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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 a right triangle where you know the length of the base and the sum of the perpendicular side and the hypotenuse.

In a circle whose circumference is 60 units, a chord is drawn forming a segment whose sagitta is 2 units. What is the length of the chord?
If 40 oranges are worth 60 apples, and 75 apples are worth 7 dozen peaches, and 100 peaches are worth 1 box of grapes and three boxes of grapes are worth 40 pounds of pecans, how many peaches can be bought for 100 oranges?
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 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?
A merchant woman buys and sells apples and pears for Denaros. How much did she invest in apples; how much in pears?
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.
There are two numbers whose sum equals the difference of their squares.
Prove that if the sums of the square opposite sides of any quadrilateral are equal, its diagonals interect at right angles.
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.

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