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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 triangle ABC has a right angle at C. Show that 1/ED=1/AC+1/AB
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 man went to a draper and bought a length of cloth 35 braccia long to make a suit of clothes.
Wanting to know the breadth of a river, I measured a base of 500 yards in a straight line close by one side of it.
Two circles, the sum of whose radii is a, are placed in the same plane with their centers at a distance 2a...
Three congruent circles of radius 6 inches are mutually tangent to one another. Compute the area enclosed between them.
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.
Find two number with sum 20 and when squared their sum is 208.
Determine the radii of three equal circles decribed within and tangent to a given circle, and also tangent to each other
Three equal circumferences with radii 6" are tangent to each other. Compute the area enclosed between them.

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