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 Bernoulli-Euler 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 Fermat-Euler Prime Number Theorem |
|
20. |
The Fermat Equation |
|
21. |
The Fermat-Gauss 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 Hermite-Lindemann 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 Straight-edge Problem |
|
35. |
The Delian Cube-doubling Problem |
|
36. |
Trisection of an Angle |
|
37. |
The Regular Heptadecagon |
|
38. |
Archimedes' Determination of the Number Pi |
|
39. |
Fuss' Problem of the Chord-Tangent 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 Poncelet-Brianchon Hyperbola Problem |
|
51. |
A Parabola as Envelope |
|
52. |
The Astroid |
|
53. |
Steiner's Three-pointed 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 Pohlke-Schwartz 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' Two-Altitude Problem |
|
80. |
Gauss' Three-Altitude 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 |