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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 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.
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 the dimensions of an isosceles trapezoid find the length of the transversal drawn parallel to the bases that divides the trapezoid into 2 equal areas.
The number 50 is divided by a certain number. If the divisor is increased by 3, the quotient decreases by 3.75. What is the number?
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.
I was employed to survey a field, which I was told was an exact geometrical square, but by reason of a river running through it, I can only obtain partial measurements.
A ladder has 100 steps. On the first step sits 1 pigeon; on the second, 2; on the third, 3; and so on up to the hundredth. How many pigeons in all?
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.

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