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Problems from Another Time

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

The sum of two numbers is 10 and their product is 40. What are the numbers?
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
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?
One says that 10 is divided into three parts and if the small part is multiplied by itself and added to the middle one multiplied by itself the result is the large one multiplied by itself...
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?
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
What is the sum of the following series, carried to infinity: 11, 11/7, 11/49, etc.?
The highest point of the Andes is about 4 miles above sea level.
Suppose that the propability of success in an experiment is 1/10. How many trials of the experiment are necessary to insure even odds on it happening at least once?
In order to encourage his son in the study of arithmetic, a father agrees to pay him 8 pennies for every problem solved correctly and to charge him 5 pennies for each incorrect solution.

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