The Garden of Archimedes
 A Museum for Mathematics

Newton and Leibniz: the birth of calculus

works in the section
  1. Gottfried Wilhelm von Leibniz, Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationales quantitates moratur, et singulare pro illis calculi genus, in Acta eruditorum, Lipsiae, 1684.
  2. Isaac Newton, Philosophiae naturalis Principia mathematica, editio secunda, Cantabrigiae, [Cambridge University], 1713 [first edition 1687]
  3. Isaac Newton, Methodus fluxionum et serierum infinitarum cum eisudem applicatione ad curvarum geometriam, in Opuscola mathematica philosophica et philologica, tomus primus, Lausannae et Genevae, apud Marcum Michaelem Bousquet, 1744.

see also

In October 1684 Leibniz published on the Acta eruditorum his Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationales quantitates moratur, et singulare pro illis calculi genus. This is traditionally considered to be the birth of infinitesimal calculus. The title could be translated as "New method for maxima and minima, and for tangents, that is not hindered by fractional or irrational quantities, and a singular kind of calculus for the above mentioned". Reference to the work of Fermat is evident. In the short report, Leibniz directly introduced the differentiation rules. He manages to overcome the limits of the previous methods by separating the difficulties deriving from the complexity of the equation that was until then considered in its totality.
Almost twenty years before the publication of the Nova Methodus of Leibniz, in 1665-1666, Newton had already elaborated his calculus. The fundamental elements, with the systematic use of developments in series, find their first version in the De analysi per aequationes numero terminorum infinitas written in 1669 but published only in 1711.

The typical formulation of the problem in terms of finding the relations between "fluxions" (meaning the velocity of increasing) of given "fluents or flowing quantities" (meaning variables) appears in the following two works: the Methodus fluxionum et serierum infinitarum and the De quadratura curvarum, written respectively in 1671 and in 1676 but published themselves only later. The first publication of the results that Newton had obtained takes place only in 1687, sometime later the Nova Methodus of Leibniz, with the Philosophiae naturalis Principia mathematica. At the opening of the first book, some lemmas illustrate the fundaments of calculus in the form of "the prime and ultimate ratios for evanescent quantities" and in the second book we find the algorithms of differentiation. In these last ones Newton recognizes in an annotation, the fundaments of his method as well as Leibniz's, method that the two scientists had communicated to each other through their correspondence of the previous ten years. In the third edition of the Principia the reference disappears. This is the sign of the well known argument between the two regarding the priority of the invention of calculus that broke out at the end of the century and that divided the mathematicians of the time.

Panels of the exhibition (only italian available)

History of calculus...

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