We probably know as much about the printing history of Newton's Principia mathematica as of any book of the seventeenth century. The definitive scholarship on the writing and printing of the Principia appears in I. B. Cohen's Introduction to Newton's "Principia" (1971), and in Koyré‚ and Cohen's variorum edition of the Principia (1972), which also contains William B. Todd's definitive bibliography of the first three editions. Other useful research on this work was conducted by A. N. L. Munby nearly forty years ago. Munby's and Todd's observations may be summarized here. The original printer's manuscript in the hand of Newton's amanuensis, Humphrey Newton, still exists, as do various copies of the first edition with Isaac Newton's autograph corrections. The expenses of publication of the first edition were borne by Edmond Halley, as neither Newton nor the Royal Society had sufficient funds, and booksellers, who in those days often acted as publishers, typically refused to risk their own money on esoteric scientific books. Halley also edited the work and saw it through the press, reporting his progress to Newton in a series of letters which are preserved at Cambridge.
Having paid for the edition himself, Halley sent out presentation copies at Newton's direction and also sent Newton twenty copies for his personal use. Halley decided to market the book by placing copies on consignment with various booksellers, and he sent Newton forty copies, some bound, some in sheets, which he asked Newton to "place in the hands of one or more of your ablest booksellers to dispose of them." Munby observed that many of the bindings of the two-line imprint issue were similar, suggesting that Halley may have had many of the copies bound at one shop.
Munby researched the significance of the two states of the title page of the Principia, concluding that the more commonly found state, with the title page uncancelled and the so-called two-line imprint, reflects Halley's initial sales strategy of placing the work on consignment with many booksellers ("apud plures Bibliopolas"). The state with the three-line imprint, including the name of the bookseller, Samuel Smith, reflects Halley's decision to turn over a significant portion of the edition to Smith, probably for foreign distribution. The antiquarian bookseller Heinrich Zeitlinger of Henry Sotheran Ltd., first made the useful observation that many of the copies with the three-line "Smith" imprint were exported to the Continent. Smith was known to be very active in the import and export of books, and Munby stated that he knew of only two "Smith" copies in contemporary English bindings.
From his bibliographical analysis of the first edition Todd concluded that the edition was divided between two compositors, one setting the first two books, the other setting the third. "The first compositor, however, was allowed too few sheets and too many foliations, a circumstance which necessitated his signing a supplementary gathering *** and paging it 377-383, 400." Todd identified typographical variants which seem to be randomly distributed throughout the edition and are thus not indicative of any priority.
Todd also described the distribution of watermarks in the Principia: "The text paper exhibits a water-mark of a fleur-de-lis within a coat of arms (Heawood 626) only in preliminaries and certain sections in the earlier portion of the books, indicating perhaps that the signatures so distinguished are of later, revised settings printed off at the same time. All copies have this water-mark in P-2K; some have it also in A, F-G, M-O, 2M-2N." The distribution of watermarks appears to have nothing to do with the distribution of the variants listed above.
In estimating the size of the first edition Munby acknowledged that the work went out of print quickly and was already difficult to obtain in December 1691, when Nicholas Fatio de Duillier discussed a new edition in a letter to Christiaan Huygens. Extrapolating from the partial census figures available in 1952, Munby conjectured that at least 150 copies of the work were then extant, concluding from this and from the book's relatively common appearances in the sale rooms that "the whole edition cannot have comprised less than three hundred copies, and the figure may well have been a hundred more than this." The plentiful sales records in the forty years since Munby's account would certainly corroborate the higher estimate. Copies with the three-line imprint are much rarer than those with the two-line, suggesting that the so-called "Smith" copies may only have comprised between seventeen and thirty-three percent of the edition.
In 2020 Mordechai Feingold and Andrej Svorenčik published "A preliminary census of copies of the first edition of Newton's Principia (1687)," Annals of Science, 77 (2020) Issue three. In that they stated that they confirmed the location of 387 copies of the first edition, suggesting that the size of the original edition was at least 500 copies.
Newton's personal copy of the first edition of the Principia, with Newton's autograph corrections for the second edition, is preserved at the Wrenn Library, Trinity College, Cambridge.
Hook & Norman, The Haskell F. Norman Library of Science and Medicine (1991) no. 1586. Cohen, Introduction to Newton's Principia, ch. IV. Munby, "The two titlepages of the distribution of the first edition of Newton's Principia," Notes and Records of the Royal Society of London 10 (October 1952). Todd, "A bibliography of the Principia. Part I: The three substantive editions," in Koyré‚ & Cohen, Isaac Newton's Philosophiae naturalis principia mathematica II, 851-853.