◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--5-proportion / Subsection: Propositions from Book 5

Subsection: Propositions from Book 5

This subsection contains the propositions from Book 5 of Euclid's “Elements”.

Table of Contents

1. Proposition: 5.01: Multiplication of Numbers is Left Distributive over Addition
2. Proposition: 5.02: Multiplication of Numbers is Right Distributive over Addition
3. Proposition: 5.03: Multiplication of Numbers is Associative
4. Proposition: 5.04: Multiples of Terms in Equal Ratios
5. Proposition: 5.05: Multiplication of Real Numbers is Left Distributive over Subtraction
6. Proposition: 5.06: Multiplication of Real Numbers is Right Distributive over Subtraction
7. Proposition: 5.07: Ratios of Equal Magnitudes
8. Proposition: 5.08: Relative Sizes of Ratios on Unequal Magnitudes
9. Proposition: 5.09: Magnitudes with Same Ratios are Equal
10. Proposition: 5.10: Relative Sizes of Magnitudes on Unequal Ratios
11. Proposition: 5.11: Equality of Ratios is Transitive
12. Proposition: 5.12: Sum of Components of Equal Ratios
13. Proposition: 5.13: Relative Sizes of Proportional Magnitudes
14. Proposition: 5.14: Relative Sizes of Components of Ratios
15. Proposition: 5.15: Ratio Equals its Multiples
16. Proposition: 5.16: Proportional Magnitudes are Proportional Alternately
17. Proposition: 5.17: Magnitudes Proportional Compounded are Proportional Separated
18. Proposition: 5.18: Magnitudes Proportional Separated are Proportional Compounded
19. Proposition: 5.19: Proportional Magnitudes have Proportional Remainders
20. Proposition: 5.20: Relative Sizes of Successive Ratios
21. Proposition: 5.21: Relative Sizes of Elements in Perturbed Proportion
22. Proposition: 5.22: Equality of Ratios Ex Aequali
23. Proposition: 5.23: Equality of Ratios in Perturbed Proportion
24. Proposition: 5.24: Sum of Antecedents of Proportion
25. Proposition: 5.25: Sum of Antecedent and Consequent of Proportion

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