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Problems from Another Time

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

Three equal circumferences with radii 6" are tangent to each other. Compute the area enclosed between them.
Given two circles tangent to each other and to a common line, determine a relationship between the radii and the distance between the tangent points.
A set of four congruent circles whose centers form a square is inscribed in a right triangle ABC where C is the right angle and serves as one corner of the square. Find their radius in terms of the sides; a,b,c, of the triangle.
Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
Two ants are 100 paces apart, crawling back and forth along the same path. The first goes 1/3 pace forward a day and returns 1/4 pace; the other goes forward 1/5 pace and returns 1/6 pace. How many days before the first ant overtakes the second?
What is the sum of the reciprocals of the triangular numbers?
Suppose a man had put out one cent at compound interest in 1620, what would have been the amount in 1824, allowing it to double once in 12 years?
Suppose the area of an equilateral triangle be 600. The sides are required.
A circle, a square and an equilateral triangle all have the same perimeter equal to 1 meter. Compare their areas.
A certain gentleman ordered that 90 measures of grain were to be transported from his house to another, 30 leucas distant.

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