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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 number with sum 20 and when squared their sum is 208.
There is a log of precious wood 18 feet long whose bases are 5 feet and 2.5 feet in circumference. Into what lengths should the log be cut to trisect its volume?
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?
A merchant gave a university 2,814 ducats on the understanding that he was to be paid back 618 ducats per year for 9 years, at the end of which the 2,814 ducats should be considered as paid.
There is a four sided field.
It is required to determine whether 30 horses can be put into 7 stalls; so that in every stall there may be, either a single horse, or an odd number of horses.
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
One says that 10 garments were purchased by two men at a price of 72 dirhams. The garments varied in value. The price of each garment of one man is 3 dirhams more than the price for each garment of the other. How many garments did each man buy?
In one day, a person can make 30 arrows or fletch [put the feathers on] 20 arrows.
There are two columns in the ruins of Persepolis left standing upright; one is 70 ft. above the plane, and the other 50 ft;

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