A pioneer of mathematical contributions in logarithms, Briggs visited Napier at Edinburgh in 1616 to discuss a suggested change to Napier's logarithms. The following year he repeated his visit 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, Briggs was incorporated master of arts.
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 these 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 ("Introduction to Logarithms"), which gave a brief account of logarithms and a long table of the first 1000 integers calculated to the 14th decimal place.