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Problems from Another Time

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

A gentleman has bought a rectangular piece of land whose perimeter is to be 100 rods; and he is to pay 1 dollar for each rod in the length of the land and 3 dollars for each rod in the breath of the land.
How long does it take a single man to do work when...
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.
Suppose General [George] Washington had 800 men and was supplied with provisions to last 2 months but he needed to feed his army for 7 months.
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.
Two men have a certain amount of money. The first says to the second, "If you give me 5 denari, I will have 7 times what you have left."
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?