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John Napier
John Napier

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6 Spreading the word about logarithms

Another person besides Briggs to recognise immediately the importance of Napier’s concept was the navigational practitioner Edward Wright, who translated Napier’s Descriptio into English, as A description of the admirable table of logarithmes. Reading 5 below comprises the Preface to that work (the translation of Napier’s original Preface, with further sentences added by Napier himself).

Reading 5: John Napier’s Preface to A Description of the Admirable Table of Logarithms

Seeing there is nothing (right well beloved students in the Mathematics) that is so troublesome to Mathematicall practise, nor that doth more molest and hinder Calculators, than the Multiplications, Division, square and cubical Extractions of great numbers, which besides the tedious expence of time, are for the most part subject to many slippery errors. I began therefore to consider in my minde, by what certaine and ready Art I might remove those hindrances. And having thought upon many things to this purpose, I found at length some excellent briefe rules to be treated of (perhaps) hereafter. But amongst all, none more profitable than this, which together with the hard and tedious Multiplications, Division, and Extractions of rootes, doth also cast away from the worke it selfe, even the very numbers themselves that are to be multiplied, divided and resolved into rootes and putteth other numbers in their place, which performe as much as they can do, onely by Addition and Subtraction, Division by two or Division by three; which secret invention, being (as all other good things are) so much better as it shall be the more common; I thought good heretofore to set forth in Latine for the publique use of Mathematicians. But now some of our good Countrymen in this Island well affected to these studies, and the more publique good, procured a most learned Mathematician to translate the same into our vulgar English tongue, who after he had finished I sent the copy of it to me, to be seene and considered on by myself. I having most willingly and gladly done the same, finde it to be most exact and precisely conformable to my minde and the originall. Therefore it may please you who are inclined to these studies, to receive it from me and the Translator, with as much good will as we recommend it unto you. Fare yee well.

Question 3

Timing: Allow about 5 minutes

What explanation does Napier give of why his work appeared first in Latin, then in English? What light does this throw on your answer to Question 1?

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Napier says his book was written in Latin ‘Tor the publique use of Mathematicians, to ensure it shall be the more common’, that is, presumably, more widespread. The English translation is for the benefit of ‘our Countrymen in this Island’ and ‘the more publique good’. This confirms our hypothesis, from Question 1, that Napier had in mind as his primary audience the international mathematical community. He sounds pleased, all the same, that non-Latin speakers in the United Kingdom might find logarithms useful too.

Knowledge of logarithms spread rapidly in various ways. Wright’s English translation was one source of knowledge; it was dedicated (by Wright’s son, for Wright died before publication) to the East India Company, another of the great trading and exploration companies of the time. This dedication suggests an audience for whom the knowledge was thought to be useful – Wright was navigational consultant to the Company for the last year or two of his life. Knowledge of logarithms spread by word of mouth too; Briggs lectured on them at Gresham College, as did Edmund Gunter, who was appointed Professor of Astronomy there in 1619. Within a decade, editions or similar tables had been published in France, Germany and the Netherlands. As an example of the impact of logarithms abroad, let us consider the response of the astronomer Johannes Kepler.