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The different waves that had awakened an interest in perspective in various circles on the Continent did not reach the British Isles until the end of the seventeenth century. Paintings were unwanted in the Protestant churches, and in Britain they were not demanded in great quantities in private homes, as had been the case in the Netherlands. The few British painters who could make a living in the early modern period mainly painted portraits with backgrounds that did not require any knowledge of perspective. In addition, the group of British mathematical practitioners and mathematicians did not take up the topic of perspective until the final decades of the seventeenth century. From then on and until around 1750, British tracts on perspective appeared at regular intervals. While all of Continental Europe, except the German states, saw the interest in writing about the subject declined during the second half of the eighteenth century, Britain experienced a boom with almost thirty new publications.

This chapter deals with the literature on perspective published in the seventeenth and eighteenth centuries in the German states, Austria and Switzerland. Although written in German, the contributions by the Alsatian scientist Johann Heinrich Lambert are not discussed in this chapter, because they are so outstanding in the history of perspective that they deserve a separate chapter.

In the history of the mathematical theory of perspective, Lambert’s work constitutes a chapter in itself, partly because of its excellent quality and partly because it is not an obvious part of any continuous development. Lambert put the final touches on thoughts that had been under way for one and a half centuries. Still, it is impossible to say where he got his inspiration. On the other hand, there is no evidence that his way of dealing with perspective had any influence on mathematicians who took up ideas comparable to his. Lambert’s approach, as previously mentioned, involved looking directly at the geometry in the picture plane. Later in the eighteenth century, Gaspard Monge created descriptive geometry by applying a similar idea to a plane containing a plan and an elevation, but it is not very likely that Monge was inspired by Lambert. Similarly, some of Lambert’s ideas pointed towards treating geometry projectively, but once again there are no indications that Lambert’s work influenced the development that led to projective geometry.

About three hundred years after Piero della Francesca presented his perspective construction based on the plan and elevation technique, this perspective method enjoyed a veritable renaissance as part of descriptive geometry. This brief chapter deals with the emergence of descriptive geometry, how the discipline shares one of its basic idea with Lambert’s perspective geometry, and how perspective is treated in descriptive geometry.

After all these pages on the history of perspective, the time has come to ask: What have we learned? In giving partial answers I return to the key issues and questions presented in the introduction. For structural reasons I have changed the order and also reformulated some of the questions. Thus, in the next pages I sum up my findings on the following points:

Finally, I ponder the driving forces behind the theory of perspective.