In the year 1619, Briggs was appointed the first Sa vilian professor of geometry at Oxford ; and in 1620 he resigned his office in Gresham College, and removed to Oxford, where he spent the remainder of his life. In consequence of being a member of the company trading to Virginia, he published in 1622, a Treatise on the North West passage to the South Sca, E.7c. which was afterwards reprinted in Purchas's Pilgrims. His time, however, was principally occupied with his Arithmetica Logarithmica, which was published in London in 1624. This work, the result of enormous labour, contains the logarithms with their differences, of 30,000 natural numbers to 14 places of figures, besides the index, viz. from 1 to 20,000, and from 90,000 to 100,000. In this work, he likewise explains the construction and use of the tables ; and such was his anxiety to induce other mathematicians to compute the intermediate numbers, that he offered to give instructions and paper ready ruled for the purpose, to any persons who were disposed to assist in the completion of the labour which he had begun. This task was undertaken and completed by Adrian Vlacq, who reprinted at Gouda in 1628, the ?rithmetica Logarithmica, with all the intermediate num bers, to 10 places of figures.
Briggs likewise completed a table of logarithmetic sines and tangents to the 100th part of each degree, to 14 places of figures, besides the index ; a table of natu ral sines to 15 places ; and a table of tangents and se cants to 10 places ; but he was taken ill while engaged in sheaving the application of these tables to plane and spherical trigonometry, and he committed the execu tion of this part of his plan to Henry Gellibrand, who willingly discharged this last duty to his friend. The cork was published at Gouda in 1633, under the care of Adrian Vlacq, and was entitled Trigonometric Britan nica.
On the 26th of January, 1630, Briggs terminated his labours at the advanced age of 74, and his remains were deposited in the choir of the chapel of Morton College, under the honorary monument of sir Henry Savilc.
In his private character, Briggs was distinguished by the frankness of his manners, and by the strictest integrity. He was fond of retirement and study, and enjoyed a high reputation among the mathematicians of the 16th and 17th centuries.
" In the construction of his two works on the loga rithms of numbers, and of sines and tangents," says the learned Dr Hutton, " our author, besides extreme la bour and application, manifests the highest powers of genius and invention ; as we here, for the first time, meet with several of the most important discoveries in the mathematics, and what have hitherto been consi dered as of much later invention ; such as the binomial theorem,* the differential method and construction of tables by differences; the interpolation by differences ; with angular sections, and several other ingenious com positions." Besides the works which we have already mentioned, Briggs published Tables for the Improvement of Navi gation. Loud. 1610, 4to. Description of an Instrumen tal Table to find the part proportional devised, by Mr E. Wright, 1616, 1618. Lucubrationes et ?nnotationes in opera posthuma, J. Neperi, Edin. 1619, 4to. Euclidis Elementorum vi. libri Jzriores. Lond. 1620, folio. Olathe viatica ab Annelids minus cognita.
The unpublished works of Briggs are, Commentaries on the Geometry of Peter Ramus. Dux Epistolze ad celeberrimum viritm, Chr. Sever. Longonzontanunz. ?ni madversiones Geometricre. De eodeni Argumento. A Treatise of common Arithmetic. .Letter to Mr. Clarke of Gravesend, Feb. 25, 1606. The last four of these MSS. were in the possession of the late Mr Jones. See IIutton's Mathematical Dictionary ; Ward's Lives of the Professors of Gresham College, p. 120.; and Smith's Comment. de vit. et stud. H. Briggil, Lond. 1707, 4to. (o)