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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 cavity of our chimney is an upright parallelepiped, the diagonal of whose base is 60"; and the height of the lower side of the lintel above the plane of the floor is 40".
In a circle whose circumference is 60 units, a chord is drawn forming a segment whose sagitta is 2 units. What is the length of the chord?
Given a number, take 1/3 of the number away from itself and add 2. If this result is multiplied by itself, it equals the number plus 24. What is the number?
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.
Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
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.
What is the sum of the reciprocals of the triangular numbers?
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.
Suppose the area of an equilateral triangle be 600. The sides are required.
The triangle ABC has a right angle at C. Show that 1/ED=1/AC+1/AB