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Problems from Another Time

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

Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it.
On a certain ground stands two poles 12 feet apart, the lesser pole is 35 ft. in height and the greater 40 ft. It is sought, if the greater pole will lean on the lesser, then in what part will it touch?
The edge of a cloud is at an altitude of 20 degrees and the sun above it at 35 degrees. The shadow cast by the edge of the cloud fall on a object 2300 yards away, how high is the cloud?
A castle has n rooms each of which has 7 samurai in it.
On a day in spring a boy has gathered cherry blossoms under a cherry tree. Nearby a poet is reading some of his poems aloud. As he reads, the boy counts out the cherry blossoms, one blossom for each word of a poem.
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
Of a collection of mango fruits, the king took 1/6; the queen 1/5 the remainder, and the three princes took 1/4, 1/3 and 1/2 (of the same remainder); and the youngest child took the remaining 3 mangoes.
Three vertical posts along a straight canal, each rising to the same height above the surface of the water. By looking at the line of vision, determine, to the nearest mile, the radius of the earth.
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?
There is a four sided field.