One segment of a course for nonscience majors using limited parts of Newton'sPrincipiais described. The relevant source material is reviewed. The class studied in detail the proofs of some of the early theorems in thePrincipia, including the law of areas for central forces and the relation between forces and motion in conic sections. In spite of warnings in the literature, this was not too difficult; the students' background in geometry proved to be adequate to the task. It is suggested that it may be possible to follow a similar approach in high-school physics, or in the last several months of high-school geometry. In contrast with the usual course for nonscience majors and with most beginning courses in physics, Newton rapidly obtains important results. Using thePrincipiaprovides an introduction to the history of science in one detailed situation where some aspects of Newton's thought processes are examined.