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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 a garden of rectangular form and wants to construct a walk of equal width half way round to take up half the garden. What must be the width of this walk?
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.
Two cog-wheels, one having 26 cogs, and the other 20 cogs, run together. In how many revolutions of the larger wheel will the smaller gain in 12 revolutions?
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?
A certain merchant increases the value of his estate by 1/3...
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.
Find the greatest value of y in the equation a4 x2= (x2 + y2)3.
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?
A square walled city of unknown dimensions has four gates, one at the center of each side.
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?

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