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Problems from Another Time

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

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.
Determine the radii of three equal circles decribed within and tangent to a given circle, and also tangent to each other
Three equal circumferences with radii 6" are tangent to each other. Compute the area enclosed between them.
What number which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?
A boy gives 11 coins of equal denomination to a man, and the man finds that their total value in yen is 4 less than his age.
A gentleman has bought a rectangular piece of land whose perimeter is to be 100 rods.
There were two men, of whom the first had 3 small loaves of bread and the other, 2.
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?
What proportions of sugar at 8 cents, 10 cents and 14 cents per pound, will compose a mixture worth 12 cents per pound?
A ladder is placed perpendicular to the plane of the horizon, and in coincidence with the plane of an upright wall.