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Convergence articles

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A small selection of Euler's works, explained by a master expositor.
The square of a certain number multiplied by itself and by 200 is 446,976. What is the number?
Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
In how many ways can a vowel and a consonant be chosen out of the word "logarithms?"
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.
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?
A man has four creditors. To the first he owes 624 ducats; to the second, 546; to the third, 492; and to the fourth 368.
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.
A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity.
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.

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