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Mathematics is often referred to today as the "science of patterns." But has this always been true historically, or is this something that happened in recent times? The question is discussed here with reference to the work of Euclid and Jacob Steiner.
There are four companies, in one of which there are 6 men, in another 8, and in each of the remaining two, 9 men. How many ways can a committee of 4 men be composed by choosing one man from each company?

Problems from a 15th century French manuscript, including one with negative solutions

A horse, halving its speed each day, travels 700 miles in 7 days. How far does it travel each day?

Curve sketching, tangent lines, and optimization, explored via interactive applets

This is page 167 from the Exercitationes mathematicae (1657) of Frans van Schooten (1615-1660). This book contained a collection of mathematical construction problems, among much else. It was one of the books read by Isaac Newton while he was a student at Cambridge University and helped to introduce him to modern mathematics. On this page we see a construction enabling one to find the distance across a river.
A description of this well-regarded website.
Three men wish to buy a horse but none have a sufficient amount of money for the purchase; to do so they must borrow from each other. How much money does each man have and what is the price of the horse?
There is a right triangle where: the sum of the upright multiplied by itself twice and the hypotenuse multiplied by itself is 700 units; and, the sum of the base multiplied by itself twice and the hypotenuse multiplied by itself is 900 units.
Divide 100 loaves of bread among 10 men including a boatman, a foreman, and a doorkeeper, who receives double portions. What is the share of each?

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