I am looking for which manuscripts and if available, through what chains of transmission copies of Newton's book "TheMethod of Fluxions" have reached us today
So far I could not find anything with google searches.
thanks for the help
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2 Answers
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Essentially, there is only one authoritative edition most closely sourced from the original. Newton's work on fluxions was not published during his lifetime even though he had in preparation an incomplete manuscript and notes for possible publication. The text we currently have is John Colson's English translation published in 1736 from a transcription belonging to William Jones. Most of the extant work of Newton can be viewed at the University of Cambridge, Newton Project. Begin with this link to the Papers of Sir Isaac Newton or continue at this link through the Newton Project. A pdf of the original 1736 text is readily available through Google.
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The question asks for chains of transmission and for manuscripts antecedent to Newton's eventual book(s) on fluxions.
So I would recommend, as the first places to start, the 8-volume series of 'Mathematical Papers of Isaac Newton' edited by D T Whiteside (Cambridge University Press 1967-81), and also, where available and if needed, the corresponding high-definition online images of the manuscripts at the University Library in Cambridge. Advantages of the book volumes include their commentaries, and the fact that many of the manuscripts in Latin have been provided with an English translation. Advantage of the manuscript images is to see the manuscripts as Newton left them.
For each of the Whiteside volumes, the full table of contents and index are now available online (see some links below). Content from the books is otherwise hard to find online. (Hardly any of the text was visible when I last looked through the Google pages, which only showed metadata.)
Much of Newton's work in the field of calculus is in volumes 1, 3 and 7 of the Whiteside series. Here, for example, to start with, is part of the contents list for volume 1 (1664-6), along with some of the manuscript numbers in the archive at the University Library at Cambridge:
First, from Volume 1 of Whiteside series:
The Mathematical Papers of Isaac Newton, Volume I: 1664-1666, (ed.) D T Whiteside (1967), from CUP website:-
Table of contents at: https://assets.cambridge.org/97805210/45957/toc/9780521045957_toc.pdf
index at: https://assets.cambridge.org/97805210/45957/index/9780521045957_index.pdf
The volume includes:--
Part II. Researches in Analytical Geometry and Calculus 1664–1666:
Early notes on Analytical Geometry (autumn 1664) ... p 155
Work on the Cartesian Subnormal (winter 1664/5) ... p 213
Miscellaneous Problems in Analytical Geometry and Calculus (1664/5) ... p 234
ULC MS Add 4004 : 5v, 8v, 87v-89v,
Normals, Curvature and the Resolution of the General Problem of Tangents (winter 1664-spring 1665) ... p 245
ULC MS Add 4004 : 6r, 30v-33v, 47r-50r,
The Calculus Becomes an Algorithm (mid-1665) ... p 298
ULC MS Add 4000 : 92v-96r, 120r-149r,
ULC MS Add 3960.12 : 206, 199-202
ULC MS Add 3958.4 : 77r,80v
ULC MS Add 4000 : 152r-163v
ULC MS Add 3958.2 : 30v,30r
The General Problems of Tangents, Curvature and Limit-Motion Analysed by the Method of Fluxions (oct 1665-may 1666) ... p 369
ULC MS Add 3958.2 : 35r,37v,34v
ULC MS Add 4004 : 50v-51r , 57r-57v, 51r-51v
The October 1666 Tract on Fluxions ... p 400 (-450)
ULC MS Add 3958.3 : 48v-63v
(The manuscripts within a numbered section of the archive are numbered by leaves (folios), not by pages, where r indicates the front or recto side of a numbered leaf and v the back or verso.)
(The online manuscript images for the last-mentioned item, the 1666 tract on fluxions, begin at https://cudl.lib.cam.ac.uk/view/MS-ADD-03958/92 .
(Meaning of the numbers:- image 92 of 190 in section 3958 shows folio 48 verso in subsection 3).
The items referred to in MS Add 4000 (the 'College notebook') from 92v onwards can be seen at https://cudl.lib.cam.ac.uk/view/MS-ADD-04000/197 onwards.
The mentioned content from MS Add 4004 (the 'Waste book') begins online at https://cudl.lib.cam.ac.uk/view/MS-ADD-04004/22 (f.5v, image 22 of 935).
Next, Volume 3 of Whiteside series (1670-73) includes:
sec.2. The tract "De methodis serierum et fluxionum" ... pp 32-330 (the first leaf is restored from contemporary transcripts, the rest survives in ULC MS Add 3960.14 : 3-132.
(I looked for the images, which are supposed to be online at https://cudl.lib.cam.ac.uk/view/MS-ADD-03960 , but the pages and images in that section seem poorly indexed.)
It is worth noting that by no means all of Newton's work and papers in the field of calculus was expressed in what became 'fluxional' notation: he seemed (awkwardly for everyone else) to think of notations as secondary compared with the substance of methods. This does mean that a search for antecedents of the published book on fluxions needs to consider, as well, the wider range of expressions used by Newton. Some of Newton's calculus work was even cast in geometrical form, and is represented like that in the Principia. Near-contemporaries in the years immediately following publication of the 'Principia' recognized the essential identity between the various forms of expression. An example was Pierre Varignon (1654-1722), who defended the Leibnizian version of the calculus, shortly after 1700, from attacks made upon it by Michel Rolle (1652-1719). (The episode amounted to an earlier 'iteration' of the better-known attacks made by Berkeley in the 1730s on the calculus, criticizing its use of infinitesimals.) Varignon, in support of his defence of the calculus, referred to Newton's demonstrations in section 1 of book 1 in the 'Principia', which are not vulnerable to the criticisms of infinitesimals made by Rolle or Berkeley (see answers and linked references in Did Michel Rolle say that the calculus is "a collection of ingenious fallacies"? and Why is calculus missing from Newton's Principia? (answer, it isn't missing)).
