chapter 2 arithmetic in euclid s elements we tend to think of euclid s elements as a compendium of geometry but as we have already noted books 7 8 and ...
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...Chapter arithmetic in euclid s elements we tend to think of as a compendium geometry but have already noted books and are devoted elementary number theory will give some indication key ideas these they remain relevant this day book begins with denitions not all them especially interesting order appreciate what say must recall the subtle distinction between magnitude that existed greek mathematics far concerned word means positive whole or integer furthermore there is no zero called here unit considered be an by virtue which each things exist one multitude composed units part less greater when it measures multiple measured prime alone numbers another those common measure composite perfect equal its own parts if mean divides greatest two their gcd proofs given do use symbols for would today instead largely verbal rhetorical often represent length line segment then argue using lengths justify his reasoning several fundamental such encounter rst year algebra course stated proved describe f...