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A merchant woman buys and sells apples and pears for Denaros. How much did she invest in apples; how much in pears?
There are two numbers which are to each other as 5 and 6 and the sum of their squares is 2196. What are the numbers?
Two ants are 100 paces apart, crawling back and forth along the same path. The first goes 1/3 pace forward a day and returns 1/4 pace; the other goes forward 1/5 pace and returns 1/6 pace. How many days before the first ant overtakes the second?
Short sketches on how mathematicians work and think.
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?
A square circumscribed about a given circle is double in area to a square inscribed in the same circle. True of false? Prove your answer.

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

Prove that if the sums of the square opposite sides of any quadrilateral are equal, its diagonals interect at right angles.
Determine the dimensions of the least isosceles triangle ACD that can circumscribe a given circle.