This chapter discusses the importance of symbols to the development of mathematics. It begins by analyzing the oldest surviving copy of Euclid's Elements, MS D'Orville 301, which shows how to prove simple identities but lacks any algebraic symbols indicating powers or plus or minus. Nevertheless, the Elements gave mathematics its fundamental nature, its first model of proof. The chapter goes on to consider one of the earliest extant histories of geometry, Proclus's A Commentary on the First Book of Euclid's Elements, and the Pythagorean theorem. It also describes how Alexandria continued to be the center for learning and scholarship in mathematics, science, and medicine for 500 years after Euclid's time. Finally, it examines Diophantus's masterwork and its influence on the development of algebra, with particular emphasis on his use of symbols for powers and unknowns.
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