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Problems from Another Time

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

Given a semicircle, Prove that if O is the circle's center, DO=OE.
Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
Of a collection of mango fruits, the king took 1/6; the queen 1/5 the remainder, and the three princes took 1/4, 1/3 and 1/2 (of the same remainder); and the youngest child took the remaining 3 mangoes.
Three vertical posts along a straight canal, each rising to the same height above the surface of the water. By looking at the line of vision, determine, to the nearest mile, the radius of the earth.
Given the fraction ax/ (a-x ), convert it into an infinite series.
A two door gate of unknown width is opened so that a 2 inch gap exists between the two doors.
The answer to the following question is obtained using as optimum strategy-the farmer is getting the "best deal" possible. Can you figure out the solution strategy?...
I am a brazen lion; my spouts are my 2 eyes, my mouth, and the flat of my foot. My right eye fills a jar in 2 days, my left eye in 3, and my foot in 4.
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

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