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Convergence articles

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A sourcebook of original materials in the history of mathematics from ancient times to the early twentieth century.
If an arc of 45 degrees on one circumference is equal to an arc of 60 degrees on another circle, what is the ratio of the areas of the circle?
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
A man entered an orchard through 7 gates, and there took a certain number of apples. When he left the orchard, he gave the first guard half the apples he had and 1 apple more.

Images from Frans van Schooten's 1659 edition of The Geometry of Rene Descartes

Now there is a wall 5 feet thick and two rats tunnel from opposite sides.
Determine the greatest cylinder that can be inscribed in a given cone.
Two officers each have a company of men, the one has 40 less than the other.
An old Chinese general led his army to a river with a steep bank. Standing atop the bank, he held a stick 6 feet long perpendicular to himself.
Now there are 100 deers [being distributed] in a city. If one household has one deer there is a remainder...Find the number of households in the city.

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