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Problems from Another Time

Individual problems from throughout mathematics history, as well as articles that include problem sets for students.

Knowing the base, b, and the altitude, a, of a triangle. Find the expression for a side of the inscribed square.
Now there are 100 deers [being distributed] in a city. If one household has one deer there is a remainder...Find the number of households in the city.
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.
Suppose General [George] Washington had 800 men and was supplied with provisions to last 2 months but he needed to feed his army for 7 months.
A guest on horseback rides 300 li in a day. The guest leaves his clothes behind and the host rides off to catch up with the guest once he discovers the clothes. Assuming the host rides without stop tell how far he can go in a day?
I have two fields of grain. From the first field I harvest 2/3 a bushel of grain/unit area; from the second, 1/2 bushel/unit area.
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
Two men have a certain amount of money. The first says to the second, "If you give me 5 denari, I will have 7 times what you have left."
Prove that the area of a regular polygon can be given by the product of its perimeter and half the radius of the inscribed circle.
Two circles of radii 25 feet intersect so that the distance between their centers is 30 feet. What is the length of the side of the largest square inscribable within their intersecting arcs?

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