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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.
To find three quantities x.y, and z...
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.
There are two numbers which are to each other as 5 and 6 and the sum of their squares is 2196. What are the numbers?
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.
Suppose a ladder 60 feet long is placed in a street so as to reach a window 37 feet above the ground on one side of the street...
Twenty-three weary travelers entered a delightful forest. There they found 63 numerically equal piles of plantain fruit.
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?...
A certain bishop ordered that 12 loaves be divided among his clergy.
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.