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Problems from Another Time

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

What number which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?
A gentleman has bought a rectangular piece of land whose perimeter is to be 100 rods.
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?
A copper water tank in the form of a rectangular parallelopiped is to made. If its length is to be a times its breadth, how high should it be that for a given capacity it should cost as little as possible?
A ladder is placed perpendicular to the plane of the horizon, and in coincidence with the plane of an upright wall.
There are two columns in the ruins of Persepolis left standing upright; one is 70 ft. above the plane, and the other 50 ft;
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.)
Two wine merchants enter Paris, one of them with 64 casks of wine, the other with 20.
The three sides of a triangular piece of land, taken in order, measure 15, 10, and 13 chains respectively.

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