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Convergence articles

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A history of attempts to develop formulas expressing the sums of powers of the first n positive integers from the Pythagoreans to Jakob Bernoulli. With exercises.
There is a round fish pond of certain dimensions, and into the pond is dropped a marble column. How high will the water rise?
A water tub holds 73 gallons; the pipe which fills it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes.
A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?

An introduction to the prime numbers in many of their aspects.

Two men have a certain amount of money. The first says to the second, "If you give me 5 denari, I will have 7 times what you have left."
What proportions of sugar at 8 cents, 10 cents and 14 cents per pound, will compose a mixture worth 12 cents per pound?

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

If you are h feet tall and walk all the way around the Earth, keeping to the same circumference, how much farther has your head gone than your feet when you complete the journey?
Determine the greatest cylinder that can be inscribed in a given cone.

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