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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 circles of varying radius are mutually tangent. The area of the triangle connecting their centers is given. Find the radius of the third circle.
A California miner has a spherical ball of gold, 2 inches in diamter, which he wants to exchange for spherical balls 1 inch in diameter. How many of the smaller spheres should he receive?
Two officers each have a company of men, the one has 40 less than the other.
The sum of two numbers is 10 and their product is 40. What are the numbers?
A number is required; that the square shall be equal to twice the cube.
In baking a hemispherical loaf of bread of 10" radius, the crust was everywhere of an equal thickness, and the solidity of the crust was equal to half the solid content of the whole loaf. What were the dimensions of the interior soft part?
A leech invited a slug for a lunch a leuca away.
Given a triangular piece of land having two sides 10 yards in length and its base 12 yards, what is the largest square that can be constructed within this piece of land so that one of its sides lies along the base of the triangle?
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
What is the sum of the following series, carried to infinity: 11, 11/7, 11/49, etc.?

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