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Problems from Another Time

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

Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
If in a circle ABDC, circumscribe an equilateral triangle ABC; the straight line AD is equal to the sum of the two straight lines BD and DC: required a demonstration.
Two men have a certain amount of money. The first says to the second, "If you give me 5 denari, I will have 7 times what you have left."
A cat sitting on a wall 4 cubits high saw a rat prowling 8 cubits from the foot of the wall;
If I were to give 7 pennies to each beggar at my door, I would have 24 pennies left in my purse. How many beggars are there and how much money do I have?
What proportions of sugar at 8 cents, 10 cents and 14 cents per pound, will compose a mixture worth 12 cents per pound?
There is a round town 8000 feet in circumference.
Fibonacci gave a practical rule for approximating the area of an equilateral triangle.
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
The dimensions of a rectangular box in inches are expressed by three consecutive numbers. The surface of the box is 292 square inches. Find the dimensions.

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