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Problems from Another Time

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

A series of circles have their centers on an equilateral hyperbola and pass through its center. Show that their envelope is a lemniscate.
Given a wooden log of diameter 2 feet 5 inches from which a 7 inch thick board is to be cut, what is the maximum possible width of the board?
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?
I wish to find three numbers of such nature that the first and the second with 1/2 of the third makes 20...
A man agreed to pay for 13 valuable houses worth $5000 each, what the last would amount to, reckoning 7 cents for the first, 4 times 7 cents for the second, and so on, increasing the price 4 times on each to the last.
A father left $20,000 to be divided among his four sons ages 6, 8, 10, and 12 years respectively so that each share placed at 4 1/2 compounded interest should amount to the same value when its possessor becomes the age 21.
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Three people buy wood together. One pays the merchant 5 coins, another 3 coins, and the last 2 coins.
Given a right triangle where you know the length of the base and the sum of the perpendicular side and the hypotenuse.

If 40 oranges are worth 60 apples, and 75 apples are worth 7 dozen peaches, and 100 peaches are worth 1 box of grapes and three boxes of grapes are worth 40 pounds of pecans, how many peaches can be bought for 100 oranges?

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