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Problems from Another Time

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

Having been given the sum of two numbers,a, and the difference of their squares,b, find the numbers.
Given a right triangle where you know the length of the base and the sum of the perpendicular side and the hypotenuse.

If 40 oranges are worth 60 apples, and 75 apples are worth 7 dozen peaches, and 100 peaches are worth 1 box of grapes and three boxes of grapes are worth 40 pounds of pecans, how many peaches can be bought for 100 oranges?
Determine the greatest cylinder that can be inscribed in a given cone.
A square walled city measures 10 li on each side. At the center of each side is a gate. Two persons start walking from the center of the city.
One hundred men besieged in a castle, have sufficient food to allow each one bread to the weight of 14 lot a day for ten months.
A merchant woman buys and sells apples and pears for Denaros. How much did she invest in apples; how much in pears?
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
A lady being asked how old she was at the time of her marriage replied that the age of her oldest son was 13; that he was born 2 years after her marriage...
Prove that if the sums of the square opposite sides of any quadrilateral are equal, its diagonals interect at right angles.

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