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Problems from Another Time

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

Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
A barrel has various holes in it. The first hole empties the barrel in three days...
X, Y and Z hired a pasture for the season for $90.00. Each has a different number of mules and are on the pasture for a different number of days. How much is each to pay?
I have two fields of grain. From the first field I harvest 2/3 sila (a measurement of grain volume) per sar (a unit of area); from the second, 1/2 sila per sar.