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Convergence articles

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Radii of Three Circles

Determine the radii of three equal circles described within and tangent to a given circle, and also tangent to each other.

Galileo's Siderius Nuncius
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.
Travelling Steamers

The steamer, Katie, leaves the wharf at New Orleans and runs an average speed of 15 mph. When Katie had gone 25 miles, the steamer R.E. Lee leaves the wharf and runs the average speed of 18 mph. How far will the Lee go before she overtakes the Katie?

Height of the Clouds

The edge of a cloud is at an altitude of 20 degrees and the sun above it at 35 degrees. The shadow cast by the edge of the cloud fall on a object 2300 yards away, how high is the cloud?

The Cog-Wheel Revolution

Two cog-wheels, one having 26 cogs, and the other 20 cogs, run together. In how many revolutions of the larger wheel will the smaller gain in 12 revolutions?

Cow Dilemma

Suppose that for every 4 cows a farmer has, he should plow 1 acre of land, and allow 1 acre of pasture for every 3 cows; how many cows could he keep on 140 acres?

Gardening

An oblong garden is a half yard longer than it is wide and consists entirely of a gravel walk...

X Marks The Spot

What is the value of X...

Learning Geometry in Georgian England

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

Horses and Stalls

It is required to determine whether 30 horses can be put into 7 stalls; so that in every stall there may be, either a single horse, or an odd number of horses.

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