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Problems from Another Time

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

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?
Three men have a pile of money, their shares being 1/2, 1/3 and 1/6. Each man takes some money from the pile until nothing is left.
A person has a circular yard that is 150 ft. in diameter, and wishes a walk of equal width made round it within the fence...
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.
In Archimedes' Book of Lemmas (ca 250), he introduces a figure that, due to its shape, has historically been known as "the shoemaker's knife" or arbelos.
Prove that if the sums of the square opposite sides of any quadrilateral are equal, its diagonals interect at right angles.
A powerful, unvanquished, excellent black snake, 80 angulas in length, enters into a hole at the rate of 7 1/2 angulas in 5/14 of a day, and in the course of a day its tail grows 11/4 of an angula.

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