Hostname: page-component-cb9f654ff-kl2l2 Total loading time: 0 Render date: 2025-09-09T18:45:27.834Z Has data issue: false hasContentIssue false
  • English
  • Français

VIII. A New Series for the Rectification of the Ellipsis; together with some Observations on the Evolution of the Formula (a2 + b2 − 2ab cos θ)n

Published online by Cambridge University Press:  17 January 2013

James Ivory
Get access Rights & Permissions [Opens in a new window]

Extract

Dear Sir,

Having, as you know, bestowed a good deal of time and attention on the study of that part of physical astronomy which relates to the mutual disturbances of the planets, I have, naturally, been led to consider the various methods of resolving the formula (a2 + b2 − 2ab cos θ)2 into infinite series of the form A + B cos θ + C cos 2θ + &c. In the course of these investigations, a series for the rectification of the ellipsis occurred to me, remarkable for its simplicity, as well as its rapid convergency. As I believe it to be new, I send it you, inclosed, together with some remarks on the evolution of the formula just mentioned, which, if you think proper, you may submit to the consideration of the Royal Society.

Information

Type
Papers Read Before the Society
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 4 , Issue 2 , 1798 , pp. 177 - 190
Copyright
Copyright © Royal Society of Edinburgh 1798

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable