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Problems from Another Time

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

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.
Three circles of varying radius are mutually tangent. The area of the triangle connecting their centers is given. Find the radius of the third circle.
A cat sitting on a wall 4 cubits high saw a rat prowling 8 cubits from the foot of the wall;
Two officers each have a company of men, the one has 40 less than the other.
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.
A number is required; that the square shall be equal to twice the cube.
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 leech invited a slug for a lunch a leuca away.
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.
Chuquet claimed that if given positive numbers a, b, c, d then (a + b) / (c + d) lies between a/c and b/d. Is he correct? Prove your answer

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