The Examination Of Nicomachus And "Introduction To Arithmetic"

In the history of Greek mathematics, the geometry has been the center of thedevelopment of Greek mathematics since100AD. It is the science of arithmetic which iscovered by geometry. Nicomachus’ book Introduction to Arithmetic changes this situation. Itis the first arithmetic book which is completely independent of the system of the geometry. Itis out of geometric forms, and it has opened up new ways of Greek mathematics. By the timethe arithmetic instead of geometry, it becomes the center of attention in Alexandria.Nicomachus’e life and his book would be introduced in this paper. By reading large amountsof data, combining with the insights of scholar, and consulting the information revealed inNicomachus’ book, the author infers Nicomachus’ childhood lives in a wealthy family inGerasa. He lives from the middle of the1stcentury AD to the middle2ndcentury AD. Whenhe goes to school in Alexandria, he is affected by the culture of Alexander, and inherits theidea of philosophy and theory of number from Pythagoreans. In his middle age, he iswelcomed by the nobility. As a tutor of a noble woman who is his sponsor, he writes the bookHarmony Manual for her. This paper focuses on the contents of Introduction to Arithmetic,and through studying this book, the author infers the source of this book, studies therelationship between Introduction to Arithmetic and Euclid, and elaborates significance of thebook. The writing style of Introduction to Arithmetic is more irregular than the axiom systemof Euclid. It has too many modifiers, and there is no proof in the book. As it cites manyexamples and some of them are wrong. However, it still plays an important role in thedevelopment of Greek arithmetic. Its contents cover a wide range of foundation knowledge,and as a textbook, it is very important for basic teaching. Introduction to Arithmetic which istranslated by Boethius is replaced by Arabic arithmetic works as a textbook in Europe untilGrusades (1095-1291).