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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 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.
What is the value of X...
Determine the radii of three equal circles decribed within and tangent to a given circle, and also tangent to each other
The radius of a circle is 3.20 meters. Compute to within .001m the areas of the inscribed and circumscribed equilateral triangles.
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.
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
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.
A cat sitting on a wall 4 cubits high saw a rat prowling 8 cubits from the foot of the wall;
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?
There is a four sided field.