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Problems from Another Time

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

A merchant woman buys and sells apples and pears for Denaros. How much did she invest in apples; how much in pears?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
There is a four-sided field whose eastern side measures 35 paces, its western side 45 paces, its southern side 25 paces and its northern side 15 paces. Find the area of this field.
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 sum of the two digits of a 2-digit number is 9. If 45 is subtracted from the number, the result will be expressed by the digits in reverse order. Find the number.
A series of circles have their centers on an equilateral hyperbola and pass through its center. Show that their envelope is a lemniscate.
To find three quantities x.y, and z...
Given a wooden log of diameter 2 feet 5 inches from which a 7 inch thick board is to be cut, what is the maximum possible width of the board?
A water tub holds 73 gallons; the pipe which fills it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes.