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Problems from Another Time

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

What is the perpendicular height of a cloud when its angles of elevation were 35 degrees and 64 degrees as taken by two observers at the same time...
When knowing the sum of their ages along with another equation, determine how old a father and son are.
The sum of the two digits of a 2-digit number is 9. If 45 is subtracted from the number, the result will be expressed by the digits in reverse order. Find the number.
To find three quantities x.y, and z...
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?
There are two numbers which are to each other as 5 and 6 and the sum of their squares is 2196. What are the numbers?
Suppose a ladder 60 feet long is placed in a street so as to reach a window 37 feet above the ground on one side of the street...
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?

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