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Problems from Another Time

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

There is a regular pentagon. The length of its side is a. Find the area of the pentagon. Generalize your result for a nonagon.
Determine the greatest cylinder that can be inscribed in a given cone.
Two men rent a pasture for 100 liras on the understanding that two cows are to be counted as being equivalent to three sheep. The first puts in 60 cows and 85 sheep; the second 80 cows and 100 sheep. How much should each pay?
A square walled city measures 10 li on each side. At the center of each side is a gate. Two persons start walking from the center of the city.