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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.
The square of a certain number multiplied by itself and by 200 is 446,976. What is the number?
Suppose that for every 4 cows a farmer has, he should plow 1 acre of land, and allow 1 acre of pasture for every 3 cows; how many cows could he keep on 140 acres?
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?
The cavity of our chimney is an upright parallelepiped, the diagonal of whose base is 60"; and the height of the lower side of the lintel above the plane of the floor is 40".
Given a number, take 1/3 of the number away from itself and add 2. If this result is multiplied by itself, it equals the number plus 24. What is the number?
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.
If an equilateral triangle whose area is equal to 10,000 square feet be surrounded by a walk of uniform width, and equal to the area of the inscribed circle, what is the width of the walk?

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