ProofWiki:Books/Euclid/The Elements/Book VII
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Euclid: The Elements: Book VII
Published c. 300 B.C.E.
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
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