Abstract
The Pathway to Knowledg presents the contents of the first four books of Euclid, as adapted to meet the needs for an understanding of the principles of Geometry by mathematical practitioners and also as an essential precursor to Recorde’s mathematical treatises yet to come. Thus, in the first definitions, those of point and line he eschews the Euclidean versions as being fit only for theoretical speculation and calls a point ‘that small print of pen, pencil or other instrument which is not moved nor drawn from his first touch, and therefore hath no notable length nor breadth’. In a similar vein, whilst not touching the content of Euclid’s text he rearranges the order of its presentation in a way that he thinks will better engage the reader. Recorde adds nothing new to the subject, but his comments disclose the wide range of sources he consulted. A number of these have been identified and show how widely Continental scholarship in the form of printed books had spread to England. The large number of errors in the Pathway illustrates how great were the obstacles to be overcome in printing new mathematical works accurately in English.
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Notes
- 1.
Easton JB (1966) A Tudor Euclid. Scripta Math XXVII(4):339–355.
- 2.
Durer A, Elementa Geometrica. Christianum Wechelum, Basiliensis MDXXXII.
- 3.
Willis J (ed) (1983) Martianus Capella, De nuptis Philologie et Mercurii. Bibliotheca Scriptorum Graecorum et Romanorum, Teubneriana, pp 252–253 (712, 22–26).
- 4.
Sel.a.253, Main Library. The Queens College, Oxford.
- 5.
Folkerts M (1970) “Boethius” Geometrie II, Ein Mathematiches Lernbuch des Mittelalters. Franz Steiner Verlag GMBH, Weisbaden, p 116, lines 54–55.
- 6.
Busard HLL (1983) The first Latin translation of Euclid’s elements commonly ascribed to Adelard of Bath. Pontifical Institute of Medieval Studies, Toronto, pp 392–396.
- 7.
Busard HLL (1967) The translation of the elements of Euclid from the Arabic into Latin by Herman of Carinthia. Janus LIV:1–140, 10.
- 8.
Bodleian Library, Byw E.i.6., 1.
- 9.
Christ Church College Library (Oxford), Rare Books, phi.A.3.12.(2).
- 10.
Merton College Library, MER. 40. J.16.
- 11.
Morrow GL (1970) Proclus, a commentary on the first book of Euclid’s elements. Princeton University Press, Princeton, pp 188–190.
- 12.
Johnson FR, Leakey SV (1935, April) Robert Recorde’s Mathematical Teaching and the Anti-Aristotelian Movement. Huntingdon Libr Bull 7, footnote p 68.
- 13.
Easton JB, loc. cit. 344–345.
- 14.
Chapman A (1995) Dividing the circle. Wiley, Chichester, p 155.
- 15.
Heilbron JL (1998) Geometry civilized: history, culture and technique. Clarendon Press, London, pp 221–228.
- 16.
Durer A,‘Geometria,’ Wechelman, Basle MDXXXII, pp. 54–55.
- 17.
Thomas Digges edited his father Leonard’s book on surveying, Pantometria [1571] and appended to it, his own text on the five Platonic geometrical solids. As a precursor to the main work he gives constructions for the inscribing of planar figures, including the pentagon, essentially repeating Ptolemy’s method. The illustration of the construction is as badly misleading as any of those to found in the Pathway.
- 18.
In the Castle of Knowledge when describing the division of the equinoctial circle into degrees, the Scholar is instructed to divide it first into three parts, and then each part successively into a further three parts which are halved and then further into fifths. Alternatively, the 3,2,3,5 sequence of sectioning can be used. These two sequences are those advised in descriptions of instrument fabrication by other authors.
- 19.
Heath, vol I, 232.
- 20.
Ibid., 223.
- 21.
Easton JB, loc. cit., 348.
- 22.
Ibid., 349.
- 23.
Easton JB, loc. cit., 349–353.
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Williams, J. (2011). The Pathway to Knowledg Containing the First Principles of Geometrie, as They May Moste Aptly Be Applied unto Practise, Both for Use of Instrumentes Geometricall, and Astronomicall and Also for the Projection of Plattes in Everye Kinde, and Therfore Much Necessary for All Sortes of Men. In: Robert Recorde. History of Computing. Springer, London. https://doi.org/10.1007/978-0-85729-862-1_8
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