ProofWiki:Books/Euclid/The Elements/Book III
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Euclid: The Elements: Book III
Published c. 300 B.C.E.
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
- Proposition 35: Intersecting Chord Theorem
- Proposition 36: Tangent Secant Theorem
- Proposition 37: Converse of Tangent Secant Theorem
