"De analysi" thereby became the first systematic discussion of the calculus by Newton to circulate in public, and is thus one of the founding documents in the history of modern mathematics.

Containing the text of two of Newton's earliest work, as well his first two published treatises, the Analysis serves as a wonderful starting place for those studying the history of the calculus.

The Priority Dispute
A full history of the priority dispute between Newton and Leibniz over the invention of the calculus is not possible here, but the role of the Analysis in the affair demands a short account.

The story may be said to begin with the composition of the "De Analysi" which, as mentioned above, was given to Isaac Barrow in 1669 and copied by John Collins.

When Leibniz independently began to work on the calculus in 1675, he was soon not only corresponding with Newton, through third parties but also corresponding with Collins. Collins even showed Leibniz his copy "De Analysi."

Scholars have determined that Leibniz did indeed arrive at his discoveries in the calculus independently. However, when he published his first work on the calculus in the Acta Eruditorum for 1684, Leibniz did not mention his correspondence with Newton or his exchanges with Collins. This gave the impression to many European mathematicians that Leibniz was the sole inventor of the calculus, because Newton had not actually published any of his mathematical work of the previous 20 years.

In 1693, however, John Wallis published a history of "fluxions" (which was Newton's name for the calculus) in his Opera Mathematica. The publication of the Newton correspondence with Leibniz, which had taken place through intermediaries such as Henry Oldenburg, soon followed. Although Leibniz had always acknowledged Newton's work in private correspondence, the grounds for a public battle were now set.

The first shot was fired by Nicolas Fatio de Diullier, who published comments in 1697 implying that Leibniz had plagiarized his calculus from Newton. In 1703 George

Cheyne published Fluxionum methodis inversa claiming that all work on the calculus in the previous 24 years was merely derivative of Newton's original methods.

Newton himself now took a step in the dispute by published the two mathematical appendices to the Opticks in 1704. Newton was careful to mention that he had made his initial discoveries in 1664 and 1665. Newton also mentioned that he had referred to general methods of squaring curvilinear figures in correspondence with Leibniz as early as 1676, and that he had at one time lent out a manuscript describing these methods in more detail. "Having met with some things copied out of it," Newton wrote — appearing to suggest that Leibniz was the copyist — he now decided to publish the material himself.

The next major event in the dispute was publication of an article by John Keill in the Philosophical Transactions of the Royal Society for 1708 who more or less directly accused Leibniz of having plagiarized the calculus from Newton, changing only the name (from fluxions) and method of notation. This edition of the Philosophical Transactions was not published until 1710 and Leibniz does not appear to have seen it until March of the following year. When he did read it, Leibniz wrote to the Secretary of the Royal Society demanding an apology.

When the letter arrived, Newton, who had been President of the Royal Society since 1705, collaborated in the composition of Keill's response which restated the charge of plagiary in even more inflammatory language. Outraged, Leibniz again wrote to the Royal Society to demand an apology.

Meanwhile, London mathematics teacher William Jones conceived the idea of publishing a volume of Newton's mathematical works. Going through the papers of the now late John Collins he found Collins' copy of "De analysi." Realizing that this copy represented independent proof of Newton's priority in the invention of the calculus, Jones included it in the Analysis book of 1711 along with extracts from correspondence relating to the original exchanges between Newton and Leibniz that had taken place more than 30 years earlier. Accordingly, Jones's volume now became an important part of the priority dispute.

How important it became can be seen from what happened after Leibniz's second demand for an apology arrived for Newton, as head of the Royal Society, set up a commission to judge the dispute. The commission naturally concluded in Newton's favor, then published a report (almost certainly written by Newton himself) entitled Commercium epistolicum d. Johannis Collins et aliorum de analysi promota (1712). That is to say, this report focused heavily on Collins' copy of "De anylysi" and his correspondence with Leibniz — all in support of Keill's original charge of plagiarism.

The priority dispute was far from over, but the Analysis had now played a crucial role in its progress.