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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.
There is a log of precious wood 18 feet long whose bases are 5 feet and 2.5 feet in circumference. Into what lengths should the log be cut to trisect its volume?
A merchant gave a university 2,814 ducats on the understanding that he was to be paid back 618 ducats per year for 9 years, at the end of which the 2,814 ducats should be considered as paid.
A number is required; that the square shall be equal to twice the cube.
A leech invited a slug for a lunch a leuca away.
It is required to determine whether 30 horses can be put into 7 stalls; so that in every stall there may be, either a single horse, or an odd number of horses.
One says that 10 garments were purchased by two men at a price of 72 dirhams. The garments varied in value. The price of each garment of one man is 3 dirhams more than the price for each garment of the other. How many garments did each man buy?
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
Determine a number having remainders 2, 3, 2 when divided by 3, 5, 7 respectively.
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?