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Problems from Another Time

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

Knowing the base, b, and the altitude, a, of a triangle. Find the expression for a side of the inscribed square.
In a certain lake, swarming with red geese, the tip of a lotus bud was seen to extend a span [9 inches] above the surface of the water.
Now there are 100 deers [being distributed] in a city. If one household has one deer there is a remainder...Find the number of households in the city.
What number which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?
There is a tree with 100 branches. How many nests, eggs and birds are there?
A gentleman has bought a rectangular piece of land whose perimeter is to be 100 rods.
Two men starting from the same point begin walking in different directions. Their rates of travel are in the ratio 7:3.
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 cylindrical tin tomato can is to be made which shall have a given capacity. Find what should be the ratio of the height to the radius of the base that the smallest possible amount of tin shall be required.
A ladder is placed perpendicular to the plane of the horizon, and in coincidence with the plane of an upright wall.