◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--7-elementary-number-theory / Subsection: Propositions from Book 7

Subsection: Propositions from Book 7

This subsection contains the propositions from Book 7 of Euclid's “Elements”.

Table of Contents

1. Proposition: 7.01: Sufficient Condition for Coprimality
2. Proposition: 7.02: Greatest Common Divisor of Two Numbers - Euclidean Algorithm
3. Proposition: 7.03: Greatest Common Divisor of Three Numbers
4. Proposition: 7.04: Smaller Numbers are Dividing or not Dividing Larger Numbers
5. Proposition: 7.05: Divisors Obey Distributive Law (Sum)
6. Proposition: 7.06: Division with Quotient and Remainder Obeys Distributive Law (Sum)
7. Proposition: 7.07: Divisors Obey Distributive Law (Difference)
8. Proposition: 7.08: Division with Quotient and Remainder Obeys Distributivity Law (Difference)
9. Proposition: 7.09: Alternate Ratios of Equal Fractions
10. Proposition: 7.10: Multiples of Alternate Ratios of Equal Fractions
11. Proposition: 7.11: Proportional Numbers have Proportional Differences
12. Proposition: 7.12: Ratios of Numbers is Distributive over Addition
13. Proposition: 7.13: Proportional Numbers are Proportional Alternately
14. Proposition: 7.14: Proportion of Numbers is Transitive
15. Proposition: 7.15: Alternate Ratios of Multiples
16. Proposition: 7.16: Natural Number Multiplication is Commutative
17. Proposition: 7.17: Multiples of Ratios of Numbers
18. Proposition: 7.18: Ratios of Multiples of Numbers
19. Proposition: 7.19: Relation of Ratios to Products
20. Proposition: 7.20: Ratios of Fractions in Lowest Terms
21. Proposition: 7.21: Co-prime Numbers form Fraction in Lowest Terms
22. Proposition: 7.22: Numbers forming Fraction in Lowest Terms are Co-prime
23. Proposition: 7.23: Divisor of One of Co-prime Numbers is Co-prime to Other
24. Proposition: 7.24: Integer Co-prime to all Factors is Co-prime to Whole
25. Proposition: 7.25: Square of Co-prime Number is Co-prime
26. Proposition: 7.26: Product of Co-prime Pairs is Co-prime
27. Proposition: 7.27: Powers of Co-prime Numbers are Co-prime
28. Proposition: 7.28: Numbers are Co-prime iff Sum is Co-prime to Both
29. Proposition: 7.29: Prime not Divisor implies Co-prime
30. Proposition: 7.30: Euclidean Lemma
31. Proposition: 7.31: Existence of Prime Divisors
32. Proposition: 7.32: Natural Number is Prime or has Prime Factor
33. Proposition: 7.33: Least Ratio of Numbers
34. Proposition: 7.34: Existence of Least Common Multiple
35. Proposition: 7.35: Least Common Multiple Divides Common Multiple
36. Proposition: 7.36: Least Common Multiple of Three Numbers
37. Proposition: 7.37: Integer Divided by Divisor is Integer
38. Proposition: 7.38: Divisor is Reciprocal of Divisor of Integer
39. Proposition: 7.39: Least Number with Three Given Fractions

Thank you to the contributors under CC BY-SA 4.0!

Github: