Description of details of Euclid's works in development of theory of number system
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He began Book VII of his Elements by defining a number as “a multitude composed of units.” The plural here excluded 1; for Euclid, 2 was the smallest “number.” He later defined a prime as a number “measured by a unit alone” (i.e., whose only proper divisor is 1), a composite as a number that is not From there, Euclid proved a sequence of theorems that marks the beginning of number theory as a mathematical (as opposed to a numerological) enterprise. Four Euclidean propositions deserve special mention.
The first, Proposition 2 of Book VII, is a procedure for finding the greatest common divisor of two whole numbers. This fundamental result is now called the Euclidean algorithm in his honour.
prime, and a perfect number as one that equals the sum of its “parts” (i.e., its proper divisors).