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Problems from Another Time

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

A wooden beam is stood vertically against a wall. The length of the beam is 30 units.
A lady has two silver cups, and only one cover for both. The first cup weighs 16 oz, and when it is covered it weighs 3 times as much as the second cup; but when the second cup is covered, it weighs 4 times as much as the first.
Make of 10 three parts such that one part multiplied by 3 makes as much as the other multiplied by 4 and as the other multiplied by 5.
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.
X, Y and Z hired a pasture for the season for $90.00. Each has a different number of mules and are on the pasture for a different number of days. How much is each to pay?
A horse, halving its speed each day, travels 700 miles in 7 days. How far does it travel each day?
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.
A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity.