Geometry

Geometry

‘GEOMETRY is a Science by which we search out and come to know either the whole Magnitude, or some part of any proposed Quantity; and it is to be obtained by comparing it with another known Quantity of the same kind, which will always be one of these, viz. A LINE (or Length only) A SURFACE (that is Length and Breadth) or A SOLID (which hath Length, Breadth and Depth, or Thickness) Nature admitting of no other Dimensions but these three.’

John Ward, The Young Mathematician’s Guide, p. 2.

Euclid, Elementorum Euclidis libri tredecim. Secundum vetera exemplaria restituti. Ex versione Latina Federici Commandini aliquam multis in locis castigate (London, 1620), p. 1.

David Gregory (1656-1708), in his 1692 inaugural lecture for the Savilian chair of astronomy at the University of Oxford, emphasised the importance of geometry for ‘all the arts necessary for improving life, such as geography, the rules of navigation, the determining of times’. This statement, by a highly influential Newtonian mathematician and astronomer, highlights the importance of the study of geometry in Oxford in the 1690s, only a few years before Worth would study there. In line with Newton’s approach in the Principia, Gregory focused on the geometrical underpinning of astronomy and drew particular attention to the study of Euclid. Following earlier Savilian professors of geometry such as John Wallis, Gregory also drew attention to the practical applications of the discipline. Given its centrality in the mathematical courses at Cambridge and Oxford, it is hardly surprising that Worth owned a host of works on geometry and a number of editions of the bible of geometry: Euclid’s Elements. In fact, Worth purchased no fewer than three editions of Euclid’s Elements and the text (and commentaries on it) could also be found in his many compilatory mathematical works such as Samuel Marolois’ Mathematicvm opus absolvtissimvm: continens geometriae, fortificationis, architecturæ, & perspectivæ theoreticæ ac practicæ regulas (Amsterdam, 1633) or the Jesuit Christopher Clavius’ Opera mathematica (Mainz, 1611), not to mention commentaries specifically on it such as Peter Ryff’s Quaestiones geometricae: in Euclidis et P. Rami Stoicheiosin. in vsum scholae mathematicae (Frankfurt, 1621).

As Jacqueline Stedall (2008) notes, ‘Euclid’s Elements is the earliest surviving attempt to deduce geometric truths from basic definitions, postulates and axioms.’ At the very beginning of Book I Euclid states his basic definitions, beginning with the celebrated line ‘A Point is that which hath no part’. Written c 250 BC, Euclid’s Elements sought to bring together all known theorems of plane and solid geometry. As Stedhall notes, it became ‘the longest running textbook ever’. The fact that no ancient Greek copies survived ensured that its textual history was long and complex. Worth’s editions clearly reflect not only the complexity of the task of editing such a work but also the pre-eminent place of geometry in the mathematical sciences.

The crucial importance of mathematics generally, and geometry specifically is vividly illustrated on the frontispiece of Worth’s copy of Gregory’s 1703 edition of Euclid’s Elements (visible on the Contact Us webpage). Picturing the Socratic philosopher Aristippus arriving on dry land following his shipwreck, it depicts him pointing out signs on the ground and accompanies the image with a caption from Vitruvius ‘We can hope for the best for I see the signs of men’ – the signs in this case being geometrical designs. As Remmert (2010) notes, the frontispiece thus not only drew attention to the antiquity of geometry but also to its civilising role: for Gregory, being a mathematician was intrinsic to being a civilised human being – the message to the reader was clear.

Sources

Lawrence, P. D. and A. G. Molland, ‘David Gregory’s Inaugural Lecture at Oxford’, Notes and Records of the Royal Society of London, 25, no 2 (1970), 143-178.

Remmert, Volker R., ‘Antiquity, nobility, and utility: picturing the Early Modern mathematical sciences’ in Eleanor Robson and Jacqueline Stedall (eds.) The Oxford Handbook of The History of Mathematics (Oxford University Press, 2010), 537-564.

Stedhall, Jacqueline, Mathematics Emerging. A Sourcebook 1540-1900 (Oxford University Press, 2008)

Text: Elizabethanne Boran.