The nature and purpose of analysis. A definition (Q2762623)

The book is devoted to the study of one of the methods of mathematics, namely analysis (as opposed to synthesis). In Chapter I the type of analysis applied in proving theorems and in solving problems by ancient Greeks is considered. Chapter II is devoted to other forms of analysis which appeared both in Greek and Arabic mathematics. Further (Chapter III) reasons from using the method of analysis are studied. The last three chapters, which according to the author are more important than the first three, are devoted to the discussion of particular works from the point of view of the book. In Chapter IV ``Data'' of Euclid are discussed (not only directly but also through their applications by Pappus and Ibn-al-Haytham). In Chapter V new forms of analysis in ``La Géométrie'' of Descartes are considered, and finally in Chapter VI the heritage of Apollonius with respect to the problem of analysis is studied. The book has a historical and methodological character.