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A Note on Robert Recorde and the Dienes Blocks
Published online by Cambridge University Press: 22 November 2016
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- Copyright © Mathematical Association 1966
References
page 363 note * Dienes, Z. P.: Building up Mathematics: London, 1960 Google Scholar.
page 363 note † Ibid.: pp. 102-103.
page 363 note ‡ Ibid. : pp. 106-7. This is what he terms the Conceptual Variability Principle.
page 364 note * No copy of the first edition is known to be extant. I have used an edition dated 1543. Recorde, R.: The Groüd of Artes: London, 1543 Google Scholar.
page 364 note † Although many variations exist in the method of marking or pricking digits most writers marked every third digit in some way. Leonardo of Pisa in the 1228 edition of the Liber Abbaci grouped the digits in threes thus 
. Pacioli in his Summa writes 
. Peurbach, Rudolff and Tonstall among others all marked every third digit.
page 364 note ‡ Recorde, R.: The Whetstone of Witte, whiche is the seconde parte of Axithmetike : containyng the extraction of Rootes : The Cossike practise, with the rule of Equation: and the woorkes of Surde Nombers: London, 1557.
page 365 note * Ibid.: p.28v.
page 365 note † Rudolff, C.: Behend unnd Hubach Rechnung durch die kunstreichen regeln Algebre—sogemeincklich die Coss geneṅt werden: Strassburg, 1525 Google Scholar. See also, Stifel, M.: Die Cosa Christoffs Rudolffs durch Michael Stifel gebessert und sehr gemehrt: Königsberg, 1653 Google Scholar.
page 366 note * The Whetstone of Witte : op. cit. : p. 32v. ‘And although the names that I doe give, maie seme to some menne (whiche are scarse apte judges) more odiouse, for the newe invention (as thei maie thinke) then nedefull to the practise of tharte : yet shal you see in theim a naturali sequele, and orderly propagation.’
page 366 note † Euclid: The Elemente: Books VII-VIII.
page 367 note * The Whetstone of Witte: op. cit.: p. 31v. ‘Wherfore thei appeare to bee oversene, that call those formers nombers Surdesolides, seing thei are not any waiea Surde nombers, but have their rootes. And yet, to confesse the truthe, I cannot well tell you the true etymologie of their name ; except thei be so named as it were solide upon solide. And that interpretation were to streightly racked.’
p. 32. ‘This name therfore of theim, I meane Sursolides, in Arithmetike, maie serve to admonishe you of their roote. But in Geometrie, or in composition of sounde bodies, it serveth no use.’