There has been some disagreement about when circles (or closed curves) began being used for representing classical syllogisms. They seem to have first been put to this use in the Middle Ages. However, there seems to be agreement that it was Leonhrad Euler, in the eighteenth century, who proposed using circles to illustrate relations between classes. This diagrammatic method of Euler's was greatly improved by a nineteenth century logician John Venn. And in this century, it was Charles Peirce who made a great contribution to the further development of Venn diagrams.

This chapter explores the essence of Euler diagrams and their descendants, and will serve to prepare the reader for my approach to Venn diagrams presented in the following chapters. In each section, along with the main ideas of each system and its limits, I focus on how some of the main limits of one system are overcome by the following system. That is, the Venn system solves some of the main problems that the Euler system has. This improvement was significant enough to make necessary a distinction between Euler diagrams and Venn diagrams. I will show that Peirce's revolutionary ideas about diagrams not only overcame some important defects of Venn diagrams but opened the way to a totally new horizon for logical diagrams. This last aspect will be discussed in detail in the third section. I will also point out where this new horizon stopped, and will claim that my approach to Venn diagrams (in Chapters 3 and 4) is the natural completion of these predecessors' incomplete projects.