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I was employed to survey a field, which I was told was an exact geometrical square, but by reason of a river running through it, I can only obtain partial measurements.
Historical Problems can be used to enliven any mathematics class. Here are some examples from medieval times, from a 19th century American textbook, and from a 19th century Armenian textbook, among other sources.

Author Keith Devlin argues that the impact of the Pisan merchant and his Arabic numbers on medieval Europe was even greater than previously thought.

I have two fields of grain. From the first field I harvest 2/3 a bushel of grain/unit area; from the second, 1/2 bushel/unit area.
Suppose the area of an equilateral triangle be 600. The sides are required.
A castle has n rooms each of which has 7 samurai in it.
This is a page from the Rechenbuch of Adam Riese. It deals with the measurement of barrels. Also a page that has a table showing numbers both in German words, in Roman numerals, and in the Hindu-Arabic numerals.
A historically minded textbook designed to teach real analysis by considering some of the problems faced by 19th century mathematicians.
A leech invited a slug for a lunch a leuca away.
There are four companies, in one of which there are 6 men, in another 8, and in each of the remaining two, 9 men. How many ways can a committee of 4 men be composed by choosing one man from each company?