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Problems from Another Time

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

Find two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27.
Knowing the base, b, and the altitude, a, of a triangle. Find the expression for a side of the inscribed square.
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.
Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
What is the sum of the reciprocals of the triangular numbers?
A guest on horseback rides 300 li in a day. The guest leaves his clothes behind and the host rides off to catch up with the guest once he discovers the clothes. Assuming the host rides without stop tell how far he can go in a day?
I have two fields of grain. From the first field I harvest 2/3 a bushel of grain/unit area; from the second, 1/2 bushel/unit area.
Suppose the area of an equilateral triangle be 600. The sides are required.
A certain gentleman ordered that 90 measures of grain were to be transported from his house to another, 30 leucas distant.
Prove that the area of a regular polygon can be given by the product of its perimeter and half the radius of the inscribed circle.

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