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Problems from Another Time

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

In baking a hemispherical loaf of bread of 10" radius, the crust was everywhere of an equal thickness, and the solidity of the crust was equal to half the solid content of the whole loaf. What were the dimensions of the interior soft part?
Given a triangular piece of land having two sides 10 yards in length and its base 12 yards, what is the largest square that can be constructed within this piece of land so that one of its sides lies along the base of the triangle?
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
What is the sum of the following series, carried to infinity: 11, 11/7, 11/49, etc.?
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
Suppose that the propability of success in an experiment is 1/10. How many trials of the experiment are necessary to insure even odds on it happening at least once?
A water tub holds 73 gallons; the pipe which fills it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes.
Two merchants, A and B, loaded a ship with 500 hhds (hogshead) of rum; A loaded 350 hhds, and B the rest; in a storm the seamen were obliged to throw overboard 100 hhds; how much must each sustain of the loss?
In a square box that contains 1000 marbles, how many will it take to reach across the bottom of the box in a straight row?
The king of France entered into a battle and was defeated. How many soldiers did he have before he was defeated?

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