient Chinese mathematical texts, and it is wonderful to see them collected in one place. Yet, there are more treasures to be found here. Dauben next discusses the "Ten Classics" compiled during the Tang dynasty and presents extensive extracts from several of these. The seventh section of this chapter outlines the mathematical achievements of the Song and Yuan dynasties (960-1368 CE) including the work of Qin Jiushao, Li Zhi, Yang Hui, and Zhu Shije. …