General
Main content blocks
- Lecturer: Profile: Christopher Hollings
A prior course on the history of mathematics is desirable but not essential. Knowledge of the classical (focus/directrix) construction of conic sections would be useful, as would be some prior knowledge of the structure and mathematical language of Euclid’s Elements, i.e., the Euclidean style of geometrical construction and the language of ratio. The relevant ideas concerning conics and the Elements will, however, be introduced as we go along. Otherwise, the mathematical prerequisites for reading the Principia are slight — one of the remarkable aspects of the Principia is that it starts from some quite elementary ideas and then pushes them a very long way.
Students who have taken introductory courses on dynamics will see some of the same material presented here in a very different language and context. Those who have taken further courses on classical mechanics and fluid dynamics will have seen how Newton’s ideas were developed further, but such courses should not be considered as prerequisites.
In this reading course, we will read selected portions from Isaac Newton’s Philosophiæ naturalis principia mathematica (1687), a key text for the European science of the late seventeenth and subsequent centuries. The Principia laid out, among other things, the foundations of Newtonian mechanics and the law of universal gravitation. Readings directly
from the Principia will be supplemented by appropriate secondary sources, with the aim of understanding the arguments of the text on their own terms. The course will also situate the Principia within its seventeenth-century context, examining its origins and its subsequent impact on mathematics and natural philosophy. In doing so, it will provide historical perspective for some of the applied courses that students may already have taken.
The first session will take the form of a lecture, but thereafter students will be expected to do the reading and to present on it each week.
Students will gain:
• an understanding of the content of Newton’s Principia in its original form;
• an appreciation of the place of the Principia in European science, from its origins to its impact;
• a historical perspective on some of the applied courses that they may already have taken.
Skills developed will include:
• the ability to decipher mathematics written in an unfamiliar form;
• the use of secondary sources to support the last point;
• efficient note-taking;
• oral discussion and presentation