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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, x and y, such that their sum is 10 and x/y + y/x = 25
What is the perpendicular height of a cloud when its angles of elevation were 35 degrees and 64 degrees as taken by two observers?
Now there are 100 deer [being distributed] in a city. If one household has one deer there is a remainder...Find the number of households in the city.
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.
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
A two door gate of unknown width is opened so that a 2 ts'un gap exists between the two doors.
A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity.