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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 fish sees a heron looking at him from across a pool, so he quickly swims towards the south. When he reaches the south side of the pool, he has the unwelcome surprise of meeting the heron.
Gun metal of a certain grade is composed of 16% tin and 84% copper. How much tin must be added to 410 lbs. of this gun metal to make a composition of 18% tin?
Now there are six-headed four legged animals and four-headed two-legged birds. Find the total number of animals and birds.
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 certain merchant increases the value of his estate by 1/3...
Seven men held equal shares in a grinding stone 5 feet in diameter. What part of the diameter should each grind away?
Find the greatest value of y in the equation a4 x2= (x2 + y2)3.
Given a pyramid 300 cubits high, with a square base 500 cubits to a side, determine the distance from the center of any side to the apex.
A square walled city of unknown dimensions has four gates, one at the center of each side.
In a rectangle, having given the diagonal and perimeter, find the sides