Introduction to Arithmetic

This is Martin Luther D'Ooge's 1926 Macmillan translation of Nicomachus of Gerasa's Introduction to Arithmetic, composed in Greek around 100 CE and long treated as the standard textbook that carried Pythagorean number theory, figurate numbers and the doctrine of proportion into late antique and medieval curricula through Boethius's Latin adaptation. Its strength is that it is a primary text in a widely used scholarly translation, the edition most cited in the history of mathematics literature for exactly this reason. Its limits are the limits of any nearly two thousand year old technical work: Nicomachus's own arithmetic is philosophical and pedagogical rather than rigorous by later mathematical standards, several of his claimed proofs are informal, and the text should be read as a record of what Pythagorean number mysticism taught rather than as settled mathematics.