Book:Euclid/The Elements/Book III

Contents

 * Book III: Circles
 * Definitions
 * Proposition 1: Finding Center of Circle
 * Proposition 2: Chord Lies Inside its Circle
 * Proposition 3: Conditions for Diameter to be Perpendicular Bisector
 * Proposition 4: Chords Do Not Bisect Each Other
 * Proposition 5: Intersecting Circles Have Different Centers
 * Proposition 6: Touching Circles Have Different Centers
 * Proposition 7: Relative Lengths of Lines Inside Circle
 * Proposition 8: Relative Lengths of Lines Outside Circle
 * Proposition 9: Condition for Point to be Center of Circle
 * Proposition 10: Two Circles Have At Most Two Points of Intersection
 * Proposition 11: Line Joining Centers of Two Circles Touching Internally
 * Proposition 12: Line Joining Centers of Two Circles Touching Externally
 * Proposition 13: Circles Touch at One Point at Most
 * Proposition 14: Equal Chords in Circle
 * Proposition 15: Relative Lengths of Chords of Circles‎
 * Proposition 16: Line at Right Angles to Diameter of Circle
 * Proposition 17: Construction of Tangent from Point to Circle
 * Proposition 18: Radius at Right Angle to Tangent
 * Proposition 19: Right Angle to Tangent to Circle goes through Center
 * Proposition 20: Inscribed Angle Theorem
 * Proposition 21: Angles in Same Segment of Circle are Equal
 * Proposition 22: Opposite Angles of Cyclic Quadrilateral
 * Proposition 23: Segment on Given Base Unique
 * Proposition 24: Similar Segments on Equal Bases are Equal
 * Proposition 25: Construction of Circle from Segment
 * Proposition 26: Equal Angles in Equal Circles
 * Proposition 27: Angles on Equal Arcs are Equal
 * Proposition 28: Straight Lines Cut Off Equal Arcs in Equal Circles
 * Proposition 29: Equal Arcs of Circles Subtended by Equal Straight Lines
 * Proposition 30: Bisection of an Arc
 * Proposition 31: Relative Sizes of Angles in Segments
 * Proposition 32: Angles made by Chord with Tangent‎
 * Proposition 33: Construction of Segment on Given Line Admitting a Given Angle
 * Proposition 34: Construction of Segment on Given Circle Admitting a Given Angle