 In this section, we examine the historical development of Euler and Venn diagrams as a case study to illustrate the following aspects: First, this process will show us how one mathematician’s simple intuition about diagramming syllogistic reasoning has gradually been developed into a formal representation system. Second, we will observe different emphases given to different stages of extension and modification of a diagrammatic system. Thirdly and relatedly, this historical development illustrates an interesting tension and trade-off between the expressive power and visual clarity of diagrammatic systems. Most importantly, the reader will witness logicians tackle the issue of whether there is any intrinsic reason that sentential systems, but not diagrammatic systems, could provide us with rigorous proofs, and their success in answering this question in the negative.