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Problems from Another Time

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

The edge of a cloud is at an altitude of 20 degrees and the sun above it at 35 degrees. The shadow cast by the edge of the cloud fall on a object 2300 yards away, how high is the cloud?
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 lady has two silver cups, and only one cover for both. The first cup weighs 16 oz, and when it is covered it weighs 3 times as much as the second cup; but when the second cup is covered, it weighs 4 times as much as the first.
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.
Make of 10 three parts such that one part multiplied by 3 makes as much as the other multiplied by 4 and as the other multiplied by 5.
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.
X, Y and Z hired a pasture for the season for $90.00. Each has a different number of mules and are on the pasture for a different number of days. How much is each to pay?
A horse, halving its speed each day, travels 700 miles in 7 days. How far does it travel each day?
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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