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Problems from Another Time

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

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.
If in a circle ABDC, circumscribe an equilateral triangle ABC; the straight line AD is equal to the sum of the two straight lines BD and DC: required a demonstration.
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.
A cat sitting on a wall 4 cubits high saw a rat prowling 8 cubits from the foot of the wall;
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
A square circumscribed about a given circle is double in area to a square inscribed in the same circle. True of false? Prove your answer.
Given the fraction ax/ (a-x ), convert it into an infinite series.
Given a guest on horseback rides 300 li in a day. The guest leaves his clothes behind. The host discovers them after 1/3 day, and he starts out with the clothes.
A two door gate of unknown width is opened so that a 2 inch gap exists between the two doors.
A bridge is built across a river in 6 months by 45 men. It is washed away by the current. Required the number of workmen sufficient to build another of twice as much worth in 4 months.

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