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Problems from Another Time

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

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?
Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
What is the sum of the reciprocals of the triangular numbers?
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.
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.
A series of circles have their centers on an equilateral hyperbola and pass through its center. Show that their envelope is a lemniscate.
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?