The Garden of Archimedes
A Museum for Mathematics |

works in the section

- 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. - Isaac Newton,
*Philosophiae naturalis Principia mathematica*, editio secunda, Cantabrigiae, [Cambridge University], 1713 [first edition 1687] - 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

Almost twenty years before the publication of the

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.