remarkable work of Agricola, De Re Metallica, first published in 1546, followed as it was, before the end of the century, by the writings and researches of Ercher, Fachs, and Palissy (the great improver of the manufacture of enamelled pottery), may be said to have already established the science of Mineralogy, and also to have furnished some indications of that of Geology.

In England, meanwhile, much of this progress that had been made in other countries probably remained unknown. We have most to boast of in the physical sciences; medicine was both practised and taught on the revived principles of the ancient physicians, in the early part of the sixteenth century, by the learned Linacre, the translator of Galen, the founder of the medical lectureships at Oxford and Cambridge, and the first president of the College of Physicians, which was incorporated by Henry VIII. in 1518; some valuable works on botany and zoölogy were published in the latter half of the century by William Turner, particularly the earliest English Herbal, the first part of which appeared at London in 1551, the second and third at Cologne in 1562 and 1568;1 the north and south poles of the magnet are described by Robert Norman, a writer on navigation, in 1581; and at the head of the modern sciences of navigation and electricity stands the name of Dr. William Gilbert, whose treatise De Magnete, published in 1600, afforded one of the most remarkable specimens that had then appeared both of ingenious experimenting and of sound inductive reasoning. To Gilbert is assigned the invention of artificial magnets. In the pure sciences, and those more immediately dependent upon mathematics, we did very little during this period. Cuthbert Tonstall, or Tunstall, Bishop of London, and afterwards of Durham, published a Latin Treatise on Arithmetic (De Arte Supputandi) at London in 1522, which was frequently reprinted abroad in the course of the century. This performance, so far from containing anything new, scarcely attempts even to explain the principles of the old rules and processes which it details and exemplifies; but it has the merit of a simplicity and a freedom from extraneous matter which were very rare in that age.2 From what Tonstall

1 Lobel, also, already mentioned, though a Fleming by birth, spent the latter years of his life in England, where James I. gave him the appointment of royal botanist.

2 Notices of English Mathematical and Astronomical writers between the Norman Conquest and the year 1600, in Companion to the Almanac for 1837, p. 30.

says in the dedication of his book to his friend Sir Thomas More, it would appear that, like almost every other nation in Europe, we were already possessed of arithmetical manuals in the vernacular tongue, though of a very low order. Of much greater importance were various works produced about the same date, or a little later, by William Recorde, the physician. "He was the first," says the authority to which we have just referred," who wrote on arithmetic in English (that is, anything of a higher cast than the works mentioned by Tonstall); the first who wrote on geometry in English; the first who introduced algebra into England; the first who wrote on astronomy and the doctrine of the sphere in English; and finally, the first Englishman (in all probability) who adopted the system of Copernicus."1 Recorde's Ground of Arts, a treatise on arithmetic, first published in 1551, was many times reprinted, and kept its ground as a common schoolbook till the end of the seventeenth century. His Pathway to Knowledge, also first printed in 1551, is a treatise of practical geometry, but containing also an account of the theorems in the first four books of Euclid, though without the demonstrations. His Castle of Knowledge, published in 1556, is a treatise on astronomy, both theoretical and practical; and it is in this work that Recorde shows himself, in the words of the writer before us," as much of a Copernican as any reasonable man could well be at the time; at least as much so (in profession) as was Copernicus himself, who makes no decided declaration of belief in his own system, but says, it is by no means necessary that hypotheses should be true, or even probable, — it suffices that they make calculation and observation agree. 2 Recorde's Whetstone of Wit, first published in 1553, is a treatise of algebra, although the author does not use that name except in calling the application of indeterminate numbers to the solution of equations "the rule of Algeber.” “In this treatise," says the writer of the Notices, "he appears to have compounded, for the first time, the rule for extracting the square roots of multi-nominal algebraical quantities, and also to have first used the sign In other respects he follows Scheubel, whom he cites, and Stifel, whom he does not cite. There is nothing on cubic equations, nor does he appear to have known anything of the

1 Companion to the Almanac for 1837. An interesting account of Recorde's various works follows, pp. 30-37.

2 Companion to the Almanac for 1837, p. 36.

Italian algebraists. . . Recorde was one of the first who had a distinct perception of the difference between an algebraical operation and its numerical interpretation, to the extent of seeing that the one is independent of the other; and also he appears to have broken out of the consideration of integer numbers to a much greater extent than his contemporaries." In his perception of general results connected with the fundamental notation of algebra, this writer conceives Recorde to show himself superior even to Vieta himself, though of course immeasurably below the Italian in the invention of means of expression. "All his writings considered together," it is added, "Recorde was no common man. It is evident that he did not write very freely at first in English, but his style improves as he goes on. His writings continued to the end of the century to be those in common use on the subjects on which he wrote, though we must gather this more from the adoption of ideas and notation than from absolute citation." 1 Another English Copernican of this early date was John Field, the author of an Ephemeris for 1557, published in the preceding year. In the earliest English work on cosmography, nevertheless, The Cosmographical Glass, compiled by William Cunningham, London, 1559, the system taught is that of Ptolemy, nor is the least hint of that of Copernicus to be found in the book.2 In 1573 was published the first English translation of Euclid, professedly by the famous John Dee, the astrologer and soi-disant magician, but commonly believed to have been actually the performance of Sir Henry Billingsley, whom, however, the writer of the Notices before us supposes to have been a pupil of Dee, who only executed the more mechanical part of the undertaking, working under his master's general, if not special, instructions. The first Latin translation of the Elements of Euclid, that of Campanus, had appeared at Venice in 1482 (the original Greek not having been printed till 1530); and the only translations into any modern European tongues which preceded that of Dee were, that of Tartalea into Italian, Venice, 1543; those of Scheubel of the 7th, 8th, and 9th books, and of Holtzmann of the preceding six, into German, Augsburg, 1562 and 1565; and that of Henrion into French, Paris, 1565 (as is supposed). Dee's translation appears either to have been made from the original, or at least to have been corrected by the Greek text. "It contains," says the

1 Companion to the Almanac for 1837, p. 37.

2 Ibid. pp. 35 and 37.

writer before us, "the whole of the fifteen books commonly considered as making up the Elements of Euclid, and forms the first body of complete mathematical demonstration which appears in our language. For, though the works of Recorde were much less dogmatical than the elementary schoolbooks of the eighteenth, and (for the most part) of the present century, yet they partake of the character which they tended perhaps to perpetuate, and in many instances teach rules without demonstration, or with at most a rough kind of illustration. . . . . The appearance of Euclid in an English form probably saved the credit of the exact sciences, and in this point of view Dee and Billingsley have exercised a material and beneficial influence upon their favorite pursuits."1 Of Dee's scientific works the greater number still remain in manuscript; among those that have been published are a Latin treatise on Parallax, and a preface to Field's Ephemeris for 1557 (mentioned above), from which latter it appears that Dee also was a CoperniContemporary with this mathematician was Leonard Digges, who died in 1574, after having published various works, most of which were republished, with additions, by his son, Thomas Digges, who lived till 1595. The writings of both father and son relate for the most part to mensuration and the art of war, and are characterized by the application of arithmetical geometry in these departments. One, a work of Thomas Digges, entitled Alae sive Scalae Mathematicae, 1573, being a tract upon parallaxes, undertaken at the suggestion of Lord Burleigh, in consequence of the appearance of the remarkable new star discovered the preceding year by Tycho Brahe in the constellation Cassiopeia, "is," says the author of the Notices, "the first work of an English writer in which we have noticed anything on spherical trigonometry, and the writings of Copernicus are more than once referred to as the source of the subject." From some passages, Thomas Digges appears, this writer thinks, "to have been a believer in the real motion of the earth, and not merely an admirer of the system of Copernicus as an explanatory hypothesis." " On the whole it may be said that nearly the whole history of the advancement of English mathematical science in the sixteenth century is connected with the names of Recorde, Dee, and Digges. If a judgment might be formed from some works published between 1580 and 1600, the author of the Notices is inclined to suppose that, instead 1 Companion to the Almanac for 1837, p. 39. 2 Ibid. pp. 40, 41.

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of making any progress, science rather declined among us in that interval. "The writers," he observes," seem to have abandoned what had been newly introduced, and to have betaken themselves to older authors and other notions." Among the productions in question are, the Mathematical Jewel, by John Blagrave, of Reading, 1585, a treatise on a new mathematical instrument, apparently a projection of the sphere, for the construction of problems in astronomy, which proceeds upon the Ptolemaic system of the world, and does not contain a hint of the Copernican, although Copernicus is several times alluded to as an observer; a work on the projection of the sphere, described as very poor and insufficient," published in 1590, by Thomas Hood, the inventor of an astronomical instrument called Hood's Staff; M. Blundevile's Exercises, containing six treatises on arithmetic, cosmography, &c., 1594, in which is found a set of tables of sines, tangents, and seconds, being the first printed in England, but the author of which expressly denounces the Copernican system of the world as a "false supposition," although he admits that by help of it Copernicus had "made truer demonstrations of the motions and revolutions of the celestial spheres than ever were made before"; and various works by a Thomas Hill, one of which, The School of Skill, London, 1599, is described as "an account of the heavens and the surface of the earth, replete with those notions on astrology and physics which are not very common in the works of Recorde or Blundevile."1 Hill notices the scheme of Pythagoras and Copernicus, by which, as he expresses it, they "took the earth from the middle of the world, and placed it in a peculiar orb." But," he adds, "overpassing such reasons, lest by the newness of the arguments they may offend or trouble young students in the art, we therefore (by true knowledge of the wise) do attribute the middle seat of the world to the earth, and appoint it the centre of the whole."

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1 Companion to the Almanac for 1837, p. 43.