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Problems from Another Time

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

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 two circle tangent at the point P with parallel diameters AB, CD, prove that APD and BPC are straight lines.
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
The highest point of the Andes is about 4 miles above sea level.
In a given square, inscribe 4 equal circles so that...
An erect pole of 10 cubits has its base moved 6 cubits. Determine the new height and the distance the top of the pole is lowered.
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.
There is a round town 8000 feet in circumference.
Determine the dimensions for a right-angled triangle, having been given the hypotenuse, and the side of the inscribed square.
Three equal circumferences with radii 6" are tangent to each other. Compute the area enclosed between them.

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