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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 circle whose circumference is 60 units, a chord is drawn forming a segment whose sagitta is 2 units. What is the length of the chord?
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 lady has two silver cups, and only one cover for both. The first cup weighs 16 oz, and when it is covered it weighs 3 times as much as the second cup; but when the second cup is covered, it weighs 4 times as much as the first.
Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
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.
What is the sum of the reciprocals of the triangular numbers?
Suppose the area of an equilateral triangle be 600. The sides are required.
The answer to the following question is obtained using as optimum strategy-the farmer is getting the "best deal" possible. Can you figure out the solution strategy?...
A certain gentleman ordered that 90 measures of grain were to be transported from his house to another, 30 leucas distant.
I am a brazen lion; my spouts are my 2 eyes, my mouth, and the flat of my foot. My right eye fills a jar in 2 days, my left eye in 3, and my foot in 4.

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