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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.
Find the height of a window.
A man entered an orchard through 7 gates, and there took a certain number of apples. When he left the orchard, he gave the first guard half the apples he had and 1 apple more.
A man is walking across a bridge, when a boat passes under the bridge.How rapidly are the boat and the pedestrian separating after the boat passes under the bridge?
One person possesses 7 asavas horses, another 9 hayas horses, and another 9 camels. Each gives two animals away, one to each of the others.
Age
My age is a number consisting of two digits, 1/2 of this number is a mean proportional between these two digits, and two years hence, my age will be a third proportional to the same two digits, directly as they stand in my present age.
Thirty flasks-10 full, 10 half-empty, and 10 completely empty- are to be divided among 3 sons so that flasks and contents should be shared equally. How may this be done?
There are two numbers whose sum equals the difference of their squares.
A four-sided town measures 1100 feet on one side and 1000 feet on the other side, on one edge 600 and the other edge 600.
There are four companies, in one of which there are 6 men, in another 8, and in each of the remaining two, 9 men. How many ways can a committee of 4 men be composed by choosing one man from each company?

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