A number of pamphlets and other writings relevant to the Analyst controversy are available here, and are listed below under the following headings:

The following texts by Isaac Newton, from the Principia and elsewhere, are particularly relevant to the Analyst controversy:

- Philosophiae Naturalis Principia Mathematica, Book Two, Lemma II.
- Philosophiae Naturalis Principia Mathematica, Book One, Section I.
- Introductio ad Quadraturam Curvarum (Introduction to the Quadrature of Curves)
- An Account of the Book entituled Commercium Epistolicum Collinii & aliorum, De Analysi promota; published by order of the Royal-Society, in relation to the Dispute between Mr. Leibnitz and Dr. Keill, about the Right of Invention of the Method of Fluxions, by some call'd the Differential Method.

In 1734, George Berkeley, Bishop of Cloyne, in Ireland, published The Analyst; or a Discourse Addressed to an Infidel Mathematician. Wherein it is examined whether the Object, Principles and Inferences of the modern Analysis are more distinctly conceived, or more evidently deduced, than Religious Mysteries and Points of Faith. As is apparent from the title, Berkeley was motivated by more than simply a concern for the soundness of the mathematical methods then in vogue. Nevertheless he developed his argument by criticising certain passages to be found in the Philosophiae Naturalis Principia Mathematica and the Introductio ad Quadraturum Curvarum of Isaac Newton, and in the Analyse des infiniment petits pour l'intelligence des lignes courbes of the Marquis de l'Hôpital. Berkeley subsequently published a number of other works arising out of the controversy generated by the Analyst, replying to responses by `Philalethes Cantabrigiensis' [James Jurin] and Jacob Walton.

The following texts are available here:

- The Analyst
- A Defence of Free-Thinking in Mathematics
- Reasons for not replying to Mr. Walton's Full Answer

Berkeley's parting shot took the form of a footnote in Siris

The first to respond to Berkeley's Analyst was James Jurin, who wrote under the pseudonym of `Philalethes Cantabrigiensis'. Jurin had for a time been Secretary of the Royal Society, and was a noted physician in London.

The following responses to Berkeley are available here:

- Geometry no Friend to Infidelity; or a Defence of Sir Isaac Newton and the British Mathematicians
- The Minute Mathematician

The differing approaches taken by James Jurin and Benjamin Robins in their respective defences of the methods of Isaac Newton subsequently gave rise to a controversy between Robins and Jurin, conducted in the pages of The Present State of the Republick of Letters.

Another who responded to Berkeley's Analyst was the Dublin-based mathematician Jacob Walton. Very little is known about Walton; some information about him is however to be found in the following article:

Wallis, Ruth, `Who was J. Walton, adversary of Bishop Berkeley?', Annals of science 51 (1994), 539-540.

The following responses to Berkeley are available here:

- Vindication of Sir Isaac Newton's Principles of Fluxions
- The Catechism of the Author of the Minute Philosopher fully answer'd
- An Appendix in answer to the `Reasons for not replying to Mr. Walton's full answer'

Benjamin Robins wrote what is perhaps the most thorough and well-written response to Berkeley, with the exception of Colin Maclaurin's two-volume Treatise of Fluxions.

Works of Robins are available here include the following:

Benjamin Robins and James Jurin differed considerably in their interpretation of certain passages in the works of Sir Isaac Newton. These differences were discussed in the pages of The Present State of the Republick of Letters in the years 1735 and 1736. (The dispute was continued between James Jurin and Henry Pemberton, in December 1836 and in 1837.)

The following contributions to this controversy are available here:

- Benjamin Robins, Account of `A discourse concerning the nature and certainty of Sir Isaac Newton's methods of fluxions, and of prime and ultimate ratios'. (The present state of the Republick of Letters, October 1735, pp. 245-270.)
- James Jurin, Considerations upon some passages contained in two letters to the Author of the Analyst, written in defence of Sir Isaac Newton, and the British Mathematicians. (The present state of the Republick of Letters, November 1735, pp. 369-396.)
- Benjamin Robins, A review of some of the principal objections that have been made to the doctrines of fluxions and ultimate proportions; with some remarks on the different methods that have been taken to obviate them. (The present state of the Republick of Letters, December 1735, pp. 436-447.)
- James Jurin, Considerations occasioned by a paper in the last Republick of Letters, concerning some late objections against the doctrine of fluxions, and the different methods that have been taken to obviate them. (The present state of the Republick of Letters, January 1736, pp. 72-91.)
- Benjamin Robins, A dissertation shewing, that the account of the doctrines of fluxions, and of prime and ultimate ratios, delivered in a treates entitled, A discourse concerning the nature and certainty of Sir Isaac Newton's methods of fluxions, and of prime and ultimate ratios, is agreeable to the real sense and meaning of their great inventor. (The present state of the Republick of Letters, April 1736, pp. 290-335.)
- James Jurin, Considerations upon some passages of a Dissertation concerning the doctrine of fluxions, published by Mr. Robins in the Republick of Letters for April last. (The present state of the Republick of Letters, July 1736, pp. 45-82.)
- Benjamin Robins, Remarks on the considerations relating to fluxions, &c. that were published by Philalethes Cantabrigiensis in the Republick of Letters for the last month. (The present state of the Republick of Letters, August 1736, pp. 87-110.)
- James Jurin, The remainder of the paper begun in our last, entituled, Considerations upon some passages of a Dissertation concerning the doctrine of fluxions, published by Mr. Robins in the Republick of Letters for April last. (The present state of the Republick of Letters, August 1736, pp. 111-179)
- Benjamin Robins, Remarks on the remainder of the considerations relating to fluxions, &c. that was published by Philalethes Cantabrigiensis in the Republick of Letters for the last Month. To which is added by Dr. Pemberton a postscript occasioned by a passage in the said considerations. (The present state of the Republick of Letters, September 1736, Appendix, pp. 2-40.)
- James Jurin, Observations upon some remarks relating to the method of fluxions, published in the Republick of Letters for August last, and in the appendix to that for September. (The present state of the Republick of Letters, November 1736, pp. 2-79)
- Benjamin Robins, Advertisement. (The present state of the Republick of Letters, December 1736, Appendix, pp. 491-492.)

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David R. Wilkins(

School of Mathematics

Trinity College, Dublin