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Problems from Another Time

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

Two officers each have a company of men, the one has 40 less than the other.
The cavity of our chimney is an upright parallelepiped, the diagonal of whose base is 60"; and the height of the lower side of the lintel above the plane of the floor is 40".
A number is required; that the square shall be equal to twice the cube.
Given a number, take 1/3 of the number away from itself and add 2. If this result is multiplied by itself, it equals the number plus 24. What is the number?
A leech invited a slug for a lunch a leuca away.
If an equilateral triangle whose area is equal to 10,000 square feet be surrounded by a walk of uniform width, and equal to the area of the inscribed circle, what is the width of the walk?
Chuquet claimed that if given positive numbers a, b, c, d then (a + b) / (c + d) lies between a/c and b/d. Is he correct? Prove your answer
Imagine an urn with two balls, each of which may be either white or black. One of these balls is drawn and is put back before a new one is drawn.
Determine a number having remainders 2, 3, 2 when divided by 3, 5, 7 respectively.
Suppose a lighthouse is built on the top of a rock; the distance between a place of observation and that part of the rock level with the eye is 620 yds.

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