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Problems from Another Time

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

Now a good horse and an inferior horse set out from Chang'an to Qi. Qi is 3000 li from Chang'an.
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 number is required; that the square shall be equal to twice the cube.
A leech invited a slug for a lunch a leuca away.
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.
Make of 10 three parts such that one part multiplied by 3 makes as much as the other multiplied by 4 and as the other multiplied by 5.
Chuquet claimed that if given positive numbers a, b, c, d then (a + b) / (c + d) lies between a/c and b/d. Is he correct? Prove your answer
Determine a number having remainders 2, 3, 2 when divided by 3, 5, 7 respectively.
X, Y and Z hired a pasture for the season for $90.00. Each has a different number of mules and are on the pasture for a different number of days. How much is each to pay?
A horse, halving its speed each day, travels 700 miles in 7 days. How far does it travel each day?

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