Mathematical Contribution
In 1616 Briggs visited Napier at Edinburgh in order to discuss the suggested change to Napier's logarithms. The following year he again visited for a similar purpose. During these conferences the alteration proposed by Briggs was agreed upon; and on his return from his second visit to Edinburgh, in 1617, he published the first chiliad of his logarithms.
In 1619 he was appointed Savilian professor of geometry at Oxford, and resigned his professorship of Gresham College in July 1620. Soon after his settlement at Oxford he was incorporated master of arts.
In 1622 he published a small tract on the Northwest Passage to the South Seas, through the Continent of Virginia and Hudson's Bay.
In 1624 his Arithmetica Logarithmica, in folio, a work containing the logarithms of thirty thousand natural numbers to fourteen decimal places (1-20,000 and 90,001 to 100,000). This table was later extended by Adriaan Vlacq, but to 10 places, and by Alexander John Thompson to 20 places in 1952. Briggs was one of the first to use finite-difference methods to compute tables of functions.
He also completed a table of logarithmic sines and tangents for the hundredth part of every degree to fourteen decimal places, with a table of natural sines to fifteen places, and the tangents and secants for the same to ten places; all of which were printed at Gouda in 1631 and published in 1633 under the title of Trigonometria Britannica; this work was probably a successor to his 1617 Logarithmorum Chilias Prima ("The First Thousand Logarithms"), which gave a brief account of logarithms and a long table of the first 1000 integers calculated to the 14th decimal place.
Briggs discovered, in a somewhat concealed form and without proof, the binomial theorem. English translations of Briggs's Arithmetica and the first part of his Trigonometria Britannica are available on the web.
Briggs was buried in the chapel of Merton College, Oxford. Dr Smith, in his Lives of the Gresham Professors, characterizes him as a man of great probity, a condemner of riches, and contented with his own station, preferring a studious retirement to all the splendid circumstances of life.
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