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

- Proposition: 5.01: Multiplication of Numbers is Left Distributive over Addition
- Proposition: 5.02: Multiplication of Numbers is Right Distributive over Addition
- Proposition: 5.03: Multiplication of Numbers is Associative
- Proposition: 5.04: Multiples of Terms in Equal Ratios
- Proposition: 5.05: Multiplication of Real Numbers is Left Distributive over Subtraction
- Proposition: 5.06: Multiplication of Real Numbers is Right Distributive over Subtraction
- Proposition: 5.07: Ratios of Equal Magnitudes
- Proposition: 5.08: Relative Sizes of Ratios on Unequal Magnitudes
- Proposition: 5.09: Magnitudes with Same Ratios are Equal
- Proposition: 5.10: Relative Sizes of Magnitudes on Unequal Ratios
- Proposition: 5.11: Equality of Ratios is Transitive
- Proposition: 5.12: Sum of Components of Equal Ratios
- Proposition: 5.13: Relative Sizes of Proportional Magnitudes
- Proposition: 5.14: Relative Sizes of Components of Ratios
- Proposition: 5.15: Ratio Equals its Multiples
- Proposition: 5.16: Proportional Magnitudes are Proportional Alternately
- Proposition: 5.17: Magnitudes Proportional Compounded are Proportional Separated
- Proposition: 5.18: Magnitudes Proportional Separated are Proportional Compounded
- Proposition: 5.19: Proportional Magnitudes have Proportional Remainders
- Proposition: 5.20: Relative Sizes of Successive Ratios
- Proposition: 5.21: Relative Sizes of Elements in Perturbed Proportion
- Proposition: 5.22: Equality of Ratios Ex Aequali
- Proposition: 5.23: Equality of Ratios in Perturbed Proportion
- Proposition: 5.24: Sum of Antecedents of Proportion
- Proposition: 5.25: Sum of Antecedent and Consequent of Proportion