Briggs, Henry

(bap. 1561, d. 1631), mathematician

by Wolfgang Kaunzner

© Oxford University Press 2004 All rights reserved

Briggs, Henry (bap. 1561, d. 1631), mathematician, was born at Daisy Bank in the township of Warley, near Halifax, Yorkshire, and baptized on 23 February 1561 at St John's Church, Halifax, the son of Thomas Briggs, farmer, and his wife, Isabel Beste. Mary Briggs, who was probably either his sister or half-sister (Isabel Beste seems to have been Thomas Briggs's second wife), was baptized on 28 October 1557, and Richard Briggs, who matriculated from St John's College, Cambridge, in 1577 or 1578, was possibly his brother. The family lived at Daisy Bank, Warley. After attending grammar school locally Briggs matriculated on 15 March 1578 from St John's College, Cambridge, and as a founder's scholar of the county of Yorkshire on 5 November 1579. He graduated BA in 1581 or 1582, MA in 1585, and on 29 March 1588 was admitted an Ashton fellow of the county of Yorkshire. Subsequently he was appointed topicus sublector (9 July 1591) and mathematicus examinator (7 July 1592), which implies that he lectured in mathematics, and, on 8 September 1592, to the Linacre lectureship in physic.

According to Hallowes, Briggs allied himself to the strong puritan faction then in St John's College. His political and religious stance is indicated in three petitions that he supported during his time in Cambridge. In early March 1597 he became professor of geometry in the newly founded Gresham College in London, at £50 per annum. His work on astronomy, geography, and navigation (subjects which the new college aimed to improve) began with A Table to Find the Height of the Pole (1602), and Tables for the Improvement of Navigation (1610). The latter included closely calculated tables for the declination of the sun between 1608 and 1612. Briggs's association with Cambridge nevertheless continued after he took up the Gresham post, and he seems to have had a prominent position in the administration of the affairs of his old college. A letter of March 1600 shows him participating, on behalf of St John's, in a discussion with the fellows of Trinity over the planned enclosure of the Backs. Although not formally elected as one of the eight governing senior fellows, his signature on a college decree of 24 February 1602 indicates that he was considered as such.

In 1609 Briggs became acquainted with James Ussher, later archbishop of Armagh. Two of Briggs's letters to him survive. One, of August 1610, dealt with the possibility of an anonymous publication in England of a manuscript written by the Calvinist Ussher (presumably of some political and religious sensitivity). Among other things, it included a discussion of eclipses with the comment that Johannes Kepler had confused all with his unconventional approach to the laws of planetary motion. Briggs also sought to become personally acquainted with other prominent mathematicians of the day. In a second letter, of 10 March 1616, having encountered John Napier's Mirifici logarithmorum canonis descriptio (1614), he informed Ussher that

Napper [elsewhere spelt Neper or Naper], Lord of Markinston, hath set my Head and Hands a Work, with his new and admirable Logarithms. I hope to see him this Summer if it please God, for I never saw Book which pleased me better, or made me more wonder. (Parr, 36)
This encounter determined the course of his future life and he was lecturing on Napier's logarithms at Gresham College as early as 1615.

Logarithms simplified the astronomical and navigational calculations central to the research programme at Gresham College by enabling multiplication of two many-digit numbers to be performed by addition of their corresponding logarithms. A feature of Napier's original definition was that logarithms were what has become known as 'hyperbolic' (for their base was approximately 1/e), so that as the numbers increased their corresponding logarithms decreased. Thus the logarithm of 1 was about 161,000,000 and the logarithm of 10,000,000 was zero. Napier indicated in an 'Admonitio' on the last leaf of some copies of the book that he was developing a simpler definition.

Briggs now wrote to Napier suggesting that it would be more convenient to work in steps of 10. Thus the logarithm of 10,000,000 (the value commonly taken for the 'whole sine', i.e. the sine of 90° or the radius, R, of the circle in relation to which the trigonometric sine and cosine were then defined as lengths) would remain zero, but the logarithm of R/10 (i.e. of sine 5° 44' 21") would be equal to 10,000,000,000; he calculated numerical values on this basis, and in the summer of 1615 went to visit Napier in Edinburgh. During his one-month stay, and a second visit in the summer of 1616, Briggs and Napier agreed on a redefinition suggested by Napier (presumably that already hinted at in his 'Admonitio') which gave logarithms increasing as the corresponding number increased, namely, log 1 = 0 and log R = 10,000,000,000. In his Rabdologia (1617) Napier declared that Briggs and he had developed a better method for logarithms, whose manner and use they hoped to publish, but poor health compelled him to leave these extensive calculations to other learned men, especially Henry Briggs, his most highly esteemed friend. Briggs and Napier were, however, dissimilar in nature, Briggs being opposed to astrology, and a severe Presbyterian.

In a letter of 6 December 1617 Henry Bourgchier informed James Ussher that soon after Napier's death on 4 April 1617, Briggs's Logarithmorum chilias prima (undated) had been published in London. Briggs had replaced log R = 10,000,000,000 with log 10 = 1, thus producing logarithms to base 10. The work consisted of sixteen pages each containing 67 numbers, the base 10 logarithms of 1 to 1000 calculated to fourteen decimal places. From 501 the 4th order differences relating to the seventh decimal place are given for interpolation. Only one copy of this, the first base 10 logarithm table, is extant. The English translation, The First Chiliad of Logarithmes, is also undated, but was probably issued in 1626.

Briggs undoubtedly computed the first base 10 logarithms. Controversy over what part Napier played in formulating the theory seems to have sprung from the fact that the 'Admonitio' was absent from several copies of Napier's Descriptio. This controversy was later fuelled by remarks about Napier's role made by the mathematician Charles Hutton, though these were in turn challenged by Napier's descendant Mark Napier when he published Napier's early treatise as De arte logistica in 1839. Today it is clear that the friendly relations between John Napier and Henry Briggs remained unbroken up to the end, and this friendship explains the inclusion of important sections written by Briggs in the English translation of Napier, Description (1616), in the Rabdologia, and in the Mirifici logarithmorum canonis constructio (1619). While Justus Bürgi is credited as an independent inventor of logarithms, Briggs is acknowledged as the creator of one of the most useful systems for mathematics (without having had any knowledge of power notation in the twentieth-century sense). On the continent the contributions of Napier and Briggs have generally been met with greater acclaim than those of Bürgi, Adriaan Vlacq, or Henry Gellibrand. Briggs's tables simplified the otherwise laborious computations involving multiplication and division of numbers to several decimal places, which had led the great European astronomers to fear that greater exactness in trigonometry was unattainable as it demanded impracticably arduous calculations.

In 1619 Briggs was appointed to the professorship of geometry in Oxford, newly established by Henry Saville, and on 8 January 1620 he took up the position at a salary of £150 a year. He lived in Merton College and was incorporated MA on 7 July 1620. After seven years' untiring computation his chief work, Arithmetica logarithmica (1624), appeared, containing the logarithms of the numbers 1 to 20,000 and 90,001 to 100,000, calculated to fourteen decimal places, with their complete differences. In it he explained at length his method of calculation which was based on the axiom 'Logarithmi sunt numeri qui proportionalibus adiuncti aequales servant differentias' ('Logarithms are numbers that, proportional parts co-ordinated, create equal differences') . From first principles he calculated to thirty-two decimal places the values of 10, √10, 22 √10, 23 √10, ... 254 √10, together with the corresponding forty-decimal place logarithms (1, 1/2, 1/22, 1/23, ... 1/254). These enabled him to find close-meshed starting values from which he could interpolate using nth order differences (derived recursively) to obtain the intervening logarithms. In deriving the differences Briggs formulated, in anticipation of Newton, the first four terms of the binomial expansion (1 + x)1/2. His notation has peculiarities, thus 59321 stands for the decimal fraction 5.9321/10000 and l(3)8 stands for 3√8. Briggs coined the terms 'mantissa' for the decimal part of the logarithm, and 'characteristic' for the whole number; moreover he assisted with terminology for John Minsheu's multilingual Ductor in linguas (1617) in this period of consolidation of the western European literary languages.

Although Briggs was busily employed in calculating the remaining logarithms (for 20,001 to 90,000), it was Adriaan Vlacq who completed the work, publishing logarithms to ten decimal places for all the numbers between 1 and 100,000 in a second edition of Arithmetica logarithmica (1628). An English edition, Logarithmicall arithmetike, was published in London in 1631. After Briggs's death Henry Gellibrand published as Trigonometria Britannica (1633) two volumes of Briggs's posthumous works. Briggs also published Lucubrationes et annotationes in opera postuma J. Neperi (1619), and Euclidis elementorum vi libri priores (1620), the author being identified only as H. B. Since 28 April 1619 Briggs had been auditor for the Virginia Company and this was the origin of his publication of A Treatise of the Northwest Passage to the South Sea (1622), which has a map ascribed to him. A group of islands there was subsequently named 'Brigges his Mathematickes' by Luke Fox though the name fell out of use. In Mathematica ab antiquis minus cognita (1630) Briggs summarized the more important mathematical inventions up to that time. Four additional treatises dealing principally with geometry remained unpublished.

Briggs died on 26 January 1631 in Merton College, Oxford. The entry in the college register shows the high reputation he enjoyed. At his interment on 29 January 1631, William Sellar conducted the service and Hugh Cressy gave the funeral oration. Briggs was buried in the choir of Merton College chapel with a gravestone bearing only his name and a lozenge. His will of 16 November 1629 was proved on 11 February 1631 by Jeremy and Miles Briggs, his executors. No known portrait of him survives. Briggs was regarded by contemporaries as an upright, extraordinary individual: 'beyond all praise, too famous for any panegyric ... worthy, therefore to receive our infinite thanks which are beyond calculation even by your own logarithms', wrote Isaac Barrow (Hallowes, 86). He had taken an active part in the society of his day; indeed Hill judged his role as 'contact and public relations man' (Hill, 38) to outweigh his importance as a mathematician.

WOLFGANG KAUNZNER

Sources  
D. M. Hallowes, 'Henry Briggs, mathematician', Halifax Antiquarian Society (1961), 79-92
private information (2004) [M. G. Underwood]
J. Ward, The lives of the professors of Gresham College (1740)
T. Smith, 'Vitae quorundam eruditissimorum et illustrium virorum', trans. J. T. Foxell, in A. J. Thompson, Logarithmetica Britannica, 1 (1952)
Biographia Britannica, or, The lives of the most eminent persons who have flourished in Great Britain and Ireland, 2 (1748)
R. Parr, ed., The life of the most reverend father in God, James Usher ... with a collection of three hundred letters (1686)
C. Hill, Intellectual origins of the English revolution (1965)
H. S. Carslaw, 'The discovery of logarithms by Napier', Mathematical Gazette, 8 (1915-16), 76-84, 115-19
'Briggs, Henry', 'Logarithm', 'Napier, John', 'Table, mathematical', Encyclopaedia Britannica, 11th edn (1910-11)
D. T. Whiteside, 'Patterns of mathematical thought in the later seventeenth century', Archive for History of Exact Sciences, 1 (1960-62), 179-388
D. T. Whiteside, 'Henry Briggs: the binomial theorem anticipated', Mathematical Gazette, 45 (1961), 9-12
parish register (baptism), Halifax, St John, 23 Feb 1561

Archives  
Bodl. Oxf., MS Bodley 313
Bodl. Oxf., MS Birch 4395
Pulkowo Observatory, Kepler MSS, vol. 11, fols. 269-72 [Johannes Kepler, Gesammelte Werke, 18 (1959), 220-29]


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