Feature of the month: Cocker's Decimal Arithmetic

In 2016 Senate House Library is commemorating the quartercentenary of the death of William Shakespeare. This year’s Features of the Month celebrate books published in the same year as Shakespeare’s first four folios: 1623, 1632, 1664 and 1685. This is the final book in the series, the third of three books featured from 1685.

Cocker's Decimal Arithmetic
Edward Cocker
London: T. Passinger and T. Lacy, 1685
[DeM] L.1 [Cocker] SSR

Cocker's Decimal Arithmetic
Cocker's Decimal Arithmetic

Cocker's Decimal Arithmetic needs to be seen in the context of Cocker's Arithmetic. Cocker's Arithmetic had first been published from the author’s notes in 1678, two years after Edward Cocker’s death, by his friend and successor as writing-master at Southwark School, John Hawkins. It was an instant bestseller, perhaps because it aimed at a practical, trade audience rather than gentry and their tutors, and reached its 55th numbered edition by 1758; the actual quantity of editions was above one hundred, allowing for editions outside the numbering system, such as unnumbered editions and editions with repeat numbering. So popular and reliable was the work that the phrase “according to Cocker” entered the English language to denote something done properly or according to rules. But Cocker's Arithmetic had not acknowledged the potential usefulness of decimal fractions. With Cocker's Decimal Arithmetic, published in 1685, Hawkins attempted to serve the needs of those wanting to go beyond the first book by providing an alternative method of calculating. The book includes logarithms (using Napier’s notation) and algebra. Hawkins noted the use of decimals to solve “questions arithmetical, and such geometrical as are necessary in the mensuration of the most usual planes and solids”, and provided tables for calculating simple and compound interest. He claimed thereby to be following:

the method of several famous authors … and especially of that most famous, and no less laborious mathematician of our age and nation, Mr. John Kersey, whose memory deserves highly to be honoured by all the professors of this science (leaf A3v).

All his persuasion, however, failed to convince the public, and Cocker's Decimal Arithmetic proved far less popular than its non-decimal predecessor, reaching its sixth and final edition in 1729.

Augustus De Morgan, who owned the copy of the first edition featured, had a low opinion of Cocker. He attributed Cocker’s work to Hawkins (a view since discredited), and ended a long description and discussion of Cocker in his Arithmetical Books from the Invention of Printing to the Present Time (1847) by stating:

The famous book looks like a patchwork collection, and, I believe, is nothing more. The reason of its reputation I take to be the intrinsic goodness of the processes, in which the book has nothing original; and the systematic puffing with which it was introduced. […] This same Edward Cocker must have had great reputation, since a bad book under his name pushed out the good ones.

De Morgan’s copy is distinguished by the ownership inscription of an early owner, John Foche, who purchased it for three shillings in July 1699. De Morgan has added his own note, to the effect that the book is, beyond all doubt, the first edition (a comment generated by the statement of the bibliographer William Thomas Lowndes among others that the first edition was probably printed in 1669). He has also pasted in the English translation of a short dedicatory letter from John Hawkins to his friend John Perkes of Wigan, printed in cipher in leaf A4r.

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