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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 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.