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Problems from Another Time

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

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?
Three circles of varying radius are mutually tangent. The area of the triangle connecting their centers is given. Find the radius of the third circle.
There are two columns in the ruins of Persepolis left standing upright; one is 70 ft. above the plane, and the other 50 ft;
Two officers each have a company of men, the one has 40 less than the other.
If 12 cattle eat up 3 1/3 acres of meadow in 4 weeks and 21 cattle eat up 10 acres of exactly similar meadow in 9 weeks, how many cattle shall eat up 36 acres in 18 weeks? (Hint: The grass continues to grow.)
A number is required; that the square shall be equal to twice the cube.
If a ball 6 inches in diameter weighs 32 lbs, what will be the weight of a ball 3 inches in diameter?
A leech invited a slug for a lunch a leuca away.
Find the two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27