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Problems from Another Time

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

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?
The purchase price for an apple and an orange is 100 yen. When n oranges and n + 3 apples are bought the price is 520 yen. Find the number n of oranges and the price of one orange.
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?
Determine the dimensions of the least isosceles triangle ACD that can circumscribe a given circle.
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?
Given four numbers whose sum is 9900; the second exceeds the first by 1/7 of the first...
The king of France entered into a battle and was defeated. How many soldiers did he have before he was defeated?
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.