Skip to main content Accessibility help
×
Hostname: page-component-7479d7b7d-k7p5g Total loading time: 0 Render date: 2024-07-12T11:26:57.676Z Has data issue: false hasContentIssue false
This chapter is part of a book that is no longer available to purchase from Cambridge Core

Discussion of Fluxions: from Berkeley to Woodhouse

from The Eighteenth Century

Marlow Anderson
Affiliation:
Colorado College
Victor Katz
Affiliation:
University of the District of Columbia
Robin Wilson
Affiliation:
Open University
Get access

Summary

The first direct statement of Newton's method and notation of fluxions was printed in 1693 in Wallis's Algebra. Here and in the Principia of 1687 Newton made use of infinitely small quantities, but in his Quadrature of Curves of 1704 he declared that “in the method of fluxions there is no necessity of introducing figures infinitely small.” No other publication of Newton, printed either before 1704 or after, equalled the “Quadrature of Curves” in mathematical rigor. Here Newton reached his high water mark of rigidity in the exposition of fluxions. By a fluxion, Newton always meant a finite velocity. With one exception, all British writers on the new calculus before the appearance of Berkeley's Analyst in 1734 used the Newtonian notation consisting of dots or “prick'd letters,” and also Newton's word “fluxion.” But strange to say, most of these writers did not use Newton's concepts. They applied the term “fluxion” to the infinitely small quantities of Leibniz—thus using a home label on goods of foreign manufacture. Of sixteen or more writers in Great Britain during the period of 1693–1734, nine or more call a fluxion an infinitely small quantity; three writers do not define their terms, while only four follow Newton's exposition of 1687 or 1693, involving fluxions as finite velocities and “moments” as infinitely small quantities, or else follow Newton's exposition of 1704, involving fluxions as finite velocities and avoiding infinitely small quantities almost entirely.

Type
Chapter
Information
Sherlock Holmes in Babylon
And Other Tales of Mathematical History
, pp. 325 - 331
Publisher: Mathematical Association of America
Print publication year: 2003

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.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×