◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--8-continued-proportion / Subsection: Propositions from Book 8

Subsection: Propositions from Book 8

This subsection contains the propositions from Book 8 of Euclid's “Elements”.

Table of Contents

1. Proposition: 8.01: Geometric Progression with Co-prime Extremes is in Lowest Terms
2. Proposition: 8.02: Construction of Geometric Progression in Lowest Terms
3. Proposition: 8.03: Geometric Progression in Lowest Terms has Co-prime Extremes
4. Proposition: 8.04: Construction of Sequence of Numbers with Given Ratios
5. Proposition: 8.05: Ratio of Products of Sides of Plane Numbers
6. Proposition: 8.06: First Element of Geometric Progression not dividing Second
7. Proposition: 8.07: First Element of Geometric Progression that divides Last also divides Second
8. Proposition: 8.08: Geometric Progressions in Proportion have Same Number of Elements
9. Proposition: Prop. 8.09: Elements of Geometric Progression between Co-prime Numbers
10. Proposition: Prop. 8.10: Product of Geometric Progressions from One
11. Proposition: Prop. 8.11: Between two Squares exists one Mean Proportional
12. Proposition: Prop. 8.12: Between two Cubes exist two Mean Proportionals
13. Proposition: Prop. 8.13: Powers of Elements of Geometric Progression are in Geometric Progression
14. Proposition: Prop. 8.14: Number divides Number iff Square divides Square
15. Proposition: Prop. 8.15: Number divides Number iff Cube divides Cube
16. Proposition: Prop. 8.16: Number does not divide Number iff Square does not divide Square
17. Proposition: Prop. 8.17: Number does not divide Number iff Cube does not divide Cube
18. Proposition: Prop. 8.18: Between two Similar Plane Numbers exists one Mean Proportional
19. Proposition: Prop. 8.19: Between two Similar Solid Numbers exist two Mean Proportionals
20. Proposition: Prop. 8.20: Numbers between which exists one Mean Proportional are Similar Plane
21. Proposition: Prop. 8.21: Numbers between which exist two Mean Proportionals are Similar Solid
22. Proposition: Prop. 8.22: If First of Three Numbers in Geometric Progression is Square then Third is Square
23. Proposition: Prop. 8.23: If First of Four Numbers in Geometric Progression is Cube then Fourth is Cube
24. Proposition: Prop. 8.24: If Ratio of Square to Number is as between Two Squares then Number is Square
25. Proposition: Prop. 8.25: If Ratio of Cube to Number is as between Two Cubes then Number is Cube
26. Proposition: Prop. 8.26: Similar Plane Numbers have Same Ratio as between Two Squares
27. Proposition: Prop. 8.27: Similar Solid Numbers have Same Ratio as between Two Cubes

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