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Problems from Another Time

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

Find two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27.
Given a semicircle, Prove that if O is the circle's center, DO=OE.
Of a collection of mango fruits, the king took 1/6; the queen 1/5 the remainder, and the three princes took 1/4, 1/3 and 1/2 (of the same remainder); and the youngest child took the remaining 3 mangoes.
One hundred men besieged in a castle, have sufficient food to allow each one bread to the weight of 14 lot a day for ten months.
A vessel is anchored in 3 fathoms of water and the cable passes over a sheave in the bowspirt which is 6 ft above the water.
A merchant woman buys and sells apples and pears for Denaros. How much did she invest in apples; how much in pears?
Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it.
A castle has n rooms each of which has 7 samurai in it.
Prove that if the sums of the square opposite sides of any quadrilateral are equal, its diagonals interect at right angles.
Find two number with sum 20 and when squared their sum is 208.

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