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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 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 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.
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
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?
One says that 10 is divided into three parts and if the small part is multiplied by itself and added to the middle one multiplied by itself the result is the large one multiplied by itself...
A speculator bought stock at 25% below par and sold it at 20% above par. He gained $1560. How much did he invest?
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
Given: a circle with an inscribed equilateral triangle. The triangle has an area of 12 square units. What is the area of the circle?
The highest point of the Andes is about 4 miles above sea level.
If 80 dollars worth of provisions will serve 20 men for 25 days, what number of men will the same amount of provisions serve for 10 days?

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