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Problems from Another Time

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

One hundred men besieged in a castle, have sufficient food to allow each one bread to the weight of 14 lot a day for ten months.
A merchant woman buys and sells apples and pears for Denaros. How much did she invest in apples; how much in pears?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
An official asks a woman why she has so many bowls to wash. The woman explains that she had dinner guests who ate meat, rice, and soup. Judging by the number of bowls, how many guests were there?
Prove that if the sums of the square opposite sides of any quadrilateral are equal, its diagonals interect at right angles.
A powerful, unvanquished, excellent black snake, 80 angulas in length, enters into a hole at the rate of 7 1/2 angulas in 5/14 of a day, and in the course of a day its tail grows 11/4 of an angula.
Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
A series of circles have their centers on an equilateral hyperbola and pass through its center. Show that their envelope is a lemniscate.
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.

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