Book:Euclid/The Elements/Book III

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Euclid: The Elements: Book III

Published $c. 300 B.C.E$.


Contents

Book $\text{III}$: Circles

Definitions
Proposition $1$: Finding Center of Circle
Porism to 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
Porism to 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 of 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 sum to Two Right Angles
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 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 Given Angle
Proposition $34$: Construction of Segment on Given Circle Admitting Given Angle
Proposition $35$: Intersecting Chord Theorem
Proposition $36$: Tangent Secant Theorem
Proposition $37$: Converse of Tangent Secant Theorem