ARITHMETICAL PROBLEMS 

1. 
Archimedes' Problem Bovinum 

2. 
The Weight Problem of Bachet de Méziriac 

3. 
Newton's Problem of the Fields and Cows 

4. 
Berwick's Problem of the Seven Sevens 

5. 
Kirkman's Schoolgirl Problem 

6. 
The BernoulliEuler Problem of the Misaddressed Letters 

7. 
Euler's Problem of Polygon Division 

8. 
Lucas' Problem of the Married Couples 

9. 
Omar Khayyam's Binomial Expansion 

10. 
Cauchy's Mean Theorem 

11. 
Bernoulli's Per Sum Problem 

12. 
The Euler Number 

13. 
Newton's Exponential Series 

14. 
Nicolaus Macerator's Logarithmic Series 

15. 
Newton's Sine and Cosine Series 

16. 
André's Derivation of the Secant and Tangent Series 

17. 
Gregory's Arc Tangent Series 

18. 
Buffon's Needle Problem 

19. 
The FermatEuler Prime Number Theorem 

20. 
The Fermat Equation 

21. 
The FermatGauss Impossibility Theorem 

22. 
The Quadratic Reciprocity Law 

23. 
Gauss' Fundamental Theorem of Algebra 

24. 
Sturm's Problem of the Number of Roots 

25. 
Abel's Impossibility Theorem 

26. 
The HermiteLindemann Transcendence Theorem 

PLANIMETRIC PROBLEMS 

27. 
Euler's Straight Line 

28. 
The Feuerbach Circle 

29. 
Castillon's Problem 

30. 
Malfatti's Problem 

31. 
Monge's Problem 

32. 
The Tangency Problem of Apollonius 

33. 
Mascheroni's Compass Problem 

34. 
Steiner's Straightedge Problem 

35. 
The Delian Cubedoubling Problem 

36. 
Trisection of an Angle 

37. 
The Regular Heptadecagon 

38. 
Archimedes' Determination of the Number Pi 

39. 
Fuss' Problem of the ChordTangent Quadrilateral 

40. 
Annex to a Survey 

41. 
Alhazen's Billiard Problem 

PROBLEMS CONCERNING CONIC SECTIONS AND CYCLOIDS 

42. 
An Ellipse from Conjugate Radii 

43. 
An Ellipse in a Parallelogram 

44. 
A Parabola from Four Tangents 

45. 
A Parabola from Four Points 

46. 
A Hyperbola from Four Points 

47. 
Van Schooten's Locus Problem 

48. 
Cardan's Spur Wheel Problem 

49. 
Newton's Ellipse Problem 

50. 
The PonceletBrianchon Hyperbola Problem 

51. 
A Parabola as Envelope 

52. 
The Astroid 

53. 
Steiner's Threepointed Hypocycloid 

54. 
The Most Nearly Circular Ellipse Circumscribing a Quadrilateral 

55. 
The Curvature of Conic Sections 

56. 
Archimedes' Squaring of a Parabola 

57. 
Squaring a Hyperbola 

58. 
Rectification of a Parabola 

59. 
Desargue's Homology Theorem (Theorem of Homologous Triangles) 

60. 
Steiner's Double Element Construction 

61. 
Pascal's Hexagon Theorem 

62. 
Brianchon's Hexagram Theorem 

63. 
Desargues' Involution Theorem 

64. 
A Conic Section from Five Elements 

65. 
A Conic Section and a Straight Line 

66. 
A Conic Section and a Point 

STEREOMETRIC PROBLEMS 

67. 
Steiner's Division of Space by Planes 

68. 
Euler's Tetrahedron Problem 

69. 
The Shortest Distance Between Skew Lines 

70. 
The Sphere Circumscribing a Tetrahedron 

71. 
The Five Regular Solids 

72. 
The Square as an Image of a Quadrilateral 

73. 
The PohlkeSchwartz Theorem 

74. 
Gauss' Fundamental Theorem of Axonometry 

75. 
Hipparchus' Stereographic Projection 

76. 
The Mercator Projection 

NAUTICAL AND ASTRONOMICAL PROBLEMS 

77. 
The Problem of the Loxodrome 

78. 
Determining the Position of a Ship at Sea 

79. 
Gauss' TwoAltitude Problem 

80. 
Gauss' ThreeAltitude Problem 

81. 
The Kepler Equation 

82. 
Star Setting 

83. 
The Problem of the Sundial 

84. 
The Shadow Curve 

85. 
Solar and Lunar Eclipses 

86. 
Sidereal and Synodic Revolution Periods 

87. 
Progressive and Retrograde Motion of the Planets 

88. 
Lambert's Comet Problem 

EXTREMES 

89. 
Steiner's Problem Concerning the Euler Number 

90. 
Fagnano's Altitude Base Point Problem 

91. 
Fermat's Problem for Torricelli 

92. 
Tacking Under a Headwind 

93. 
The Honeybee Cell (Problem by Réaumur) 

94. 
Regiomontanus' Maximum Problem 

95. 
The Maximum Brightness of Venus 

96. 
A Comet Inside the Earth's Orbit 

97. 
The Problem of the Shortest Twilight 

98. 
Steiner's Ellipse Problem 

99. 
Steiner's Circle Problem 

100. 
Steiner's Sphere Problem 

Index of Names 