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Problems from Another Time

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

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.
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...
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.
Find the greatest value of y in the equation a4 x2= (x2 + y2)3.
A square walled city of unknown dimensions has four gates, one at the center of each side.
In a right triangle, let the perpendicular be 5 and the sum of the base and hypotenuse 25. Find the lengths of the base and hypotenuse
A cliff with a tower on its edge is observed from a boat at sea; find the height of the cliff and the tower.
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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