Claremont Center for the Mathematical Sciences

What is the trajectory of a projectile launched into the air? Archimedes, Tartaglia, Galileo, Torricelli, Descartes, Newton and Bernoulli are just a few among the many mathematicians who had investigated this question by the time it caught the attention of Leonhard Euler. Not to mention that his boss at the time was more than a little interested in specific applications of the solution, such as determining the horizontal range of a musket ball with 3/4 inch diameter and an initial velocity of 1700 feet per second when fired at an angle of 45 degrees.

The 18^th century saw significant advances in the analysis of the trajectory of a projectile in air. In the first half of this century, Benjamin Robins, a British mathematician and military engineer, published New Principles of Gunnery, the first book to deal extensively with external ballistics. Robins' work motivated a deeper mathematical analysis of projectile motion and invited ``commentary'' from Euler. In this talk we consider the influence of Robins' work and look at how Euler used it to attack the problem of projectile motion.