**Henry Briggs** was the man most responsible for scientists' acceptance of logarithms. He is of great importance in the development of mathematics but, as Hill writes in [8]:-

... significant though Briggs was as a mathematician in his own right, his greatest importance was as a contact and public relations man.

Briggs was born at Warley Wood (or Warleywood) in the parish of Halifax, Yorkshire. His birth is recorded in the Halifax parish register as February 1561 yet this information contradicts a notice by J Mede written at Christ's College Cambridge on 6 February 1630, a few days after Briggs died, which states (see for example [1]):-

Mr Henry Briggs of Oxford, the great mathematician, is lately dead, at74years of age.

If Mede were correct then Briggs would have been born in 1556, but it seem highly unlikely that he is correct, for there seems no possible reason to think that the Halifax parish records could be wrong. We know little of Briggs's family but there is a history of Norfolk, by Blomefield, which states that Briggs's family were originally from Salle in that county. Blomefield is known to be wrong in a number of other such claims so not too much weight should be put on this statement, although, on the other hand, there is some evidence that other members of Briggs's family did have Norfolk connections. In fact Richard Briggs, who was Henry Briggs's brother, became headmaster of a school in Norfolk. Richard Briggs had important friends such as Ben Jonson, the dramatist, poet, and literary critic and a letter from Ben Jonson to Richard Briggs still exists.

Henry Briggs attended a grammar school near Warley Wood where he became highly proficient at Greek and Latin. After completing his school studies, he entered St John's College of Cambridge University in 1577. Admitted as a scholar on 5 November 1577, Briggs received the degree of B.A. in 1581, receiving his M.A. four years later. In 1588 (some sources give 1589) he was elected a fellow of St John's College and then, in 1592, he became:-

Reader of the Physic Lecture founded by Dr Linacre.

Thomas Linacre, born almost exactly 100 years before Briggs, had been so upset by the fact that medicine was practiced by barbers and clergymen without proper qualifications that he founded the Royal College of Physicians of London. The Linacre lectureship that Briggs was appointed to was therefore a medical lectureship but, in the same year of 1592, Briggs was also appointed as an examiner and lecturer in mathematics at Cambridge. It certainly appears that his talents were wide ranging.

In 1596 Briggs became the first professor of geometry at Gresham College, London which had just been founded. He was to hold this position in Gresham College for 23 years, the College being famed as the birthplace of the Royal Society of London about 25 years after Briggs left. We know something of Briggs's work at this time since he became firm friends with James Ussher in 1609. Ussher was then a professor at Trinity College, Dublin, but later, in 1625, became archbishop of Armagh. Letters sent to Ussher have survived and some have been published, in particular one written by Briggs in August 1610. This letter shows that at this time Briggs was greatly interested in astronomy, in particular he was studying eclipses. This was a topic which involved many heavy calculations so Briggs was greatly struck when he read Napier's work on logarithms by the great help that they would provide to those involved in astronomy.

It was not only the fact that logarithms were so useful for astronomical calculations which attracted Briggs to them. He was already highly involved in producing tables to aid calculation and he had published two types of tables before he read about Napier's logarithms. In 1602 Briggs had published *A Table to find the Height of the Pole, the Magnetic Declination being given* and in 1610 he had published *Tables for the Improvement of Navigation.*

Briggs read Napier's 1614 Latin text on logarithms and, on the 10 March 1615, wrote in a letter to his friend James Ussher that he was:-

... wholly employed about the noble invention of logarithms, then lately discovered.

Briggs continued:-

Napper, 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 a book which pleased me better or made me more wonder.

As soon as Briggs had read about logarithms he began thinking about improvements and was soon teaching his students about the new topic. He wrote (see for example [1]):-

I myself, when expounding this doctrine publicly in London to my auditors in Gresham College, remarked that it would be much more convenient that0should be kept for the logarithm of the whole sine ... concerning this matter I wrote immediately to the author himself.

Let us look at the problem which Briggs was attempting to address. The logarithms Nap.log invented by Napier are different from the logarithms that we use today. The fact that Nap.log 1 does not equal 0 is a major difficulty which makes Nap.logs much less convenient for calculations than today's logarithms. It is often written in books on the history of mathematics that Briggs was responsible for the change to logarithms with log 1 = 0. However, although logarithms with log 1 = 0 first appear in print in Briggs's work, he himself gives the credit for the idea to Napier. Certainly the idea came about in discussions between Napier and Briggs.

Briggs made the difficult journey from London to Edinburgh to see Napier in the summer of 1615. It was not the easy journey of 4 hours by train that we could make today, but rather for Briggs it was a journey of at least 4 days by horse and coach. It was not a journey one would undertake lightly but Briggs was desperately keen to meet Napier. A description of their meeting was told by John Marr to William Lilly who writes the following (see [6]):-

Mr Briggs appoints a certain day when to meet at Edinburgh; but failing thereof, Merchiston was fearful he would not come. It happened one day as John Marr and the Lord Napier were speaking of Mr Briggs, "Oh! John," saith Merchiston, "Mr Briggs will not come now"; at the very instant one knocks at the gate, John Marr hastened down and it proved to be Mr Briggs to his great contentment. He brings Mr Briggs into my Lord's chamber, where almost one quarter of an hour was spent, each beholding the other with admiration, before one word was spoken. At last Mr Briggs began, -"My Lord, I have undertaken this long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help unto astronomy, viz. the Logarithms; but, my Lord, being by you found out, I wonder nobody else found it out before, when now known it is so easy.

Briggs had suggested to Napier in a letter sent before their meeting that logs should be (in our terminology) to base 10 and Briggs had begun to construct such tables. Napier replied that he had had the same idea but ([6]):-

... he could not, on account of ill-health and for other weighty reasons undertake the construction of new tables.

At their meeting Napier suggested to Briggs the new tables should be constructed with base 10 and with log 1 = 0. Briggs wrote that Napier proposed (see for example [1]):-

... that0should be the logarithm of unity and10,000,000,000that of the whole sine, which I could not but admit was by far the most convenient.

Indeed Briggs did construct such tables. He spent a month with Napier on his first visit of 1615, made a second journey from London to Edinburgh to visit Napier again in 1616, and would have made yet a third visit the following year but Napier died in the spring before the planned summer visit.

Briggs's first work on logarithms *Logarithmorum Chilias Prima* was published in London in 1617. The recent death of Napier is referred to in the preface as is Briggs reason to publish that work, namely:-

... for the sake of his friends and hearers at Gresham College.

Briggs published an article *A Description of an Instrument Table to find the Part Proportional, devised by Mr Edward Wright* in Wright's English translation of Napier's *Canon.* After Wright's death, Briggs published two further editions of this work (1616 and 1618) with a preface he wrote himself. Briggs's mathematical treatise *Arithmetica Logarithmica* was published in 1624. This gave the logarithms of the natural numbers from 1 to 20,000 and 90,000 to 100,000 computed to 14 decimal places. It also gave tables of natural sine functions to 15 decimal places, and the tan and sec functions to 10 decimal places. In this book Briggs suggested that the logs of the missing numbers might be computed by a team of people and he even offered to supply specially designed paper for the purpose.

You can see translations by Ian Bruce of *Arithmetica Logarithmica* and of *Trigonometria Britannica*.

The completed tables were printed at Gouda, in the Netherlands, in 1628 in an edition by Vlacq in which Vlacq had added the logarithms of the natural numbers from 20,000 to 90,000. The tables were also published in London in 1633 under the title of *Trigonometria Britannica.* The printing of the London edition took place after Briggs had died but he had asked his friend Henry Gellibrand to look after the project on his behalf. Gellibrand was professor of astronomy at Gresham College and was particularly interested in applications of logarithms to trigonometry. He therefore added a preface of his own on applications of logarithms to both plane trigonometry and to spherical trigonometry.

We have followed through Briggs involvement with logarithms but we should go back and look at his other work and the final stage of his life after he left Gresham College. His interest in astronomy continued throughout his years at Gresham College and six letters still exist which were written to him between 1603 and 1619 by Sir Christopher Heydon on comets and other astronomical and mathematical topics.

In 1619 Savile founded a chair of geometry at Oxford because:-

... geometry is almost totally unknown and abandoned in England.

Savile gave the first lectures himself then asked Briggs to fill the chair. Briggs accepted and after receiving high praise from Savile in his last lecture, took over the course continuing from the point that Savile had reached, namely the ninth proposition of Euclid's *Elements.* Briggs was made a fellow of Merton College Oxford to enable him to hold the Savilian chair but he did not resign his position in Gresham College until a few months later, ending his 23 year employment with the Gresham College on 25 July 1620.

Briggs's first publication after his appointment at Oxford was an edition of the first six book of Euclid's *Elements* which he published in 1620. He chose not to include the fact that he was the editor on these texts, merely attributing the entire work to Euclid. His next work published in 1622 was not on a mathematical topic, but rather on one of great interest at the time: *A Treatise of the Northwest Passage to the South Sea, Through the Continent of Virginia and by Fretum Hudson.* This publication was more natural than it appears for Briggs had interests outside the academic world, being a member of a company trading with Virginia. Again Briggs chose not to put his name on the work, the author simply appearing as H. B.

In addition to his publications, Briggs wrote a number of other works which have never been published. These include works on the geometry of Ramus and on Longomontanus's treatise on squaring the circle. A treatise on geometry and another on arithmetic were similarly never published.

Briggs was highly regarded by other mathematicians. We have already referred to Savile's high regard for him and another contemporary, Oughtred, described Briggs as:-

... the mirror of the age for excellent skill in geometry.

Barrow, born the year the Briggs died, was appointed professor of geometry at Gresham College in 1662. In his inaugural lecture he referred to Briggs, who had held the same post some 50 years earlier, as the man who made logarithms a vital tool for all scientists.

Of his character we know only his modesty from his writings, his fairness in giving full attributions to others and [12]:-

... from the references to him by his contemporaries ... that he was a man of amiable character.

A final comment on his character is worth making, namely that in an age where astrology was an important topic for most men of learning, Briggs strongly opposed it. William Lilly, from who we quoted the description of the meeting of Napier and Briggs above, wrote that (see for example [12]):-

... Napier was a great lover of astrology, but Briggs was the most satirical man against it that hath been known.

**Article by:** *J J O'Connor* and *E F Robertson*

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