Reviel Netz的學術著作The Shaping of Deduction in Greek Mathematics（1999）被學界認為是古希臘數學史學界最重要的著作之一。他發現古希臘數學圖形有一個明顯的特徵，亦即，圖形中總是會出現字母作為圖形上的標示。藉由這個特點，在面對無古代史料現存的困境下，Netz提出了一個以文字作為分析對象的古希臘數學圖形研究方法。然而，其他近年來的研究在比較幾個希臘數學著作的中世紀抄本以及現代版本中的圖形的過程中，發現即便是用於同一個數學命題的圖形也可能有極大的差異。而這樣的差異可能大大影響研究者對古代圖形的詮釋。因此，進一步檢視這些圖形的差異以及分析現存史料之間的關聯性便顯得更為重要。
　　在這篇論文中，筆者將從四個面向來討論歐幾里得《幾何原本》中數學圖形的流傳。首先，筆者將討論學界近來對於希臘數學圖形的詮釋，並分析其優缺點以及方法論上的問題。其次，筆者將進一步檢視現存史料中圖形的差異，並以數據化的方式呈現出這些差異，探討某些後世圖形上的特徵是否可能也存在於古代圖形之中。第三，筆者將探討文本分析以及生物譜系學的方法在版本分析上的應用，並以這些方法進行版本分析，嘗試分析圖形之間可能的關聯性及譜系圖。最後，筆者將以十六世紀的英國學者Robert Recorde為案例，藉由比較與其他文藝復興時期的數學圖形之差異，分析改變既有數學圖形的可能理由，以此進一步討論圖形是在哪些可能的因素或環境下被改變。

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.

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