The abstract to a biographical article on William Viscount Brouncker (Breathnach, 2006) reads as follows:
William Brouncker was the grandson of Sir Henry Brouncker, President of Munster during the Elizabethan Plantation of Ireland in the 16th century. William’s date and place of birth are uncertain; he was born about 1620, most probably at Castlelyons, County Cork, and educated at Oxford where he shone in mathematics and languages. Until his death in 1684 he served the Stuarts as a senior member of the Navy Board from which sprang the Admiralty, and we owe much of what we know about his life to the warts-and-all diary of his younger naval colleague, Samuel Pepys (1633-1703). Although William was granted a doctorate in medicine by Oxford in 1646, music and mathematics were his major interests. He was the first President of the Royal Society and he held that position from 1662 to 1677, when his tenure was brought to a reluctant close by an election, sardonically recorded in the diary of the curator of experiments, Robert Hooke (1635-1703). If Brouncker did not add any empirical facts, he certainly contributed to the promotion and dissemination of natural knowledge.
However, McIntyre (2004) gives his place of birth as Castle Lyons, Co. Dublin, while Burke (1866) states that his father (also William) ‘was created a peer of Ireland, 12 September, 1645, as Baron Brouncker, of Newcastle, and Viscount Brouncker, of Lyons, co. Dublin’. It seems likely, then, that William Brouncker (the second Viscount) was born and spent some of his childhood in Ireland, although he lived in England from at least his mid-teens. Scott and Hartley (1960) wrote a biography with an emphasis on his contribution to the Royal Society.
Philosophical transactions and collections, to the end of the year 1700; abridg’d, and dispos’d under general heads. In three volumes. By John Lowthorp (London, 1716), plate 1, figure 9.
The problem of finding the area bounded by a given curve (and possibly including some straight lines) is known as quadrature. The quadrature of conic sections (circles, ellipses, parabolas and hyperbolas) has a special place in mathematics. Archimedes solved the quadrature of the parabola and made a fundamental contribution to that of the circle. Van Ceulen’s calculation of to 35 decimal places built on Archimedes’ quadrature of the circle. Brouncker was the first to give a numerical quadrature of the hyperbola, published in the Philosophical Transactions of the Royal Society in 1668, the first mathematical result to be published in a scientific journal (Stedall, 2008, p. 84).
Philosophical transactions and collections, to the end of the year 1700; abridg’d, and dispos’d under general heads. In three volumes. By John Lowthorp (London, 1716), plate 1, figures 10 and 11.
Some of the details of the analysis are shown below and illustrated in this diagram. Although Brouncker did not publish widely, his role as President of the Royal Society for its first decade and a half was of crucial importance; moreover he had very close ties with the accomplished mathematician, John Wallis, another founder of the Royal Society.
Philosophical transactions and collections, to the end of the year 1700; abridg’d, and dispos’d under general heads. In three volumes. By John Lowthorp (London, 1716), p. 10 detail.
Breathnach, C.S., ‘William Brouncker MD Viscount Castlelyons (c 1620-84) First President of the Royal Society’, Journal of Medical Biography, 14 (4) (2006), 223-229.
Burke, J.B., Burke’s genealogical history of the dormant, abeyant, forfeited and extinct peerages of the British Empire (London, 1866), 78.
McIntyre, G.S., ‘Brouncker, William, second Viscount Brouncker of Lyons (1620-1684)’, Oxford Dictionary of National Biography, Oxford University Press, 2004; online edn, Jan 2011].
Scott, J. F. and Hartley, H., ‘William, Viscount Brouncker, P.R.S. (1620-1684)’, Notes and Records: the Royal Society journal of the history of science, 15 (1) (1960), 147-157.
Stedhall, Jacqueline, Mathematics Emerging: A Sourcebook 1540-1900 (Oxford University Press, 2008).
Text: Maurice OReilly.