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Problems from Another Time

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

Three circles of varying radius are mutually tangent. The area of the triangle connecting their centers is given. Find the radius of the third circle.
Two officers each have a company of men, the one has 40 less than the other.
A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity.
As for a square piece of land that amounts to 100 square cubits, if it is said to you, "Cause it to make a piece of land that amounts to 100 square cubits that is round," what is the required diameter?
A number is required; that the square shall be equal to twice the cube.
A leech invited a slug for a lunch a leuca away.
There is a regular pentagon. The length of its side is a. Find the area of the pentagon. Generalize your result for a nonagon.
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?
Chuquet claimed that if given positive numbers a, b, c, d then (a + b) / (c + d) lies between a/c and b/d. Is he correct? Prove your answer
Determine a number having remainders 2, 3, 2 when divided by 3, 5, 7 respectively.