A "Logarithm Bestseller"
GARDINER, William. Tables of Logarithms for all numbers from 1 to 102100 and for the Sines and Tangents... with other useful and necessary tables. London, G. Smith, 1742.
Small folio, (3) ff., 14 pp., (113) ff. Bound in contemporary French mottled calf, spine stamped in gold in compartments with royal monogram (a crown); title & early leaves lightly foxed. Generally very good.
$2,200 Rare. First edition of the first work on logarithms to extend calculations to the seventh figure, celebrated for the accuracy of its computations as well as the legibility and elegance of its printing. Both made the work something of a 'logarithm bestseller,?' receiving editions in the major European languages soon after, and consulted by mathematicians and technical scientists throughout Europe.
The work's introduction is of exceptional and apparently neglected historical interest in charting the conceptual evolution of the logarithm from an arithmetic series, in one-to-one correspondence with terms of a geometric series, to the exponent, an advance usually credited to Euler in his Introductio of 1748. Cajori, however, remarks that this union of exponential and logarithmic notions has an earlier history, and that it was recognized by John Wallis (1685) and Bernouilli (1694), "but not till 1742 do we find a systematic exposition of logarithms based on this idea. It is given in the introduction to Gardiner's Tables of Logarithms, London, 1742" - History of Mathematics, p. 235.
Gardiner states that this introduction is "collected wholly from the papers" of the Newtonian William Jones (1675-1749). In 1708, Jones somehow came into possession of the bulk of the scientific papers and correspondence of John Collins, including Collins' transcription of Newton's De Analysi and other of his mathematical papers. The task of separating Collins' work from Jones', and Newton's from Collin's has only recently been achieved by D.T. Whiteside in his exemplary edition of Newton's Mathematical Papers.
The subscriber's list of 117 names includes Halley, Hartley, Hauksbee, Maupertuis, Le Monnier and Benjamin among others.
* Taylor, Hanoverian England, p. 159; DSB VII.162-163; The Newton Handbook, p. 282.