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Johannes Kepler's Astronomia Nova

Three images from Kepler's 1609 Astronomia Nova, the text in which he introduced his first two laws of planetary motion

Prove the Straight Lines

Given two circles tangent at the point P with parallel diameters AB and CD, prove that APD and BPC are straight lines.

Conic Contents

Determine the greatest cylinder that can be inscribed in a given cone.

Tree and Vine

A tree is 2 zhang tall and has a circumference of 3 chi. There is a vine that winds seven equally spaced times around the tree and reaches the top. What is the length of the vine?

Lotus in the Lake

In a certain lake, swarming with red geese, the tip of a lotus bud was seen to extend a span above the surface of the water.

Two Numbers

Find two numbers with sum 20 and when squared their sum is 208.

Sick Leave

A teacher agreed to teach 9 months for $562.50 and his board. At the end of the term, on account of two months' absence caused by sickness, he received only $409.50. What was his board worth per month?

A Disquisition on the Square Root of Three

The author compares Greek ladder, continued fraction, and Newton's Method approximations, noting that the Greek ladder easily gives both of Archimedes' famous bounds.

Four Circles in a Square

In a given square, inscribe 4 equal circles so that...

Tools of American Mathematics Teaching, 1800-2000

A survey of the use of technology in American mathematics teaching over the past 200 years.