An Episode in the History of Dynamics: Jakob Hermann's Proof (1716–1717) of Proposition 1, Book 1, of Newton'sPrincipia
✍ Scribed by Niccolò Guicciardini
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 183 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0315-0860
No coin nor oath required. For personal study only.
✦ Synopsis
Proposition 1 of Book 1 of Newton's Principia (1687), which states that Kepler's area law holds for any central force, plays a fundamental role in the study of central force motion. Newton's geometric proof of this proposition is based on an intuitive theory of limits. In 1716-1717 the Swiss mathematician, Jakob Hermann, gave a proof of Proposition 1 based on infinitesimals. The present paper discusses both Newton's and Hermann's solutions. A comparison of the two gives us an insight into an episode of the process that led from the geometric style of Newton's Principia to the analytic style of Euler's Mechanica (1736).