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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...
Two merchants, A and B, loaded a ship with 500 hhds (hogshead) of rum; A loaded 350 hhds, and B the rest; in a storm the seamen were obliged to throw overboard 100 hhds; how much must each sustain of the loss?
The king of France entered into a battle and was defeated. How many soldiers did he have before he was defeated?
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?
What is the perpendicular height of a cloud when its angles of elevation were 35 degrees and 64 degrees as taken by two observers at the same time...
When knowing the sum of their ages along with another equation, determine how old a father and son are.
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.