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Problems from Another Time

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

Determine the radii of three equal circles decribed within and tangent to a given circle, and also tangent to each other
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.
The radius of a circle is 3.20 meters. Compute to within .001m the areas of the inscribed and circumscribed equilateral triangles.
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.
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 castle has n rooms each of which has 7 samurai in it.
A cat sitting on a wall 4 cubits high saw a rat prowling 8 cubits from the foot of the wall;
Find two number with sum 20 and when squared their sum is 208.
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.
Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?

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