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Problems from Another Time

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

You have two sums of money, the difference of which is 2 dirhams; you divide the smaller sum by the larger and the quotient is equal to 1/2. What are the two sums of money?
A man and his wife drink a barrel of wine at different rates. Find the rate it takes both of them together to drink the wine.
Having been given the sum of two numbers,a, and the difference of their squares,b, find the numbers.
An old Chinese general led his army to a river with a steep bank. Standing atop the bank, he held a stick 6 feet long perpendicular to himself.
Make a crown of gold copper, tin, and iron weighing 60 minae: gold and copper shall be 2/3 of it; gold and tin, 3/4 of it; and gold and iron, 3/5 of it. Find the required weights of gold, copper, tin, and iron.
Determine the greatest cylinder that can be inscribed in a given cone.
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.
If a ladder, placed 8 ft. from the base of a building 40 ft. high, just reached the top, how far must it be placed from the base of the building that it may reach a point 10 ft. from the top?
Assume that the human population after the flood was 6 and that 200 years later the population was 1,000,000. Find the annual growth of the population.
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

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