Robert Recorde

The Life and Times of a Tudor Mathematician

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• Publisher: University of Wales Press
• Year: 2012
• Print ISBN: 9780708326824, 9780708325261
• eBook ISBN: 9781783161089
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Mathematics General
• Index: Technology & Engineering

The inventor of the equals sign (=), Robert Recorde (1510?-1558) was the first English-writing mathematics educator: this book celebrates his work

SIX

The Whetstone of Witte: content and sources

ULRICH REICH

IN 1557, BARELY A YEAR before his death, Recorde published his most noted work, The Whetstone of Witte, in which he presents algebraic ideas in the vernacular. Best known for its introduction of the sign

to indicate equality, the work has a number of other remarkable features, explored in this chapter. The chapter also reveals some of Recorde’s sources and compares them with Recorde’s own formulations.

Overview

In the Preface to the second book in his earlier work on geometry, The Pathway to Knowledg,1 Recorde had already indicated his intention to publish a book on algebra, which was to include examples ‘appertaynyng to the rule of Algeber, applied vnto quantitees partly rationall, and partly surde’ (Pathway, sig. a.iij^v).

The Whetstone of Witte was published in quarto format and contains 164 folios and two folded pull-out pages.2 The title page indicates the broad content of the work as being ‘the seconde parte of Arithmetike: containyng thextraction of Rootes:The Cossike practise, with the rule of Equation: and the woorkes of Surde Nombers’. These terms are explored further within this chapter.

A sixteen-line poem is added, in which Recorde compares his book with a whetstone to sharpen the mind, having prepared his readers in a previous publication: ‘The grounde of artes did brede this stone’. He promises that all may benefit from the work, both those of quick intellect and those who are slower learners:

Here if you lift your wittes to whette,
Moche sharpenesse therby shall you gette.
Dull wittes hereby doe greately mende,
Sharpe wittes are fined to their fulle ende.

The title page ends with an announcement that ‘These Bookes are to bee solde, at the Weste doore of Poules, by Jhon Kyngstone’, the book’s printer. Table 1 provides a breakdown of the content of the book.

In a five-page Dedicatory Epistle (sigs a.ii–[a.iiij]), typical of its period, Recorde dedicates the book as follows: ‘To the right worshipfull, the gouerners, Consulles, and the reste of the companie of venturers into Moscouia, Robert Recorde Physitian, wissheth healthe with continualle increase of commoditie, by their worthie and famous trauell.’

The Muscovy Company was an association of merchant adventurers founded by the explorer Sebastian Cabot in 1555 and given a monopoly of Anglo-Russian trade. The Company also had as one of its aims to search for the North-East Passage. It seems that Recorde advised the Muscovy Company on navigation. Recorde states that he is sure that his book will be gladly received and goes on to announce his intention to write a book on navigation ‘as I dare saie, shall partly satisfie and contente, not onely your expectation, but also the desire of a greate nomber beside’. The dedication concludes with ‘At London the .xii. daie of Nouember.1557.’

The six-page Preface (sigs b.i–b.iii^v) is addressed to ‘the gentle Reader’. Recorde describes the importance of numbers and refers to ‘the Bookes of Plato, Aristotell, and other aunciente Philosophers’ as well as to ‘Nicomachus, and diuerse other writers’ who declared ‘that Arithmetike is the fountaine of all the other [artes]’. He underlines the importance of number to Divinity, Law and Astronomy, ‘And as for Physicke, without knowledge and aide of nomber is nothynge.’ Finally, Recorde cites Plato on a further five occasions as he describes the connections between number, measure and weight. The Preface is followed by two eight-line poems entitled ‘Of the rule of Cose’ and ‘To the curiouse scanner’. The former plays with the idea of using a variable – the cose – to represent number in the abstract, so that the learner may see ‘What thynges by one thyng knowen maie bee’. The latter juxtaposes two types of people, those who ‘mende’ and those who ‘blame’, and Recorde exhorts the reader, in prophetic terms, to ‘be wise, and learne before, Sith slaunder hurtes it self moste sore’.

The main body of the work is presented in four sections: Part I presents some details of elementary number theory; Part II is a continuation of Recorde’s arithmetic The Ground of Artes; Part III, the most significant and well-known section, as well as the largest, is a treatise on algebra; and Part IV completes the book with a discussion of surds.

As far as is known, there are no other editions. The author has been able to trace twenty-one original copies of the book in public libraries in the UK,3 a further eleven copies in the USA4 and one copy in Germany.5 Numerous microfilms and other copies of the book also exist.6

In this chapter we shall concentrate largely on the algebraic content of the book, including both the introduction of variables (referred to by Recorde as ‘Coßike numbers’7) and his discussion of equations, which famously includes his introduction of the equals sign. We shall also draw attention to some of the interesting and extraordinary details in other sections of the book.

Recorde’s sources

In the sixteenth century, authors were not required to cite the sources of their information. Nevertheless Robert Recorde openly cites on no fewer than forty occasions8 a range of authors including: Aristotle, Euclid, Nicomachus and Plato from the classical period; the Roman scholar Boethius (c.480–524); and Recorde’s own contemporaries, the Italian Cardano (1501–76) and the Germans Stifel (1487–1567) and Scheubel (1494–1570). As we shall see, he also refers twice to the writings of the great Arab mathematician al-Khwārizmi (c...

Table of contents

• Half Title
• Title Page
• Copyright
• Contents
• List of illustrations
• Notes on contributors
• Acknowledgements
• Preface
• Editorial conventions
• Introduction
• ONE: The lives and works of Robert Recorde
• TWO: Robert Recorde and his remarkable Arithmetic
• THREE: Recorde and The Vrinal of Physick: context, uroscopy and the practice of medicine
• FOUR: The Pathway to Knowledg and the English Euclidean tradition
• FIVE: The Castle of Knowledge: astronomy and the sphere
• SIX: The Whetstone of Witte: content and sources
• SEVEN: The Welsh context of Robert Recorde
• EIGHT: Commonwealth and Empire: Robert Recorde in Tudor England
• NINE: Data, computation and the Tudor knowledge economy
• APPENDIX: From Recorde to relativity: a speculation1
• Bibliography