The book ''Introduction to Arithmetic'' ( grc-gre, Ἀριθμητικὴ εἰσαγωγή, ''Arithmetike eisagoge'') is the only extant work on mathematics by

Nicomachus Nicomachus of Gerasa ( grc-gre, Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician and music theorist, best known for his works ''Introduction to Arithmetic'' and '' Manual of Harmonics'' in Greek. He was born i ...

(60–120 AD).

Summary

The work contains both philosophical prose and basic mathematical ideas. Nicomachus refers to

Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...

quite often, and writes that

philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. S ...

can only be possible if one knows enough about mathematics. Nicomachus also describes how

natural numbers In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal n ...

and basic mathematical ideas are eternal and unchanging, and in an abstract realm. It consists of two books, twenty-three and twenty-nine chapters, respectively. Although he was preceded by the

Babylonians Babylonia (; Akkadian: , ''māt Akkadī'') was an ancient Akkadian-speaking state and cultural area based in the city of Babylon in central-southern Mesopotamia (present-day Iraq and parts of Syria). It emerged as an Amorite-ruled state ...

and the

Chinese Chinese can refer to: * Something related to China * Chinese people, people of Chinese nationality, citizenship, and/or ethnicity **''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation ** List of ethnic groups in China, people of v ...

, Nicomachus provided one of the earliest Greco-Roman

multiplication table In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essen ...

s, whereas the oldest extant Greek multiplication table is found on a wax tablet dated to the 1st century AD (now found in the

British Museum The British Museum is a public museum dedicated to human history, art and culture located in the Bloomsbury area of London. Its permanent collection of eight million works is among the largest and most comprehensive in existence. It docu ...

Influence

The ''Introduction to Arithmetic'' of Nicomachus was a standard textbook in Neoplatonic schools and become the basis of the Boethius' treatise titled '' De institutione musica''. The ''Arithmetic'' (in Latin: ''De Institutione Arithmetica'') of Boethius was a

Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...

paraphrase A paraphrase () is a restatement of the meaning of a text or passage using other words. The term itself is derived via Latin ', . The act of paraphrasing is also called ''paraphrasis''. History Although paraphrases likely abounded in oral tr ...

and a partial translation of the ''Introduction to Arithmetic''. The work of Boethius on arithmetic and music was exposed in the context of the '' Quadrivium'' liberal arts and had a great diffusion during the

Middle Age In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire a ...

Editions

* Nicomachus of Gerasa ''Introduction to arithmetic'', translated into English by Martin Luther D'Ooge; with studies in Greek arithmetic by Frank Egleston Robbins and Louis Charles Karpinski, University of Michigan studies (London: Macmillan, 1926). * Nicomachus of Gerasa ''Introduction to arithmetic'', translated into English by Martin Luther D'Ooge; with studies in Greek arithmetic by Frank Egleston Robbins and Louis Charles Karpinski (London: Johnson Reprint Corp., 1972).

References

Bibliography

; Archivistic sources *

External links

* Nicomachus
"Introduction to Arithmetic"
translated by ''Martin Luther D'Ooge'' at archive.org. *
Nicomachus of Gerasa: Introduction to Arithmetic
' (1926) translated in English by Martin Luther D'Ooge with studies in Greek arithmetic by Frank Egleston Robbins and

Louis Charles Karpinski Louis Charles Karpinski (5 August 1878 – 25 January 1956) was an American mathematician. Background Louis Charles Karpinski was born on August 5, 1878, in Rochester, New York. His parents were Henry Hermanagle Karpinski of Warsaw, Poland, an ...