''De analysi per aequationes numero terminorum infinitas'' (or ''On analysis by infinite series'', ''On Analysis by Equations with an infinite number of terms'', or ''On the Analysis by means of equations of an infinite number of terms'') is a mathematical work by
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
.
Creation
Composed in 1669,
[Carl B. Boyer, Uta C. Merzbach ] during the mid-part of that year probably, from ideas Newton had acquired during the period 1665–1666.
Newton wrote
The explication was written to remedy apparent weaknesses in the ''logarithmic series''
, that had become republished due to
Nicolaus Mercator
Nicholas (Nikolaus) Mercator (c. 1620, Holstein – 1687, Versailles), also known by his German name Kauffmann, was a 17th-century mathematician.
He was born in Eutin, Schleswig-Holstein, Germany and educated at Rostock and Leyden after which he ...
,
[Britannica Educational ] or through the encouragement of Isaac Barrow in 1669, to ascertain the knowing of the prior authorship of a general method of ''infinite series''. The writing was circulated amongst scholars as a manuscript in 1669,
including
John Collins a mathematics ''
intelligencer
Intelligencer is an archaic word for a person who gathers intelligence, like a spy or secret agent. The term may refer to:
Newspapers
* ''Daily Intelligencer (disambiguation)'', multiple papers
* ''Edwardsville Intelligencer'' (1862–present) ...
'' for a group of British and continental mathematicians. His relationship with Newton in the capacity of informant proved instrumental in securing Newton recognition and contact with
John Wallis
John Wallis (; la, Wallisius; ) was an English clergyman and mathematician who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 he served as chief cryptographer for Parliament and, later, the royal ...
at the Royal Society.
Both Cambridge University Press and Royal Society rejected the treatise from publication,
being instead published in London in 1711 by William Jones, and again in 1744, as ''Methodus fluxionum et serierum infinitarum cum eisudem applicatione ad curvarum geometriam'' in ''
Opuscula mathematica, philosophica et philologica
''Opus'' (pl. ''opera'') is a Latin word meaning "Work (disambiguation), work". Italian equivalents are ''opera'' (singular) and ''opere'' (pl.).
Opus or OPUS may refer to:
Arts and entertainment Music
* Opus number, (abbr. Op.) specifying order ...
'' by Marcum-Michaelem Bousquet at that time edited by Johann Castillioneus.
Content
The
exponential series, i.e. tending toward infinity, was discovered by Newton and is contained within the ''Analysis''. The treatise contains also the sine series and cosine series and arc series, the logarithmic series and the binomial series.
M. Woltermann
Washington & Jefferson College
Retrieved 8 February 2012
See also
* Newton's method
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valu ...
References
External links
Text of ''De analysi'' (Latin)
- PDF version
{{Isaac Newton
Latin texts
Works by Isaac Newton
Infinity