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Problems from Another Time

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

Now there are six-headed four-legged animals and four-headed two-legged birds placed together.
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.
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
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 men brought their fish through customs. Find how much the fish cost, and what is the customs fee.
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?
The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.

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 certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?
One says that 10 is divided into three parts and if the small part is multiplied by itself and added to the middle one multiplied by itself the result is the large one multiplied by itself...