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Problems from Another Time

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

Two cog-wheels, one having 26 cogs, and the other 20 cogs, run together. In how many revolutions of the larger wheel will the smaller gain in 12 revolutions?
A man bought a number of sheep for $225; 10 of them having died, he sold 4/5 of the remainder for the same cost and received $150 for them. How many did he buy?
A teacher agreed to teach 9 months for $562.50 and his board. At the end of the term, on account of two months absence caused by sickness, he received only $409.50. What was his board worth per month?
A barrel has various holes in it. The fist hole empties the barrel in three days...
Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.
Determine the different values of x, when a certain function hits a minimum.
In a right triangle, the hypotenuse is 9.434 and the sum of the sides around the right angle is 13. Find the lengths of the sides around the right angle.
Given a door and a measuring rod of unknown dimensions, the rod is used to measure the door.
Four men already having denari found a purse of denari; each man has a different amount of denari before they found the purse. Find out how much denari each man has.
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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