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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 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 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.
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
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.
What is the value of X...
The triangle ABC has a right angle at C. Show that 1/ED=1/AC+1/AB
On a day in spring a boy has gathered cherry blossoms under a cherry tree. Nearby a poet is reading some of his poems aloud. As he reads, the boy counts out the cherry blossoms, one blossom for each word of a poem.
A man went to a draper and bought a length of cloth 35 braccia long to make a suit of clothes.
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
Two circles, the sum of whose radii is a, are placed in the same plane with their centers at a distance 2a...

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