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Problems from Another Time

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

If you are h feet tall and walk all the way around the Earth, keeping to the same circumference, how much farther has your head gone than your feet when you complete the journey?
The square root of half the number of bees in a swarm has flown out upon a jessamine bush; 8/9 of the swarm has remained behind.
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 man hired a horse in London at 3 pence a mile. He rode 94 miles due West to Bristol then due north to Chester, whence he returned toward London for 66 miles, which put him in Coventry.
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 tree is 20 feet tall and has a circumference of 3 feet. There is a vine that winds seven equally spaced times around the tree and reaches the top. What is the length of the vine?
A castle has n rooms each of which has 7 samurai in it.
A speculator bought stock at 25% below par and sold it at 20% above par. He gained $1560. How much did he invest?
Find two number with sum 20 and when squared their sum is 208.
Given: a circle with an inscribed equilateral triangle. The triangle has an area of 12 square units. What is the area of the circle?

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