Oughtred, William (DNB00)

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OUGHTRED, WILLIAM (1575–1660), mathematician, son of the Rev. Benjamin Oughtred, and descended from an ancient family of the same name in the north of England, was born at Eton on 5 March 1574-5, and educated at the college. On 1 Sept. 1592 he entered at King's College, Cambridge, and while still an undergraduate devoted his attention to mathematics and composed his 'Easy Method of Geometrical Dialling,' This work, on being circulated in manuscript, attracted the notice of some eminent mathematicians : and Sir Christopher Wren in 1647, when a fellow-commoner of Wadham College, Oxford, translated it into Latin ; but his translation was not published until 1648. In 1595 Oughtred was admitted a fellow of his college. About 1600 he conceived the invention of a projected horizontal instrument for delineating dials upon any kind of plane, and for working most questions which could be performed by the globe. An account of this invention was translated into English and published in 1633, together with his ' Circles of Proportion,' by William Foster, who had been one of his pupils (Ward, Gresham, Professors, p. 88).

About 1603 he was ordained priest, and in 1605, on being presented to the living of Shalford in Surrey, quitted the university. Five years later he was presented to the rectory of Albury, near Guildford, in the same county, and here he appears to have been for the most part resident until his death. He occasionally visited London, although, according to his own statement, not oftener than once a year. 'As oft,' he says, 'as I was toiled with the labours of my own profession, I have allayed that tediousness by walking in the pleasant and more than Elysian fields of the diverse and various parts of human learning, and not of the mathematics only.' He also took pupils, and, according to Lloyd (Memoires, ed. 1668, p. 608), 'his house was full of young gentlemen that came from all parts to be instructed by him ; 'among these he names a son of Sir William Backhouse, Mr. Stokes, Dr. William Lloyd, and Mr. Arthur Haughton. For a time, too, he seems to have resided in the family of the Earl of Arundel as tutor to his second son, Henry Frederick Howard, afterwards third earl of Arundel [q. v.] During the first fourteen years of his incumbency the parish registers, with the entries in his beautiful clear hand, seem to have been regularly kept; but after that time only an occasional entry presents itself. About 1632 he seems to have been seeking pecuniary aid, and to have suffered from a consciousness of neglect (Rigaud, i. 16). According to Lloyd, he was frequently invited to reside in Italy, France, and Holland, and the list of his correspondents includes the names of the most eminent mathematicians of the time, by whom he was equally respected for his sobriety of judgment and modesty of disposition. The living was a good one; and Oughtred's known sympathy with the royalist party marked him out as an object of suspicion to the committee of sequestrations in 1645. Lilly says : 'Several inconsiderable articles were deposed and sworn against him, material enough to have sequestered him, but that, on his day of leaving, I applied myself to Sir Bulstrod Whitlock, and all my old friends, who in such numbers appeared in his behalf that, though the chairman and many other Presbyterian members were stiff against him, yet he was cleared by the major number' (Life and Times, ed. 1822, p. 136). It is probably in connection with this persecution that, writing in the same year, he describes himself as 'daunted and broken with these disastrous times' (Rigaud, i. 66). But, generally speaking, his life appears to have been spent peacefully in the conscientious discharge of the duties of his office, relieved by congenial studies and a not inconsiderable correspondence with learned friends. In 1618 he writes : ' I, being in London, went to see my honoured friend, Master Henry Briggs, who then brought me acquainted with Master Gunter [q.v.], with whom, falling into speech about his quadrant, I shewed him my horizontall instrument' ('Apologet. Epist.' in Ward's Lives, p. 78). In 1630 he was attacked by Richard Delamaine the elder [q. v.], and replied in a pamphlet entitled 'To the English gentrie . . . the just Apologie of W. Oughtred against the slanderous insinuations of Richard Delamain, in a pamphlet called "Grammelogia," ' 4to. The merits of the controversy may be gathered from the expressions of W. Robinson, who 'cannot but wonder at the indiscretion of R. D., who, being conscious to himself that he is but the pickpurse of another man's wit, would thus inconsiderably provoke and awake a sleeping lion' (Rigaud, i. 11). In 1631 appeared the 'Clavis Mathematics,' which Oughtred compiled while residing with the family of the Earl of Arundel. He was encouraged to publish the work by his friend, Sir Charles Cavendish, a younger brother of the Duke of Newcastle, and, like himself, an eminent mathematician. The 'Clavis' was a good systematic text-book on algebra and arithmetic, embodying practically all that was then known on the subject. Oughtred here introduced the symbols x for multiplication, and :: in proportion. The work grew steadily in favour and attained a wide popularity. Wallis, writing to Collins in 1667, speaks of it as a 'lasting book' and Oughtred himself as a 'classic author.' In 1632 was published his treatise on navigation, under the title of 'Circles of Proportion.' In a letter to Keylway, written in 1645, he states as effectively, perhaps, as any modern writer the mathematical argument which demonstrates the futility of the endeavour to prove the equality of any given square and circle. Notwithstanding the deep concern with which he regarded the puritan despotism, Lloyd describes him as enjoying a green old age, 'handling his cube and other instruments at eighty as steadily as others did at thirty,' a fact which he himself attributed to 'temperance and archery.' The statement that he died of joy on hearing of the vote of Convention for the restoration of Charles II is somewhat discredited by the fact that his death did not take place until 30 June 1660.

He was married; and Seth Ward, writing in 1652, presents his 'hearty service to Mrs. Oughtred and your children,' but nothing would seem to be known of his descendants. Aubrey, describing his person, says: 'He was a little man, had black hair and black eyes, with a great deal of spirit. His wit was always working. His eldest son, Benjamin, told me that his father did use to lye a bed till eleven or twelve o'clock, with his doublet on, ever since he can remember. Studied late at night . . . had his tinderbox by him; and on the top of his bed-staffe he had his ink-horn fixt. He slept but little. Sometimes he went not to bed in two or three nights, and would not come down to meals till he had found out the quaesitum.' An engraving of Oughtred by W. Faithorne is prefixed to his 'Trigonometria,' 1657, and another by Hollar to his 'Clavis Mathematics.'

His library and manuscripts passed into the possession of William Jones [q. v.] the mathematician, who in turn bequeathed them to Lord Macclesfield. The letters in the collection by that nobleman have for the most part been printed in Rigaud, but a considerable quantity of mathematical papers still remain unprinted. The miscellaneous tracts in No. 11 in the subjoined list were collected and published by Sir Charles Scarborough the physician, the common friend of Oughtred and Christopher Wren.

Notwithstanding Oughtred's undoubted originality, he was not unindebted to earlier writers; and Gilbert Clerk, in his 'Oughtredus Explicatus' (pp. 121, 159), points out his obligations to Vieta. But his labours obtained the warmest commendation from men of science in his own and the subsequent age. Robert Boyle, writing to Harthb in 1647, speaks of 'Englishing' the 'Clavis,' which, he adds, 'does much content me, I having formerly spent much study on the original of that algebra, which I have long since esteemed a much more instructive way of logic than that of Aristotle' (Life, ed. 1744, p. 81). Newton speaks of him as 'that very good and judicious man, whose judgement (if any man's) may be safely relyed upon' (Cotes Corr. p. 291). Twysden, in his preface to the 'Miscellanies' of Samuel Foster [q. v.], written the year before Oughtred's death, assigns him a first place among the mathematicians of the age, and declares that he 'exceeds all praise we can bestow upon him.' 'The best Algebra yet extant is Oughtred's' (Life of Locke, ed. King, i. 227). De Morgan assigns to him the credit of the valuable invention of trigonometrical abbreviations (Budget of Paradoxes, p. 457).

The following is a list of his principal works: 1. 'Arithmeticæ in numeris et speciebus Institutio: quæ tum logisticæ, tum analyticæ, atque adeo totius Mathematicæ, quasi Clavis Mathematicæ est,' London, 1631, 8vo. 2. 'Clavis Mathematicæ, cum Tract. de resolutione æquationum in numeris, et declaratione x. xiii. xiv. Elementi Euclidis,' London, 1648, 8vo; a translation, entitled 'Key of the Mathematicks,' was made by Edmund Halley, and published at London in 4to in 1694. 3. 'Clavis Mathematicæ denuo limata, sive potius fabricata, cum variis aliis Tractt.,' Oxford, 1652 and 1667, 8vo. 4. 'Circles of Proportion, and the Horizonal Instrument,' translated by W. Foster, London, 1632, 4to. 5. 'Description and Use of the Double Horizontal Dial,' London, 1636 and 1652, 8vo. 6. 'A most Easy Way for the Delineation of plain Sundials, only by Geometry,' &c. 1647, 8vo. 7. 'Description and Use of the general Horological Ring and the Double Horizontal Dial,' London, 1653, 8vo. 8. 'Solution of all Spherical Triangles,' Oxford, 1657, 8vo. 9. 'Trigonometria,' London, 1657, 4to. 10. 'Canones Sinuum, Tangentium, Secantium et Logarithmorum pro Sinibus et Tangentibus,' London, 1657, 4to. 11. 'Opuscula Mathematica hactenus inedita: viz. Institutiones Mechanicæ, et alia varia,' Oxford, 1677, 8vo.

[Information kindly supplied by the Rev. Canon Dundas, rector of Albury, Surrey; Aubrey's Memoir in Letters from the Bodleian, 1813, a very amusing sketch; Lloyd's Memoires; Allen's 'Liber' of Members of King's College (in manuscript at King's College); Rigaud's Correspondence of Scientific Men of the Seventeenth Century; Ball's Hist. of the Study of Mathematics at Cambridge.]

J. B. M.