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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?
Suppose the area of an equilateral triangle be 600. The sides are required.
A certain gentleman ordered that 90 measures of grain were to be transported from his house to another, 30 leucas distant.
Prove that if the sums of the square opposite sides of any quadrilateral are equal, its diagonals interect at right angles.
Given a pendulum as shown. The height of the pendulum is two units and its horizontal width is 2 units. What is the area of the pendulum?
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.
I wish to find three numbers of such nature that the first and the second with 1/2 of the third makes 20...
A series of circles have their centers on an equilateral hyperbola and pass through its center. Show that their envelope is a lemniscate.
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
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?

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