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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 certain slave fled from Milan to Naples going 1/10 of the whole journey each day. At the beginning of the third day, his master sent a slave after him and this slave went 1/7 of the whole journey each day.
There is a round fish pond of certain dimensions, and into the pond is dropped a marble column. How high will the water rise?
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
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.
If you are h feet tall and walk all the way around the Earth, keeping to the same circumference, how much farther has your head gone than your feet when you complete the journey?
You have two sums of money, the difference of which is 2 dirhams; you divide the smaller sum by the larger and the quotient is equal to 1/2. What are the two sums of money?
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
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.
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.