Shelfspace: David Gregory ‘Of Practical Geometry – and Other Practicalities’

by Duncan Lunan 

The late David Gavine  (1937-2020)  was an expert on the history of astronomy in Scotland, as well as on the aurora borealis and many other topics.  Some years ago when he gave a lecture in Airdrie on ‘James Gregory and James Nasmyth’, I took the opportunity to present him with a copy of A Treatise of Practical Geometry, in 3 Parts, by Dr. David Gregory, Professor of Mathematics, University of Edinburgh, and Savilian Professor of Astronomy at Oxford in the late 17th and early 18th centuries.

I was entrusted with the book in 1987 by Austin Osuji, an antiquarian bookseller in Glasgow who commissioned me to research its history, intending to put it up for auction.  It proved not to be valuable enough for that, and Austin’s Glasgow business folded soon afterwards when he was taken seriously ill during a return visit to Nigeria, so it seemed to be time to find the book a good home.

It was exactly 200 years old when I first saw it, the 1787 edition was the tenth, and the preface by ‘Col. Maclaurin’, dated 1st May 1745, states that the book had even then been taught at Edinburgh for sixty years, after the Elements of Euclid.  “…we are now to fubjoin fome corollaries which are eafily deduced from  [Euclid’s Elements]”, says Gregory, “that contain practical rules of great ufe in the affairs of life…”  The affairs of his own life and Maclaurin’s were not so dull, either.

a bust of the mathematician and astronomer David Gregory
Public domain, via Wikimedia Commons

David Gregory  (1661-1708)  came of an illustrious line of Scottish mathematicians and astronomers.  His father, also David, was the younger brother of James Gregory, the inventor of the Gregorian reflecting telescope.  His great work, as The  Encyclopedia Britannica describes it, was to produce in 1703 the first complete translation of Euclid since classical times.  (Topical, because ESA’s Euclid space telescope is now on the way to join the GAIA galaxy mapper and the James Webb Space Telescope at the Earth-Sun L2 point.)  The next edition was published at Heidelberg in eight volumes between 1883 and 1916, so Gregory’s was the only complete one until well into the 20th century.

Gregory lived in interesting times for science and mathematics.  Newton’s Principia were published in 1687, at the instigation and at the personal expense of Edmond Halley.  The tables Newton had used to account for the motion of the Moon had been drawn up by John Flamsteed, the first Astronomer Royal, who afterwards fell out with Newton when asked for more information of the same kind.  This may explain the events of 1691, when, to quote Sir Robert Ball in Great Astronomers, “Halley became a candidate for the Savilian Professorship of Astronomy at Oxford.  He was not, however, successful, for his candidature was opposed by Flamsteed, the Astronomer Royal of the time, and another was appointed.”  That ‘other’ whom Ball disapprovingly leaves unnamed was David Gregory:  not so much a case of ‘Jim’ll fix it’ as that John had fixed it.

Halley was excluded from the Savilian Professorship until 1703, the year in which Gregory published his translation of Euclid.  There doesn’t seem to have been too deep an animosity between Gregory and Halley, however, for on his death Gregory left the manuscript of “The Elements of Astronomy, Physical & Geometrical… to which is Annex’d Dr. Halley’s Synopsis of the Astronomy of Comets”.  A first edition of the English translation was sold at auction for £400 in 1987;  the catalogue gives its date as 1715, which is curious because the Britannica gives the first edition date as 1745.

sketch of Colin Maclaurin
Pencil and chalk on paper of Colin Maclaurin by David Stuart Erskine, Scottish National Gallery

Either date would have been significant for Maclaurin, who also lived in ‘interesting times’.  Although he missed the 1715 excitement with the Old Pretender, being at Glasgow University at the time, he was right in the thick of the next one.  An eminent mathematician in his own right, he became Professor of Mathematics in Aberdeen in 1717, when only nineteen years old.  He became a Fellow of the Royal Society in 1719, became acquainted with Newton and developed several of Newton’s theorems further.  Both were involved in the development of fluxions, i.e. calculus, which hit mathematics in that time with the kind of impact which computers have had today.  The Britannica says of him, “Of Newton’s British successors, Maclaurin alone ranked with continental mathematicians of his day.

Maclaurin also had connection with Edinburgh.  He suggested the expansion of the Medical Society of Edinburgh into the Philosophical Society, which later became the Royal Society of Edinburgh.  In 1745, when Bonnie Prince Charlie marched on Edinburgh, Maclaurin “took a prominent part in preparing trenches and barricades for its defence”.  The city fell when Lochiel’s men rushed the gate, as a coach came out with a deputation from the Provost.  Maclaurin fled to England, “to avoid making submission to the Pretender”.  This was only four months after Maclaurin had written the preface to the 1745 edition of Gregory’s text, so it’s tempting to imagine him correcting the proofs while riding in a coach for the Border, or clutching copies to his chest to ward off stray musket-balls.    

As Johannes Kepler wrote somewhat earlier, “an astronomer must be cosmopolitan because ignorant statesmen cannot be expected to value their services”.  The first version of this article was written and published in 1987, just after Roy Gibson resigned as Director of the British National Space Centre when Mrs. Thatcher, without consulting her cabinet colleagues, cancelled Roy’s British National Space Plan.  Kepler’s advice was true then and alas, some are finding it to be true even today.

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