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Problems from Another Time

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

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?
Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.
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.
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
A merchant woman buys and sells apples and pears for Denaros. How much did she invest in apples; how much in pears?
Given the fraction ax/ (a-x ), convert it into an infinite series.
A two door gate of unknown width is opened so that a 2 inch gap exists between the two doors.
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.
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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