Henry, one of the greatest mathematicians of the sixteenth century, was born at Warley Wood, in the parish of Halifax, Yorkshire, in the year 1556. In 1592 he was appointed examiner and lecturer in mathematics, and soon afterwards reader of the physical lecture founded by Dr Linacre. When Gresham College in London was established, he was chosen the first professor of geometry there, about the beginning of March 1596. In 1609 Mr Briggs contracted an intimacy with Usher, afterwards archbishop of Armagh, which continued many years, and was kept up chiefly by letters, two of which, written by the subject of this notice, are still extant. In one of these letters, dated in August 1610, he tells his friend he was engaged on the subject of eclipses; and in the other, dated in March 1615, he acquaints him with his being wholly employed about the noble invention of logarithms, then lately discovered, and in the improvement of which he had afterwards a large share. In his lectures at Gresham College, he proposed the alteration of the scale of logarithms, from the hyperbolic form which Napier had given them, to that in which unity is assumed as the logarithm of the ratio of ten to one; and soon afterwards he wrote to the inventor to make the same proposal to himself. In 1616 Briggs paid a visit to Napier at Edinburgh, in order to confer with that eminent person respecting the suggested change; and next year he repeated his visit for a similar purpose. During these conferences the alteration proposed by Briggs was agreed upon; and on the return of the latter from his second visit in 1617, he accordingly published the first chilid of his logarithms. In 1619 he was appointed Savilian professor of geometry at Oxford, and resigned his professorship of Gresham College on the 25th of July 1620. Soon after his settlement at Oxford he was incorporated master of arts in that university, where he continued a laborious and studious life, employed partly in discharging the duties of his office, and partly in the computation of logarithms and in other useful works. In 1622 he published a small tract on the North-west Passage to the South Seas, through the continent of Virginia and Hudson's Bay; and in 1624 he printed, at London, his Arithmetica Logarithmica, in folio, a work containing the logarithms of thirty thousand natural numbers to fourteen places of figures besides the index. He also lived to complete a table of logarithmic sines and tangents for the hundredth part of every degree to fourteen places of figures besides the index, with a table of natural signs 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. In the construction of these works, the author, besides immense labour and application, displayed great powers of genius and invention; and in his investigations may be detected the germs of discoveries in mathematics which are generally considered as of later invention, namely, the binomial theorem, the differential method and construction of tables by differences, the interpolation by differences, together with angular sections, and several other things of scarcely inferior importance. Mr Briggs terminated his laborious and useful life on the 26th of January 1630, in the seventy-fourth year of his age. Dr Smith gives him the character of being a man of great probity, a contemner of riches, and contented with his own station, preferring a studious retirement to all the splendid circumstances of life. His works are, 1. A Table to find the Height of the Pole, the Magnetical Declination being given, London, 1602, 4to; 2. Tables for the Improvement of Navigation, printed in the second edition of Edward Wright's treatise entitled "Certain Errors in Navigation detected and corrected," London, 1610, 4to; 3. A Description of an Instrumental Table to find the part proportional, devised by Mr Edward Wright, London, 1616 and 1618, 12mo; 4. Logarithmorum Chilias prima, London, 1617, 8vo; 5. Lucubrationes et Annotationes in opera posthuma J. Napieri, Edinburgh, 1619, 4to; 6. Euclidis Elementorum VI. libri prioris, London, 1620, folio; 7. A Treatise on the North-west Passage to the South Seas, London, 1622, 4to, reprinted in Purchas's Pilgrims, vol. iii. p. 832; 8. Arithmetica Logarithmica, London, 1624, folio; 9. Trigonometria Britannica, Gouda, 1663, folio; 10. Two Letters to Archbishop Usher; 11. Mathematica ab Antiquis minus coquita; and some other works, as his Commentaries on the Geometry of Peter Ramus, and Remarks on the Treatise of Longomontanus respecting the quadrature of the Circle, which have not been published.

William, an eminent physician in the latter end of the seventeenth century, was the son of Augustin Briggs, Esq. four times member for the city of Norwich, where our author was born. He studied at the university of Cambridge; and his genius leading him to cultivate physic, he travelled into France, where he attended the lectures of the celebrated anatomist M. Vieussens at Montpelier. After his return he published his Ophthalmographia in 1676. The year following he was created doctor of medicine at Cambridge, and soon after was made fellow of the College of Physicians at London. In 1682 he resigned his fellowship in favour of his brother; and the same year his Theory of Vision was published by Hooke. The ensuing year he sent to the Royal Society a continuation of that discourse, which was published in their Transactions; and the same year he was appointed by King Charles II. physician to St Thomas's Hospital. In 1684 he communicated to the Royal Society two remarkable cases relating to vision, which were likewise printed in their Transactions; and in 1685 he published a Latin version of his Theory of Vision, at the desire of Mr. afterwards Sir Isaac Newton, professor of mathematics at Cam-