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Propositions from Book 3

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

| | | | created: 2014-11-13 22:31:53 | modified: 2014-11-13 22:32:00 | by: bookofproofs

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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