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

- Proposition: 3.01: Finding the Center of a given Circle
- Proposition: 3.02: Chord Lies Inside its Circle
- Proposition: 3.03: Conditions for Diameter to be a Perpendicular Bisector
- Proposition: 3.04: Chords do not Bisect Each Other
- Proposition: 3.05: Intersecting Circles have Different Centers
- Proposition: 3.06: Touching Circles have Different Centers
- Proposition: 3.07: Relative Lengths of Lines Inside Circle
- Proposition: 3.08: Relative Lengths of Lines Outside Circle
- Proposition: 3.09: Condition for Point to be Center of Circle
- Proposition: 3.10: Two Circles have at most Two Points of Intersection
- Proposition: 3.11: Line Joining Centers of Two Circles Touching Internally
- Proposition: 3.12: Line Joining Centers of Two Circles Touching Externally
- Proposition: 3.13: Circles Touch at One Point at Most
- Proposition: 3.14: Equal Chords in Circle
- Proposition: 3.15: Relative Lengths of Chords of Circles
- Proposition: 3.16: Line at Right Angles to Diameter of Circle At its Ends Touches the Circle
- Proposition: 3.17: Construction of Tangent from Point to Circle
- Proposition: 3.18: Radius at Right Angle to Tangent
- Proposition: 3.19: Right Angle to Tangent of Circle Goes Through Center
- Proposition: 3.20: Inscribed Angle Theorem
- Proposition: 3.21: Angles in Same Segment of Circle are Equal
- Proposition: 3.22: Opposite Angles of Cyclic Quadrilateral
- Proposition: 3.23: Segment on Given Base Unique
- Proposition: 3.24: Similar Segments on Equal Bases are Equal
- Proposition: 3.25: Construction of Circle from Segment
- Proposition: 3.26: Equal Angles and Arcs in Equal Circles
- Proposition: 3.27: Angles on Equal Arcs are Equal
- Proposition: 3.28: Straight Lines Cut Off Equal Arcs in Equal Circles
- Proposition: 3.29: Equal Arcs of Circles Subtended by Equal Straight Lines
- Proposition: 3.30: Bisection of Arc
- Proposition: 3.31: Relative Sizes of Angles in Segments
- Proposition: 3.32: Angles made by Chord with Tangent
- Proposition: 3.33: Construction of Segment on Given Line Admitting Given Angle
- Proposition: 3.34: Construction of Segment on Given Circle Admitting Given Angle
- Proposition: 3.35: Intersecting Chord Theorem
- Proposition: 3.36: Tangent Secant Theorem
- Proposition: 3.37: Converse of Tangent Secant Theorem