Abstract
R. Netz’s monograph The Shaping of Deduction in Greek Mathematics (1999) has been often considered one of the most important recent works on the history of Greek mathematics. Netz provided a new methodology that he applied to his study on the use of lettered diagrams and on the language of ancient Greek mathematical treatises, which appeared to be efficient in the situation when the original diagrams were lacking. In turn, Saito and Sidoli (2012) compared manuscript diagrams and their modern counterparts and suggested, “The diagrams in modern editions … are often historically misleading and occasionally even mathematically misleading.” They showed that the difference between Medieval and modern diagrams is large, and if the researchers do not consult ancient editions, some information represented in ancient diagrams would not be noticed. Therefore, it is necessary to investigate the differences of diagram further, and to establish a method for studying the rela-tionships of the extant sources in order to identify the characteristics traceable to Antiquity. In this thesis, I will discuss several aspects of the history of the diagrams in Euclidean Elements. (1) I will discuss the recent interpretations of Greek diagrams, especially of the diagrams of the Elements, in order to evaluate the current ap-proaches to ancient diagrams in the studies of the Elements. (2) I will present the differences between the extant editions of the Elements dated from the 9th to 20th century, and demonstrate how extant diagrams can be different from each other. (3) I will discuss the filiation of diagrams and build the relationship trees for the dia-grams of extant editions with the methods of textual analysis and phylogenetics, in order to identify the features of hypothetical common ancestors of extant diagrams. (4) I will study the reasons of changing diagrams in the works of Robert Recorde (c. 1512 – 1558). By comparing his new diagrams to the other contemporary ones, I will discuss the reason why the early modern editors attempted to revise the diagrams, and how exactly the diagrams were changed.