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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.
There are two numbers whose sum equals the difference of their squares.
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?
A four-sided town measures 1100 feet on one side and 1000 feet on the other side, on one edge 600 and the other edge 600.
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.
A merchant bought 50,000 pounds of pepper in Portugal for 10,000 scudi and paid a tax of 500 scudi.
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
Find a number having remainder 29 when divided by 30 and remainder 3 when divided by 4.
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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