Nicomachus‘ Introduction to Arithmetic

Nicomachus was a philosopher-mathematician living circa 200 AD and originally from the city of today‘s Jerash, Jordan. His work was foundational both for the study of mathematics in the liberal arts curriculum and for the mathematical philosophy of the later Platonists. His work on Number (‘Arithmetic‘) begins with a Platonic preamble exhorting the reader to lift the eyes of the soul from the world of change to the world of stable things, namely that of mathematics. The work outlines reasons why the study of Arithmetic comes prior to Geometry, Music, and Astronomy. The sections on mathematical arithmetic include an overview of number in itself and number in relation, surveying the topics of: odd and even, prime and composite, perfect numbers, ratios, planar numbers, solid numbers, progressions of ratios, and the means of progressions. Attention is particularly drawn to musical ratios. Also included are moral analogies such as a comparison between the properties of perfect numbers and the golden mean theory of virtue. This edition is a replication of Martin D‘Ooge‘s classic 1926 translation, edited to render formulae and diagrams with clarity (no scanned pages). This edition also reintroduces D‘Ooge‘s copious notes on the text which were not included in later printed editions. These notes include descriptions of Nicomachus‘ proposed mathematical relationships written in modern notation as well as cross-references to Iamblichus, Theon, Boethius, and Philoponus in the original Greek and Latin. This text is an indispensible reference for the stuy of the history of mathematics, the relationship of philosophy to mathematics, and for mathematical study within the traditional seven liberal arts.