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Problems from Another Time

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

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.
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.
In a rectangle, having given the diagonal and perimeter, find the sides
Given two circles tangent to each other and to a common line, determine a relationship between the radii and the distance between the tangent points.
A castle has n rooms each of which has 7 samurai in it.
Find two number with sum 20 and when squared their sum is 208.
A set of four congruent circles whose centers form a square is inscribed in a right triangle ABC where C is the right angle and serves as one corner of the square. Find their radius in terms of the sides; a,b,c, of the triangle.
Two ants are 100 paces apart, crawling back and forth along the same path. The first goes 1/3 pace forward a day and returns 1/4 pace; the other goes forward 1/5 pace and returns 1/6 pace. How many days before the first ant overtakes the second?
Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?
There is a four sided field.