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Problems from Another Time

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

Determine the radii of three equal circles decribed within and tangent to a given circle, and also tangent to each other
What is the sum of the reciprocals of the triangular numbers?
The radius of a circle is 3.20 meters. Compute to within .001m the areas of the inscribed and circumscribed equilateral triangles.
Suppose the area of an equilateral triangle be 600. The sides are required.
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 certain gentleman ordered that 90 measures of grain were to be transported from his house to another, 30 leucas distant.
A cat sitting on a wall 4 cubits high saw a rat prowling 8 cubits from the foot of the wall;
Given a pendulum as shown. The height of the pendulum is two units and its horizontal width is 2 units. What is the area of the pendulum?
A square circumscribed about a given circle is double in area to a square inscribed in the same circle. True of false? Prove your answer.
I wish to find three numbers of such nature that the first and the second with 1/2 of the third makes 20...

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