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Problems from Another Time

Individual problems from throughout mathematics history, as well as articles that include problem sets for students.

Three congruent circles of radius 6 inches are mutually tangent to one another. Compute the area enclosed between them.
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Determine the radii of three equal circles decribed within and tangent to a given circle, and also tangent to each other
Curve sketching, tangent lines, and optimization, explored via interactive applets
The radius of a circle is 3.20 meters. Compute to within .001m the areas of the inscribed and circumscribed equilateral triangles.
If in a circle ABDC, circumscribe an equilateral triangle ABC; the straight line AD is equal to the sum of the two straight lines BD and DC: required a demonstration.
A vessel is anchored in 3 fathoms of water and the cable passes over a sheave in the bowspirt which is 6 ft above the water.
A cat sitting on a wall 4 cubits high saw a rat prowling 8 cubits from the foot of the wall;
Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it.
A square circumscribed about a given circle is double in area to a square inscribed in the same circle. True of false? Prove your answer.

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