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◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--3-circles / Subsection: Propositions from Book 3

Subsection: Propositions from Book 3

This subsection is dedicated to the propositions of Book 3 of “Euclid’s Elements”.

Table of Contents

  1. Proposition: 3.01: Finding the Center of a given Circle
  2. Proposition: 3.02: Chord Lies Inside its Circle
  3. Proposition: 3.03: Conditions for Diameter to be a Perpendicular Bisector
  4. Proposition: 3.04: Chords do not Bisect Each Other
  5. Proposition: 3.05: Intersecting Circles have Different Centers
  6. Proposition: 3.06: Touching Circles have Different Centers
  7. Proposition: 3.07: Relative Lengths of Lines Inside Circle
  8. Proposition: 3.08: Relative Lengths of Lines Outside Circle
  9. Proposition: 3.09: Condition for Point to be Center of Circle
  10. Proposition: 3.10: Two Circles have at most Two Points of Intersection
  11. Proposition: 3.11: Line Joining Centers of Two Circles Touching Internally
  12. Proposition: 3.12: Line Joining Centers of Two Circles Touching Externally
  13. Proposition: 3.13: Circles Touch at One Point at Most
  14. Proposition: 3.14: Equal Chords in Circle
  15. Proposition: 3.15: Relative Lengths of Chords of Circles
  16. Proposition: 3.16: Line at Right Angles to Diameter of Circle At its Ends Touches the Circle
  17. Proposition: 3.17: Construction of Tangent from Point to Circle
  18. Proposition: 3.18: Radius at Right Angle to Tangent
  19. Proposition: 3.19: Right Angle to Tangent of Circle Goes Through Center
  20. Proposition: 3.20: Inscribed Angle Theorem
  21. Proposition: 3.21: Angles in Same Segment of Circle are Equal
  22. Proposition: 3.22: Opposite Angles of Cyclic Quadrilateral
  23. Proposition: 3.23: Segment on Given Base Unique
  24. Proposition: 3.24: Similar Segments on Equal Bases are Equal
  25. Proposition: 3.25: Construction of Circle from Segment
  26. Proposition: 3.26: Equal Angles and Arcs in Equal Circles
  27. Proposition: 3.27: Angles on Equal Arcs are Equal
  28. Proposition: 3.28: Straight Lines Cut Off Equal Arcs in Equal Circles
  29. Proposition: 3.29: Equal Arcs of Circles Subtended by Equal Straight Lines
  30. Proposition: 3.30: Bisection of Arc
  31. Proposition: 3.31: Relative Sizes of Angles in Segments
  32. Proposition: 3.32: Angles made by Chord with Tangent
  33. Proposition: 3.33: Construction of Segment on Given Line Admitting Given Angle
  34. Proposition: 3.34: Construction of Segment on Given Circle Admitting Given Angle
  35. Proposition: 3.35: Intersecting Chord Theorem
  36. Proposition: 3.36: Tangent Secant Theorem
  37. Proposition: 3.37: Converse of Tangent Secant Theorem

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