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Problems from Another Time

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

When knowing the sum of their ages along with another equation, determine how old a father and son are.
Two cog-wheels, one having 26 cogs, and the other 20 cogs, run together. In how many revolutions of the larger wheel will the smaller gain in 12 revolutions?
A certain merchant increases the value of his estate by 1/3...
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?
The sum of two numbers is 10 and their product is 40. What are the numbers?
Find the greatest value of y in the equation a4 x2= (x2 + y2)3.
A square walled city of unknown dimensions has four gates, one at the center of each side.
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?
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?
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

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