Book:Euclid/The Elements/Book VII

Contents

 * Book VII: Number Theory
 * Definitions
 * Proposition 1: Sufficient Condition for Coprimality
 * Proposition 2: Greatest Common Divisor of Two Numbers (Euclidean Algorithm)
 * Proposition 3: Greatest Common Divisor of Three Numbers
 * Proposition 4: Natural Number Divisor or Multiple of Divisor of Another
 * Proposition 5: Divisors Obey Distributive Law
 * Proposition 6: Multiples of Divisors Obey Distributive Law
 * Proposition 7: Subtraction of Divisors Obeys Distributive Law
 * Proposition 8: Subtraction of Multiples of Divisors Obeys Distributive Law
 * Proposition 9: Alternate Ratios of Equal Fractions
 * Proposition 10: Multiples of Alternate Ratios of Equal Fractions
 * Proposition 11: Proportional Numbers have Proportional Differences
 * Proposition 12: Ratios of Numbers is Distributive over Addition
 * Proposition 13: Proportional Numbers are Proportional Alternately
 * Proposition 14: Proportion of Numbers is Transitive
 * Proposition 15: Alternate Ratios of Multiples
 * Proposition 16: Natural Number Multiplication is Commutative
 * Proposition 17: Multiples of Ratios of Numbers
 * Proposition 18: Ratios of Multiples of Numbers
 * Proposition 19: Relation of Ratios to Products‎
 * Proposition 20: Ratios of Fractions in Lowest Terms
 * Proposition 21: Numbers in Fractions in Lowest Terms are Coprime