Let the Diagram Speak: Compass Arcs and Visual Auxiliaries in Printed Diagrams of Euclid's Elements

The printed Elements in the sixteenth century presented more practical and functional diagrams than those of previous manuscripts. Whereas conventional diagrams were limited to implementing the description of the text, the new diagrams introduced more concise constructions and visual auxiliaries. This change toward more practical and functional diagrams reflects the increased emphasis on the pedagogical value of the diagram. As is evident from the compass arcs upon the diagram, readers of the Elements were invited to draw their own diagrams, deviating from tradition and also from the text. Also, the increased visual auxiliaries such as correspondence markers, dotted lines, and stereoscopic presentations enabled the reader to read diagrams more easily. This backdrop of increased engagement with the diagram made it easier for mathematical novices (tyrones) to learn the Elements. These tool-based and auxiliaries-laden diagrams were more effective for teaching beginners than the earlier, less-functional diagrams. This paper explores the function of these new visual vocabularies and how they were circulated. This survey comprises a brief history of how diagrams began to have their say.