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Leon Battista Alberti was the first to present a perspective construction in writing. He did so in 1435 in his , in which he also introduced a model for perspective representation. Alberti’s own way of expressing his definition is described in chapter II, but here I find it convenient to translate his definition into modern terms (figure I.1): Given a picture plane and an eye point , an object behind is depicted upon it by mapping each point in the object upon the point in which the line cuts the surface . This is the same as saying that the object is mapped upon by a perspective or central projection with its centre in .

This chapter is devoted to two of the oldest written sources on perspective constructions — and the main sources for — composed by Leon Battista Alberti and Piero della Francesca, respectively. These authors were universally gifted men with rather different approaches to perspective. Alberti was a theorist who took a strong interest in painting, architecture, and sculpture, and in the performance of these arts. He seems, however, to have been more attracted to the theory of painting than to the practice of perspective and its geometrical foundation. Piero, on the other hand, was an artist and a mathematician who wanted to connect these two disciplines. He presented many perspective constructions in great detail and speculated about how they were related to mathematics and optics.

As far as this book is concerned, one of Italy’s most famous painters and great masters, Leonardo da Vinci (1452–1519), presents a serious problem. On the one hand he was too important a thinker to be ignored, and on the other hand his ideas on perspective were so many — and often so perplexing — that a thorough presentation would require a much longer study than can be included here. Fortunately, many facets of Leonardo and perspective have already been discussed by competent historians. Keeping the extensive literature and the complications in mind, I have decided to be relatively brief on Leonardo with the somewhat blunt argument that in general his thoughts on perspective only became known after the period I consider here, hence exerting very little influence on developments. In fact, had his ideas been known, he would have contributed much more to raising doubts about perspective than to creating a mathematical understanding of the subject.

The prominence that perspective enjoyed in Italy during the fifteenth century continued into the . More and more people became acquainted with the subject, and the number of those who appreciated it, applied it, and wrote about it, increased steadily. As the century progressed, the mathematical understanding of the rules of perspective also grew deeper.

There can be no doubt that Italian sources brought about the introduction of perspective constructions North of the Alps: a connection to Italy can be established for all of the early influential non-Italians who published works on perspective. However, we do not know much about the channels through which the knowledge of perspective spread. As was the case in Italy, the texts from the North do not allow us to follow a continuous development, but indicate that essential steps were taken in workshops, or other places, without being recorded.

For reasons soon to be explained, I consider Guidobaldo del Monte to be the father of the mathematical theory of perspective and hence pay considerable attention to his work. It is natural to take up Simon Stevin’s work on perspective in connection with Guidobaldo, since Stevin’s contributions are a direct continuation of some of Guidobaldo’s accomplishments. In fact, it was through reading Guidobaldo that Stevin came to see the fundamental problems of perspective, and he was such a gifted reader that he understood the master’s ideas better than the master himself.

In previous chapters we have seen how the early Dutch literature on perspective was much influenced by Italians. Serlio’s work caught Vredeman de Vries’s interest, and Guidobaldo’s book was an extremely important source of inspiration for Stevin. This chapter deals, among other things, with how these impacts influenced the further development in the Northern Netherlands.

This chapter is relatively brief since, as stressed earlier, I have chosen to devote most of my attention to the episodes in the history of perspective that contributed to the development of a mathematical understanding of perspective procedures — and from this point of view there is not much to write about Italian perspective in the seventeenth and eighteenth centuries. Italy, which had completely dominated the field up until 1600, lost her leading position due to a drastic decline in the Italians’ interest in the mathematical aspect of perspective.

During the Renaissance and the first decades of the seventeenth-century Italian scholars dominated the fields of pure and applied mathematics. In the 1630s French mathematicians became as active as their Italian colleagues, and in the following decades they took over the leadership, championing an immense growth in pure mathematics. The history of the mathematical theory of perspective generally leads us to other people than the main protagonists in the history of mathematics. Nevertheless, when it comes to writing on perspective, there was a contemporary shift from Italy to France.