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Problems from Another Time

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

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.
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.

A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?
A castle has n rooms each of which has 7 samurai in it.
Find two number with sum 20 and when squared their sum is 208.
A man plants 4 kernels of corn, which at harvest produce 32 kernels: these he plants the second year; now supposing the annual increase to continue 8 fold, what would be the produce of the 15th year, allowing 1000 kernels to a pint?
If an arc of 45 degrees on one circumference is equal to an arc of 60 degrees on another circle, what is the ratio of the areas of the circle?
Given the cats eye as shown. Let the radius of the eye be given by R. What is the area of the pupil?
Three hundred pigs are to be prepared for a feast.
Knowing the base, b, and the altitude, a, of a triangle. Find the expression for a side of the inscribed square.

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