This subsection contains the propositions from Book 9 of Euclid's “Elements”.

- Proposition: Prop. 9.01: Product of Similar Plane Numbers is Square
- Proposition: Prop. 9.02: Numbers whose Product is Square are Similar Plane Numbers
- Proposition: Prop. 9.03: Square of Cube Number is Cube
- Proposition: Prop. 9.04: Cube Number multiplied by Cube Number is Cube
- Proposition: Prop. 9.05: Number multiplied by Cube Number making Cube is itself Cube
- Proposition: Prop. 9.06: Number Squared making Cube is itself Cube
- Proposition: Prop. 9.07: Product of Composite Number with Number is Solid Number
- Proposition: Prop. 9.08: Elements of Geometric Progression from One which are Powers of Number
- Proposition: Prop. 9.09: Elements of Geometric Progression from One where First Element is Power of Number
- Proposition: Prop. 9.10: Elements of Geometric Progression from One where First Element is not Power of Number
- Proposition: Prop. 9.11: Elements of Geometric Progression from One which Divide Later Elements
- Proposition: Prop. 9.12: Elements of Geometric Progression from One Divisible by Prime
- Proposition: Prop. 9.13: Divisibility of Elements of Geometric Progression from One where First Element is Prime
- Theorem: Prop. 9.14: Fundamental Theorem of Arithmetic
- Proposition: Prop. 9.15: Sum of Pair of Elements of Geometric Progression with Three Elements in Lowest Terms is Co-prime to other Element
- Proposition: Prop. 9.16: Two Co-prime Integers have no Third Integer Proportional
- Proposition: Prop. 9.17: Last Element of Geometric Progression with Co-prime Extremes has no Integer Proportional as First to Second
- Proposition: Prop. 9.18: Condition for Existence of Third Number Proportional to Two Numbers
- Proposition: Prop. 9.19: Condition for Existence of Fourth Number Proportional to Three Numbers
- Proposition: Prop. 9.20: Infinite Number of Primes
- Proposition: Prop. 9.21: Sum of Even Numbers is Even
- Proposition: Prop. 9.22: Sum of Even Number of Odd Numbers is Even
- Proposition: Prop. 9.23: Sum of Odd Number of Odd Numbers is Odd
- Proposition: Prop. 9.24: Even Number minus Even Number is Even
- Proposition: Prop. 9.25: Even Number minus Odd Number is Odd
- Proposition: Prop. 9.26: Odd Number minus Odd Number is Even
- Proposition: Prop. 9.27: Odd Number minus Even Number is Odd
- Proposition: Prop. 9.28: Odd Number multiplied by Even Number is Even
- Proposition: Prop. 9.29: Odd Number multiplied by Odd Number is Odd
- Proposition: Prop. 9.30: Odd Divisor of Even Number Also Divides Its Half
- Proposition: Prop. 9.31: Odd Number Co-prime to Number is also Co-prime to its Double
- Proposition: Prop. 9.32: Power of Two is Even-Times Even Only
- Proposition: Prop. 9.33: Number whose Half is Odd is Even-Times Odd
- Proposition: Prop. 9.34: Number neither whose Half is Odd nor Power of Two is both Even-Times Even and Even-Times Odd
- Proposition: 9.35: Sum of Geometric Progression
- Proposition: 9.36: Theorem of Even Perfect Numbers (First Part)