''Method of Fluxions'' ( la, De Methodis Serierum et Fluxionum) is a mathematical treatise by Sir Isaac Newton which served as the earliest written formulation of modern

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

. The book was completed in 1671, and published in 1736. Fluxion is Newton's term for a

derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...

. He originally developed the method at Woolsthorpe Manor during the closing of

Cambridge Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge bec ...

during the Great Plague of London from 1665 to 1667, but did not choose to make his findings known (similarly, his findings which eventually became the ''

Philosophiae Naturalis Principia Mathematica Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. S ...

'' were developed at this time and hidden from the world in Newton's notes for many years). Gottfried Leibniz developed his form of calculus independently around 1673, 7 years after Newton had developed the basis for differential calculus, as seen in surviving documents like “the method of fluxions and fluents..." from 1666. Leibniz however published his discovery of differential calculus in 1684, nine years before Newton formally published his fluxion notation form of calculus in part during 1693. The calculus notation in use today is mostly that of Leibniz, although Newton's dot notation for differentiation

\dot

for denoting derivatives with respect to time is still in current use throughout

mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objec ...

and

circuit analysis A network, in the context of electrical engineering and electronics, is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many ...

. Newton's ''Method of Fluxions'' was formally published posthumously, but following Leibniz's publication of the calculus a bitter rivalry erupted between the two mathematicians over who had developed the calculus first, provoking Newton to reveal his work on fluxions.

Newton's development of analysis

For a period of time encompassing Newton's working life, the discipline of

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

was a subject of controversy in the mathematical community. Although analytic techniques provided solutions to long-standing problems, including problems of quadrature and the finding of tangents, the proofs of these solutions were not known to be reducible to the synthetic rules of Euclidean geometry. Instead, analysts were often forced to invoke

infinitesimal In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally re ...

, or "infinitely small", quantities to justify their algebraic manipulations. Some of Newton's mathematical contemporaries, such as

Isaac Barrow Isaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for proof of the fundamental theorem ...

, were highly skeptical of such techniques, which had no clear geometric interpretation. Although in his early work Newton also used infinitesimals in his derivations without justifying them, he later developed something akin to the modern definition of limits in order to justify his work.

References and notes

External links

''Method of Fluxions''
at the

Internet Archive The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...

{{authority control History of mathematics Mathematics books Books by Isaac Newton 1671 books 1736 books Differential calculus Mathematics literature 1736 in science Books published posthumously

Newton's development of analysis

See also

References and notes

External links