This monograph describes how the understanding of the geometry behind perspective evolved between the years 1435 and 1800 and how new insights within the mathematical theory of perspective influenced the way the discipline was presented in textbooks. In order to throw light on these issues, the author has chosen to focus on a number of key questions, including:

. What were the essential innovations in the mathematical theory of perspective?

. Was there any interplay between the developments of the mathematical theory of perspective and other branches of geometry?

. What were the driving forces behind working out an advanced mathematical theory of perspective?

. Were there regional differences in the mathematical approach to perspective? And if so, how did they relate to local applications of perspective?

. How did mathematicians and practitioners of perspective interact?

In fact, the last issue is touched upon so often that a considerable part of this book could be seen as a case study of the difficulties in bridging the gap between those with mathematical knowledge and the mathematically untrained practitioners who wish to use this knowledge.

The author has based her work on more than 200 books, booklets, and pamphlets on perspective. She starts with the first treatise known to deal with geometrical perspective, Leon Alberti Battista's De pictura, and ends around 1800, when the theory of mathematical perspective as an independent discipline was absorbed first into descriptive geometry and later into projective geometry.

The prominent protagonists are Guidobaldo del Monte, Simon Stevin, Willem 'sGravesande, Brook Taylor, and Johann Heinrich Lambert. As far as data were available, the author has provided brief biographies of all the writers on perspective whose work she studied. The book also contains an extensive bibliography divided into two parts, one for primary sources on perspective, and the second for all other literature.

Kirsti Andersen is Associate Professor of History of Science at the University of Aarhus, Denmark. She is the author of Brook Taylor's Work on Linear Perspective, also published by Springer.

Zusammenfassung
Key Issues ver since the late 1970s when Pia Holdt, a student of mine at the time, and Jed Buchwald, a colleague normally working in another field, made E me aware of how fascinating the history of perspective constructions is, I have wanted to know more. My studies have resulted in the present book, in which I am mainly concerned with describing how the understanding of the geometry behind perspective developed and how, and to what extent, new insights within the mathematical theoryof perspective influenced the way the discipline was presented in textbooks. In order to throw light on these aspects of the history of perspective, I have chosen to focus upon a number of key questions that I have divided into two groups. Questions Concerning the History of Geometrical Perspective • How did geometrical constructions of perspective images emerge? • How were they understood mathematically? • How did the geometrical constructions give rise to a mathematical theory of perspective? • How did this theory evolve? Inconnectionwith the last question it is natural to takeup the following themes.

Inhalt
The Birth of Perspective.- Alberti and Piero della Francesca.- Leonardo da Vinci.- Italy in the Cinquecento.- North of the Alps Before 1600.- The Birth of the Mathematical Theory of Perspective Guidobaldo and Stevin.- The Dutch Development after Stevin.- Italy after Guidobaldo.- France and the Southern Netherlands after 1600.- Britain.- The German-Speaking Areas after 1600.- Lambert.- Monge Closing a Circle.- Summing Up.