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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.
What is the sum of the reciprocals of the triangular numbers?
Suppose the area of an equilateral triangle be 600. The sides are required.
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?
A certain gentleman ordered that 90 measures of grain were to be transported from his house to another, 30 leucas distant.
The sum of two numbers is 10 and their product is 40. What are the numbers?
Given a pendulum as shown. The height of the pendulum is two units and its horizontal width is 2 units. What is the area of the pendulum?
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?
I wish to find three numbers of such nature that the first and the second with 1/2 of the third makes 20...
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?