The rare first edition of Newton's Universal Arithmetics

NEWTON, Isaac.

Arithmetica universalis; sive de compositione et resolutione arithmetica liber. Cui accessit Halleiana aequationum radices arithmetice inveniendi methodus. in usum juventutis academicae.

Cambridge: Cambridge University Press for Benjamin Tooke in London, 1707.

1st Edition. Hardcover. Very Good. Item #002711

8vo (204 x 126 mm). [8], 343 [1] pp., including half-title and several diagrams in text. Modern panelled calf, spine with 5 raised bands gilt in compartments and with gilt-lettered red morocco label, board edges with gilt decoration, new endpapers. Pages untrimmed except for top margin. Internally fresh and clean with only very little occasional spotting, small faint dampstains to inner gutter and top margin of few leaves, occasional ink annotations in contemporary hand, page number removed in leaf B1 (small hole). Leaves have been slightly cleaned, but the paper stock is still crisp and sound. Provenance: J. Hanting (inscribed on half-title), Stonyhurst College (old rubber stamp to title-page). Still a fine and wide-margined copy. ----

Babson 199; Wallis 277; Gray 277; DSB X, p.93. - FIRST EDITION and one of thousand copies published of Newton's lectures delivered while Lucasian Professor of Mathematics at Cambridge University between 1669 and 1702. The book was published and edited by William Whiston, who succeeded Newton as Lucasian Professor of Mathematics at Cambridge in 1701. "The Universal Arithmetic, which is on algebra, theory of equations, and miscellaneous problems, contains the substance of Newton's lectures during the years 1673 to 1683. His manuscript of it is still extant; Whiston extracted a somewhat reluctant permission from Newton to print it, and it was published in 1707. Amongst several new theorems on various points in algebra and the theory of equations Newton here enunciates the following important results. He explains that the equation whose roots are the solution of a given problem will have as many roots as there are different possible cases; and he considers how it happens that the equation to which a problem leads may contain roots which do not satisfy the original question. He extends Descartes' rule of signs to give limits to the number of imaginary roots. He uses the principle of continuity to explain how two real and unequal roots may become imaginary in passing through equality, and illustrates this by geometrical considerations; thence he shews that imaginary roots must occur in pairs [. . .] The most interesting theorem contained in the work is his attempt to find a rule (analogous to that of Descartes for real roots) by which the number of imaginary roots of an equation can be determined." (W.W.R. Ball, A Short Account of the History of Mathematics, pp. 330-31). Newton is recorded as having taken remarkably little interest either in the work or its original publication. 14 months afterwards, David Gregory reported that Newton 'has not seen a sheet of it, nor knows he what value it is in, nor how many sheets it will make, nor does he well remember the contents of it. He intends to goe down to Cambridge this summer and see it, and if it does not please him to buy up the copyes' (The Newton Handbook, p. 33). Newton complained, in fact, that Whiston had introduced titles and headings which were not his own and that the edition contained numerous mistakes. Nevertheless, it was fifteen years before a second edition was prepared, by John Machin in 1722; yet although advertised as having been revised and corrected by the author, Newton's own changes then were in fact minimal. Despite all this, and the fact that it was first published anonymously, the work proved to be one of Newton's more popular books and in 1720 it was even translated into English.

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