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Subsection: Propositions from Book 11

This subsection contains the propositions from Book 11 of Euclid's “Elements”.

Table of Contents

  1. Proposition: Prop. 11.01: Straight Line cannot be in Two Planes
  2. Proposition: 11.02: Two Intersecting Straight Lines are in One Plane
  3. Proposition: Prop. 11.03: Common Section of Two Planes is Straight Line
  4. Proposition: Prop. 11.04: Line Perpendicular to Two Intersecting Lines is Perpendicular to their Plane
  5. Proposition: Prop. 11.05: Three Intersecting Lines Perpendicular to Another Line are in One Plane
  6. Proposition: Prop. 11.06: Two Lines Perpendicular to Same Plane are Parallel
  7. Proposition: Prop. 11.07: Line joining Points on Parallel Lines is in Same Plane
  8. Proposition: Prop. 11.08: Line Parallel to Perpendicular Line to Plane is Perpendicular to Same Plane
  9. Proposition: Prop. 11.09: Lines Parallel to Same Line not in Same Plane are Parallel to each other
  10. Proposition: Prop. 11.10: Two Lines Meeting which are Parallel to Two Other Lines Meeting contain Equal Angles
  11. Proposition: Prop. 11.11: Construction of Straight Line Perpendicular to Plane from point not on Plane
  12. Proposition: Prop. 11.12: Construction of Straight Line Perpendicular to Plane from point on Plane
  13. Proposition: Prop. 11.13: Straight Line Perpendicular to Plane from Point is Unique
  14. Proposition: Prop. 11.14: Planes Perpendicular to same Straight Line are Parallel
  15. Proposition: Prop. 11.15: Planes through Parallel Pairs of Meeting Lines are Parallel
  16. Proposition: Prop. 11.16: Common Sections of Parallel Planes with other Plane are Parallel
  17. Proposition: Prop. 11.17: Straight Lines cut in Same Ratio by Parallel Planes
  18. Proposition: Prop. 11.18: Plane through Straight Line Perpendicular to other Plane is Perpendicular to that Plane
  19. Proposition: Prop. 11.19: Common Section of Planes Perpendicular to other Plane is Perpendicular to that Plane
  20. Proposition: Prop. 11.20: Sum of Two Angles of Three containing Solid Angle is Greater than Other Angle
  21. Proposition: Prop. 11.21: Solid Angle contained by Plane Angles is Less than Four Right Angles
  22. Proposition: Prop. 11.22: Extremities of Line Segments containing three Plane Angles any Two of which are Greater than Other form Triangle
  23. Proposition: Prop. 11.23: Sum of Plane Angles Used to Construct a Solid Angle is Less Than Four Right Angles
  24. Proposition: Prop. 11.24: Opposite Planes of Solid contained by Parallel Planes are Equal Parallelograms
  25. Proposition: Prop. 11.25: Parallelepiped cut by Plane Parallel to Opposite Planes
  26. Proposition: Prop. 11.26: Construction of Solid Angle equal to Given Solid Angle
  27. Proposition: Prop. 11.27: Construction of Parallelepiped Similar to Given Parallelepiped
  28. Proposition: Prop. 11.28: Parallelepiped cut by Plane through Diagonals of Opposite Planes is Bisected
  29. Proposition: Prop. 11.29: Parallelepipeds on Same Base and Same Height whose Extremities are on Same Lines are Equal in Volume
  30. Proposition: Prop. 11.30: Parallelepipeds on Same Base and Same Height whose Extremities are not on Same Lines are Equal in Volume
  31. Proposition: Prop. 11.31: Parallelepipeds on Equal Bases and Same Height are Equal in Volume
  32. Proposition: Prop. 11.32: Parallelepipeds of Same Height have Volume Proportional to Bases
  33. Proposition: Prop. 11.33: Volumes of Similar Parallelepipeds are in Triplicate Ratio to Length of Corresponding Sides
  34. Proposition: Prop. 11.34: Parallelepipeds are of Equal Volume iff Bases are in Reciprocal Proportion to Heights
  35. Proposition: Prop. 11.35: Condition for Equal Angles contained by Elevated Straight Lines from Plane Angles
  36. Proposition: Prop. 11.36: Parallelepiped formed from Three Proportional Lines equal to Equilateral Parallelepiped with Equal Angles to it forme
  37. Proposition: Prop. 11.37: Four Straight Lines are Proportional iff Similar Parallelepipeds formed on them are Proportional
  38. Proposition: Prop. 11.38: Common Section of Bisecting Planes of Cube Bisect and are Bisected by Diagonal of Cube
  39. Proposition: Prop. 11.39: Prisms of Equal Height with Parallelogram and Triangle as Base

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