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Problems from Another Time

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

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.
In a certain lake, swarming with red geese, the tip of a lotus bud was seen to extend a span [9 inches] above the surface of the water.
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?
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.
Determine by using algebra the number of degrees in the angle A where: cos A = tan A
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?
On an expedition to seize his enemy's elephants, a king marched 2 yojanas the first day.
A teacher agreed to teach 9 months for $562.50 and his board. At the end of the term, on account of two months absence caused by sickness, he received only $409.50. What was his board worth per month?
A railway train strikes a snowdrift which creates a constant resistance. How long does it take the snow to stop the train?
Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.