This is the first book-length analysis of the techniques and procedures of ancient mathematical commentaries. It focuses on examples in Chinese Sanskrit Akkadian and Sumerian and Ancient Greek presenting the general issues by constant detailed reference to these commentaries of which substantial extracts are included in the original languages and in translation sometimes for the first time. This makes the issues accessible to readers without specialized training in mathematics or in the languages involved. The result is a much richer understanding than was hitherto possible of the crucial role of commentaries in the history of mathematics in four different linguistic areas of the nature of mathematical commentaries in general of the contribution that the study of mathematical commentaries can make to the history of science and to the study of commentaries in general and of the ways in which mathematical commentaries are like and unlike other kinds of commentaries. Language: English