rather than to him, especially as Whytehead, who had fallen into want, seems at the time when it was published to have been living in Billingsley's house. The copy of the Greek text of Theon's Euclid used by Billingsley has however been recently discovered, and is now in Princetown College, America'; and it would appear from this that the credit of the work is wholly due to Billingsley himself. The marginal notes are all in his writing, and contain comments on the edition of Adelhard and Campanus from the Arabic (see p. 4), and conjectural emendations which shew that his classical scholarship was of a high order.

Other contemporary mathematical writers are Hill, Bedwell, Hood, the two Harveys, and Forman. They are not of sufficient importance to require more than a word or two in passing.

Thomas Hill, who took his B.A. degree from Christ's College in 1553, wrote a work on Ptolemaic astronomy termed the Schoole of skil: it was published posthumously in 1599.

Thomas Bedwell entered at Trinity in 1562, was elected a scholar in the same year, proceeded B.A. in 1567, and in 1569 was admitted to a fellowship. His works deal chiefly with the applications of mathematics to civil and military engineering, and enjoyed a high and deserved reputation for practical good sense. The New River company was due to his suggestion. He died in 1595.

Thomas Hood, who entered at Trinity in 1573, proceeded B.A. in 1578, and was subsequently elected to a fellowship, was another noted mathematician of this time. In 1590 he issued a translation of Ramus's geometry, and in 1596 a translation of Urstitius's arithmetic.

He also wrote on the use of the globes

1 See a note by G. B. Halsted in vol. II. of the American journal of mathematics, 1878. The Greek text had been brought into Italy by refugees from Constantinople, and was first published in the form of a Latin translation by Zamberti at Venice in 1505: the original text (Theon's edition) was edited by Grynæus and published by Hervagius at Bâle in 1535.

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(1590 and 1592), and the principles of surveying (1598). In 1582 a mathematical lectureship was founded in London— probably by a certain Thomas Smith of Gracechurch Street— and Hood was appointed lecturer. His books are probably transcripts of these lectures: the latter were given in the Staples chapel, and subsequently at Smith's house. Hood seems to have also practised as a physician under a license from Cambridge dated 1585.

Richard Harvey, a brother of the famous Gabriel Harvey, was a native of Saffron Walden. He entered at Pembroke in 1575, proceeded B.A. in 1578, and subsequently was elected to a fellowship. He was a noted astrologer, and threw the whole kingdom into a fever of anxiety by predicting the terrible events that would follow from the conjunction of Saturn and Jupiter, which it was known would occur on April 28, 1583. Of course nothing peculiar followed from the conjunction; but Harvey's reputation as a prophet was destroyed, and he was held up to ridicule in the tripos verses of that or the following year and hissed in the streets of the university. Thomas Nash (a somewhat prejudiced witness be it noted) in his Pierce pennilesse, published in London in 1592 says, "Would you in likely reason guess it were possible for any shame-swoln toad to have the spet-proof face to outlive this disgrace?" Harvey took a living, and his later writings are on theology. He died in 1599.

John Harvey, a brother of the Richard Harvey mentioned above, was also born at Saffron Walden: he entered at Queens' in 1578 and took his B.A. in 1580. He practised medicine and wrote on astrology and astronomy-the three subjects being then closely related. He died at Lynn in 1592.

Simon Forman', of Jesus College, born in 1552, was another mathematician of this time, who like those just mentioned combined the study of astronomy, astrology, and medicine with considerable success; though he is described, apparently with

1 An account of Forman's life is given in the Life of William Lilly, written by himself, London, 1715.

good reason, as being as great a knave as ever existed. His license to practise medicine was granted by the university, and is dated 1604. He was a skilful observer and good mathematician, but I do not think he has left any writings. He died suddenly when rowing across the Thames on Sept. 12, 1611.

With the exception of Recorde, Dee, and Digges, all the above were but second-rate mathematicians; but such as they were (and they are nearly all the English mathematicians of that time of whom I know anything) it is noticeable that without a single exception they were educated at Cambridge. The prominence given to astronomy, astrology, and surveying is worthy of remark.

I come next to a group of mathematicians of considerably greater power, to whom we are indebted for important contributions to the progress of the science.

The first of these was Edward Wright', whose services to the theory of navigation can hardly be overrated. Wright was born in Norfolk, took his B.A. from Caius in 1581, and was subsequently elected to a fellowship. He seems to have had a special talent for the construction of instruments; and to instruct himself in practical navigation and see what improvements in nautical instruments were possible, he went on a voyage in 1589-special leave of absence from college being granted him for the purpose.

In the maps in use before the time of Gerard Mercator a degree whether of latitude or longitude had been represented in all cases by the same length, and the course to be pursued by a vessel was marked on the map by a straight line joining the ports of arrival and departure. Mercator had seen that this led to considerable errors, and had realized that to make this method of tracing the course of a ship at all accurate the

1 See an article in the Penny Cyclopaedia, London, 1833-43; and a short note included in the article on Navigation in the ninth edition of the Encyclopaedia Britannica.

space assigned on the map to a degree of latitude ought gradually to increase as the latitude increased. Using this principle, he had empirically constructed some charts, which were published about 1560 or 1570. Wright set himself the problem to determine the theory on which such maps should be drawn, and succeeded in discovering the law of the scale of the maps, though his rule is strictly correct for small arcs only. The result was published by his permission in the second edition of Blundeville's Exercises. His reputation was so considerable that four years after his return he was ordered by queen Elizabeth to attend the Earl of Cumberland on a maritime expedition as scientific adviser.

In 1599 Wright published a work entitled Certain errors in navigation detected and corrected, in which he very fully explains the theory and inserts a table of meridional parts. Solar and other observations requisite for navigation are also treated at considerable length. The theoretical parts are correct, and the reasoning shews considerable geometrical power. In the course of the work he gives the declinations of thirtytwo stars, explains the phenomena of the dip, parallax, and refraction, and adds a table of magnetic declinations, but he assumes the earth to be stationary. This book went through three editions. In the same year he issued a work called The haven-finding art. I have never seen a copy of it and I do not know how the subject is treated. In the following year he published some maps constructed on his principle. In these the northernmost point of Australia is shewn: the latitude of London is taken to be 51° 32'.

About this time Wright was elected lecturer on mathematics by the East India Company at a stipend of £50 a year. He now settled in London, and shortly afterwards was appointed mathematical tutor to prince Henry of Wales, the son of James I. He here gave another proof of his mechanical ability by constructing a sphere which enabled the spectator to forecast the motions of the solar system with such accuracy that it was possible to predict the eclipses for over seventeen

thousand years in advance: it was shewn in the Tower as a curiosity as late as 1675. Wright also seems to have joined Bedwell in urging that the construction of the New River to supply London with drinking water was both feasible and desirable.

As soon as Napier's invention of logarithms was announced in 1614, Wright saw its value for all practical problems in navigation and astronomy. He at once set himself to prepare an English translation. He sent this in 1615 to Napier, who approved of it and returned it, but Wright died in the same year, before it was printed: it was issued in 1616.

Whatever might have been Wright's part in bringing logarithms into general use it was actually to Briggs, the second of the mathematicians above alluded to, that the rapid adoption of Napier's great discovery was mainly due.

Henry Briggs' was born near Halifax in 1556. He was educated at St John's College, took his B.A. degree in 1581, and was elected to a fellowship in 1588. He continued to reside at Cambridge, and in 1592 he was appointed examiner and lecturer in mathematics at St John's.

In 1596 the college which Sir Thomas Gresham2 had directed to be built was opened. Gresham, who was born in 1513 and died in 1579, had been educated at Gonville Hall, and had apparently made some kind of promise to build the college at Cambridge to encourage research, so that his final determination to locate it in London was received with great disappointment in the university. The college was endowed for the study of the seven liberal sciences; namely, divinity, astronomy, geometry, music, law, physic, and rhetoric.

Briggs was appointed to the chair of geometry. He seems at first to have occupied his leisure in London by researches on

1 See the Lives of the professors of Gresham College by J. Ward, London, 1740. A full list of Briggs's works is given in the Dictionary of national biography.

2 See the Life and times of Sir Thomas Gresham, published anonymously but I believe written by J. W. Burgon, London, 1845.