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Problems from Another Time

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

An old Chinese general led his army to a river with a steep bank. Standing atop the bank, he held a stick 6 feet long perpendicular to himself.
Find two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27.
Make a crown of gold copper, tin, and iron weighing 60 minae: gold and copper shall be 2/3 of it; gold and tin, 3/4 of it; and gold and iron, 3/5 of it. Find the required weights of gold, copper, tin, and iron.
If a ladder, placed 8 ft. from the base of a building 40 ft. high, just reached the top, how far must it be placed from the base of the building that it may reach a point 10 ft. from the top?
Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
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 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.
Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.
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.
In a right triangle, the hypotenuse is 9.434 and the sum of the sides around the right angle is 13. Find the lengths of the sides around the right angle.