RECORDE, ROBERT

(b. Tenby, Pembrokeshire, Wales, ca, 1510; d. London, England, 1558)

mathematics.

Recorde was the second son of Thomas Recorde, whose father had come to Wales from Kent, and of Rose Johns of Montgomeryshire. He graduated B.A. from Oxford in 1531 and was elected a fellow of All Souls College in the same year. All Souls was a chantry and graduate foundation for the study and training of clerks in theology, civil and canon law, and medicine. At some time he removed to Cambridge and there received the M.D. degree in 1545. According to the Cambridge records he had been licensed in medicine at Oxford some twelve years earlier, and the B.M. usually went with the Oxford license. Tradition has it that he lectured on mathematics at Oxford and Cambridge; but details of his university career, and of any degrees other than the B.A. and M.D., are lacking.

Recorde was in London by 1547, probably practicing medicine. There is no evidence that he acted as physician to any of the Tudors, although he served the government in other capacities. In January 1549 he was appointed comptroller of the Bristol mint. In October 1549, at the time of Somerset’s first fall, he sided with the protector, refusing to divert money intended for King Edward to the armies of the west under Lord John Russell and Sir William Herbert. He was accused of treason by Herbert (later earl of Pembroke) and was confined at court for sixty days while the mint ceased production. This was the beginning of a permanent quarrel with Herbert which had serious consequences for Recorde’s later career.

From 1551 to 1553 Recorde was surveyor of the mines and monies in Ireland, in charge of the abortive silver mines at Wexford and, technically, supervisor of the Dublin mint. The venture was unsuccessful from the start. In addition to differences with the German miners over technology, and the personal animosity of Pembroke, the treasury was not able to bear the great expenses of the mines and their lack of profits. The work stopped in 1553 and Recorde was recalled. Not until 1570 was his estate compensated for some £ 1,000 due him for his services there.

In 1556 Recorde attempted to regain a position at court and laid charges of malfeasance as commissioner of the mints against Pembroke. Regardless of the merits of the case, it was a serious error in judgment on his part; Pembroke had the complete confidence of Queen Mary and King Philip, and it was impossible for a minor civil servant, whose last post had ended in failure, to survive the clash with the “politic old earl.” Pembroke sued for libel in a bill of 16 October 1556. The hearing was held in January 1557, with a judgment of £ 1,000 damages against Recorde awarded 10 February. Presumably Recorde was imprisoned for failure to pay this sum. His will was written in King’s Bench prison and was admitted to probate 18 June 1558.

Recorde has been justly called the founder of the English school of mathematical writers. He envisioned a course of instruction in elementary mathematics and its applications for mathematical practitioners. Deliberately choosing the vernacular, he wrote simple, clear English prose of a higher quality than his scientific contemporaries or immediate successors. Recorde made a special effort to find English equivalents for Latin and Greek technical terms, but very few of his innovations were adopted by later writers. His books indicate great skill as a teacher. His use of dialogue enabled him to carry a student step by step through the mastery of techniques, and to emphasize the proper order and method of instruction. Difficult questions were deferred until an understanding of fundamentals was achieved. Recorde took a rational view of his sources and was refreshingly critical of unquestioning acceptance of established authority. The mathematical books were written in the order in which he intended them to be studied: arithmetic, plane geometry, practical geometry, astronomy, and theoretical arithmetic and algebra. Projected works on advanced astronomy, navigation, and a translation of Euclid’s Elements probably were never completed.

The arithmetic, The Ground of Aries (1543, enlarged in 1552), was the most popular of all Recorde’s works. The first edition dealt only with whole numbers, covering the fundamental operations, reduction, progression, golden rule, and counter reckoning. In 1552 it was enlarged to include the same operations with fractions, and false position and alligation. There are three editions of the first version: 1543, 1549, and 1550[?]. The third has been dated formerly 1542[?] or 1545[?]; but bibliographers, on the basis of the state of the title-page border, now place it between the editions of 1549 and 1552.

The Pathway to Knowledge (1551) is a translation and rearrangement of the first four books of Euclid’s Elements. Like Proclus before him, and Ramus later, Recorde separated the constructions (“things to be done”) from the theorems (“things to be proved”). Proofs are not given, but explanations and examples are provided. Pedagogically, Recorde felt that it is not easy for a student to understand at the beginning both the thing that is taught and the reason why it is so.

The Gate of Knowledge dealt with measurement and the use of the quadrant. It has been lost and possibly was never published, although in the Castle it is referred to as complete.

The Castle of Knowledge (1556), on the construction and use of the sphere, is an elementary Ptolemaic astronomy with a brief, favorable reference to the Copernican theory. The often-cited edition of 1551 is a “ghost.” The Castle is based chiefly on Ptolemy, Proclus, Sacrobosco, and Oronce Fine, but is much more than a synthesis of earlier writers. More than in any other of his books, Recorde was concerned here with sources. He devoted considerable space to a critical examination of the standard authorities, offering corrections of textual errors in the Greek authors and suggesting that the mistakes of Sacrobosco and others were caused by their lack of knowledge of Greek.

The Whetstone of Witte (1557) was the only one of Recorded book not to have seen at least two editions, no doubt because it was less immediately useful to the London craftsmen than were his other works. It contains the “second part of arithmetic” promised in The Ground of Artes (from the arithmetic books of Euclid) and elementary algebra through quadratic equations. It is based on German sources, especially Johann Scheubel and Michael Stifel, and the algebra uses the German cossic notation. With Recorders addition of the “equal” sign this algebra became completely symbolic. Although it is derivative, there are several noteworthy features: the use of zero coefficients in algebraic long division; the use of arbitrary numbers to check algebraic operations rather than the check by inverse operations; and the treatment of quadratics. Recorde did not admit negative roots but did use negative coefficients in equations. All quadratics are written with the square term equal to roots plus or minus numbers, or numbers minus roots. He still had to give the three usual rules of solution; but, in the case of an equation with two positive roots, x² = px - q, he stressed the solution using the relation between the roots and coefficients: r₁ + r₂ = p, r₁ r₂ = q.

In addition to his mathematical works, Recorde published The Urinal of Physick (1547), dedicated to the Company of Surgeons. A promised anatomy has not survived. A traditional medical work on the judgment of urines, full of sensible nursing practice, the Urinal is less modern than his mathematical works and less critical of authority.

Recorde was not only an able teacher and a skillful textbook writer but was also one of the outstanding scholars of mid-sixteenth-century England. He was well trained in mathematics, and was familiar with Greek and medieval texts as well as contemporary developments. His intelligent attitude toward authority, and his appeals to reason and observation, anticipated in a more moderate manner the anti-Aristotelianism of Petrus Ramus. Recorde was learned in medicine and the law. He was an able Greek scholar who stressed the importance of a knowledge of that language for an accurate understanding of sources. He had a wide range of learning in various fields: he was a historian interested in the antiquities of Britain, a collector of manuscripts, and one of the first students of the Anglo-Saxon language.

Recorde had no international reputation because all of his works were in English and on an elementary level. In England, however, his books remained the standard texts throughout the Elizabethan period. A generation of English scientists, especially the non-university men, stated that Recorde’s books had been their first tutors in the mathematical sciences. The excellence of the English school of mathematical practitioners, fostered by growing geographical interests, has been attributed to the high quality of the vernacular movement in applied science begun by Recorde.

BIBLIOGRAPHY

I. Original Works. Recorde’s published works are Ground of Artes (London, 1543, 1549, 1550[?]; enl. ed., 1552, 1558, and many later eds.; last ed., 1699); Urinal of Physick (London, 1547, 1548, and others; last ed., 1665); Pathway to Knowledge (London, 1551, 1574, 1602); Castle of Knowledge (London, 1556, 1596); and Whetstone of Witte (London, 1557).

John Bale’s contemporary autograph notebook lists other, unpublished, works by Recorde as well as MSS from his library. Bale’s work has been published as Index Britanniae scriptorum, R. L. Poole, ed. (Oxford 1902).

II. Secondary Literature. W. G. Thomas of Tenby, Pembrokeshire, who discovered the King’s Bench records concerning Recorde and the Earl of Pembroke, is publishing a full account of the case.

For details on specific books see J. B. Easton, “The Early Editions of Robert Recorde’s Ground of Artes,” in Isis, 58 (1967), 515–532; and “A Tudor Euclid,” in Scripta mathematica, 27 (1966), 339–355; L. D. Patterson, “Recorde’s Cosmography, 1556,” in Isis, 42 (1951), 208–218 (which must be read with caution); F. R. Johnson, “Astronomical Textbooks in the Sixteenth Century,” in E. A. Underwood, ed., Science, Medicine end History (Oxford, 1953), 285–302; and L. C. Karpinski, “The Whetstone of Witte,” in Bibliotheca mathematica, 3rd ser., 13 (1912–1913), 223–228.

Recorde’s place in Renaissance science is discussed in F. R. Johnson and S. V. Larkey, “Robert Recorde’s Mathematical Teaching and the Anti-Aristotelian Movement,” in Huntigton Library Bulletin, no. 7 (1935), 59–87; F. R. Johnson, Astrononical Thought in Renaissance England (Baltimore, 1937); and Edward Kaplan, “Robert Recorde (c. 1510–4558): Studies in the Life arid Works of a Tudor Scientist,” Ph.D. diss. (New York University, 1960), available on University Microfilms (Ann Arbor, Mich., 1967).

Joy B. Easton

Robert Recorde

1510-1558

Welsh-English Mathematician

Robert Recorde introduced the "equals" symbol (=) to mathematical notation, and greatly advanced mathematical education in the British Isles. Not only was he the first to write on arithmetic, geometry, and astronomy in English rather than Latin, he introduced the study of algebra to England. Unfortunately, political intrigue cut short his career.

Born in 1510 in Tenby, Wales, Recorde was the son of Thomas and Rose Johns Recorde. His paternal great-grandparents had been English, and he spent his career in England, beginning with his studies at Oxford. He earned his B.A. from the latter in 1531, and after a stint at All Soul's College, moved to Cambridge, where he received his M.D. degree in 1545. Soon afterward, he gained a prestigious appointment at the court of King Edward VI. Recorde later married, fathering nine children.

Undoubtedly, Recorde's position at court, though it would eventually pose a liability that proved fatal, in the short run provided him with the means and the freedom to embark on his career as a mathematical writer. The first of his known publications was Grounde of Arts (1541), which in addition to its scholarly overview of contemporary mathematics provided practical knowledge concerning commercial math. The Pathway to Knowledge (1551) was a translation of the first four volumes in Euclid's (c. 325-c. 250 b.c.) Elements, and is the only one of Recorde's books not written in the form of a dialogue between master and student.

In The Whetstone of Witte (1557), Recorde presented the equals sign, using what he considered a hallmark of equality: two parallel lines of equal length. Other mathematical works included Castle of Knowledge (1556), on the properties of spheres, and The Gate of Knowledge, a text on measurement and the quadrant which has been lost. He also wrote an early urological treatise, The Urinal of Physick (1547).

Most of Recorde's books appeared in verse form, to make memorization easier, and provided students with detailed knowledge regarding how solutions were derived. His writing was highly readable by the standards of his time, and thus made his work popular in England if not on the Continent, where there were few readers of English.

In his political career, Recorde did not prove as successful as he had been in the world of mathematics. While serving as comptroller of the Bristol Mint in 1549, he came into conflict with Sir William Herbert, later Earl of Pembroke, and this led to his ostracism from court and his imprisonment for 60 days. Nor did an appointment as surveyor of mines in Ireland serve to recover his good standing. He again found himself at loggerheads with Pembroke, who he charged with malfeasance, and when the mines proved unprofitable, Recorde was removed from his position.

By then it was 1553, the same year Queen Mary I (Bloody Mary) took the throne following the death of her half-brother Edward. Three years later, when Recorde tried to gain reinstatement at court, Pembroke responded to the malfeasance charge by suing him for libel. Mary and her husband, King Philip of Spain, sided with Pembroke, and Recorde was sent to King's Bench Prison, where he was executed in 1558.

JUDSON KNIGHT

Robert Recorde

Robert Recorde (1510-1558), the founder of the English school of mathematics, introduced algebra into England; he is also given credit for the introduction of the equals sign.

Robert Recorde was born in Wales. For a time, he taught mathematics at Cambridge and Oxford universities. He had first attended Oxford but received the medical degree from Cambridge in 1545. He then went to London, where he was court physician to Edward VI and Mary Tudor. The fact that Recorde graduated in medicine and was a practicing physician did not detract him from studies in mathematics; he published four books on that subject and only one on medicine.

Recorde's first book, The Ground of Artes (1540), was very popular. At the time of its publication, England had not made nearly the progress in mathematical books that was typical of the Continent, and his book served, in part, to close the gap. It was intended to be a basic arithmetic but has been described as a book of commercial arithmetic. It went through 18 editions in the 16th century and 12 in the 17th. In the preface Recorde introduces a dialogue between the teacher and the scholar in which the teacher explains the usefulness of arithmetic, mentioning, among other subjects, how much music, physics, and law depend on numbers and proportions. He also lists the number of occupations, such as those of merchant, steward, bailiff, army officer, and treasurer, in which, the master claims, a knowledge of arithmetic is an absolute necessity.

Recorde's other books included The Castle of Knowledge (1551), a work on astronomy which served to bring the Copernican hypothesis to the attention of the English reading public. The Pathewaie to Knowledge (1551) contains an abridgment of Euclid's Elements of Geometry. Of more importance was The Whetstone of Witte (1557), where the modern equals sign first appeared in print. The work also showed methods for extracting roots, the Cossike practice (algebra), the rule of equation, and "the woorkes of Surde [irrational] Nombers."

The Ground of Artes, Recorde's most important book, appeared at a time when commerce and finance were flourishing as never before. The England of Elizabeth I welcomed a book which told its merchants and investors how to compute with both Arabic numerals and with counting machines, how to establish proportions, the methods of fractions, and many other commercial forms and topics which had been established in Renaissance Italy well before Recorde's time.

For a time Recorde held the post of comptroller of mints and monies in Ireland, but his life ended in King's Bench Prison, Southwark, London. It is said that he was in prison for debt, but some evidence indicated that he was involved in a scandal concerning Irish mines.

Further Reading

A biographical sketch of Recorde, as well as a selection from The Ground of Artes, is in James R. Newman, ed., The World of Mathematics, vol. 1 (1956). The older work of David Eugene Smith, History of Mathematics, vol. 1 (1923), gives a concise discussion of English mathematics in the early modern period. □