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Problems from Another Time

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

The king of France entered into a battle and was defeated. How many soldiers did he have before he was defeated?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
How high above the earth must a person be raised that he [or she] may see 1/3 of its surface?
Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the length of those sides.
Two men start walking at the same time and travel a distance. One is walking faster and completes the journey sooner. How fast did each man travel?
A mouse is at the top of a poplar tree 60 braccia high, and a cat is on the ground at its foot. The mouse decends 1/2 a braccia a day and at night it turns back 1/6 of a braccia.
Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.
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?
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
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.

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