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Problems from Another Time

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

Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider
Find the isoceles triangle of smallest area that circumscribes a circle of radius 1.
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
There is a right triangle where: the sum of the upright multiplied by itself twice and the hypotenuse multiplied by itself is 700 units; and, the sum of the base multiplied by itself twice and the hypotenuse multiplied by itself is 900 units.
Determine the dimensions of the least isosceles triangle ACD that can circumscribe a given circle.
Three men wish to buy a horse but none have a sufficient amount of money for the purchase; to do so they must borrow from each other. How much money does each man have and what is the price of the horse?
Given four numbers whose sum is 9900; the second exceeds the first by 1/7 of the first...
What is the perpendicular height of a cloud when it's angles of elevation were 35 degrees and 64 degrees as taken by two observers?
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
How much does Landowner A give to each worker knowing Landowner B gives a certain amount more and has few workers.

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