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Convergence articles

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Two circles of radii 25 feet intersect so that the distance between their centers is 30 feet. What is the length of the side of the largest square inscribable within their intersecting arcs?
Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
This is the title page of the Siderius Nuncius (Starry Messenger) of Galileo (1564-1642), published in 1610. This book was a report on Galileo's first investigations with a telescope. Also includes Galileo's initial sketches of the surface of the moon.
If a ball 6 inches in diameter weighs 32 lbs, what will be the weight of a ball 3 inches in diameter?
In how many ways can a vowel and a consonant be chosen out of the word "logarithms?"
A discussion not only of the mathematics of pi, but of its applications through the centuries.
There is a round fish pond of certain dimensions, and into the pond is dropped a marble column. How high will the water rise?

The copybooks of two young men reveal very different purposes in learning geometry.

A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?
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.