# Book:Nicomachus of Gerasa/Introduction to Arithmetic

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## Nicomachus of Gerasa:

## Contents

## Nicomachus of Gerasa: *Introduction to Arithmetic*

Published $\text {c. 100 B.C.E}$.

## Subject Matter

## Overview

This appears to be the first (or at least, one of the first) books to treat arithmetic as a separate discipline from geometry.

As a useful textbook it is limited.

The theorems are unproved, and in many cases incorrect, being the result of guesswork based on limited examples.

As an example, he states that:

- The $n$th perfect number has $n$ digits, and
- All perfect numbers end in $6$ and $8$ alternately.

These statements are false deductions from the four perfect numbers known at the time, namely $6, 28, 496, 8128$.

## Critical Appraisal

Apparently Pappus despised it, as did many mathematicians of his day.

However, as it was around during the time when there was very little progress in mathematical thought in the Western world, this text became a standard school text for a thousand years.

## Notable Translations and Editions

- c. 150 C.E.: a Latin translation by Apuleius

- c. 500 C.E.: a Latin translation by Boethius