William Oughtred. Cajori Florian

      William Oughtred / A great Seventeenth-Century Teacher of Mathematics

      INTRODUCTION

      In the year 1660 the Royal Society was founded by royal favor in London, although in reality its inception took place in 1645 when the Philosophical Society (or, as Boyle called it, the “Invisible College”) came into being, which held meetings at Gresham College in London and later in Oxford. It was during the second half of the seventeenth century that Sir Isaac Newton, surrounded by a group of great men – Wallis, Hooke, Barrow, Halley, Cotes – carried on his epoch-making researches in mathematics, astronomy, and physics. But it is not this half-century of science in England, nor any of its great men, that especially engage our attention in this monograph. It is rather the half-century preceding, an epoch of preparation, when in the early times of the House of Stuart the sciences began to flourish in England. Says Dr. A. E. Shipley: “Whatever were the political and moral deficiencies of the Stuart kings, no one of them lacked intelligence in things artistic and scientific.” It was at this time that mathematics, and particularly algebra, began to be cultivated with greater zeal, when elementary algebra with its symbolism as we know it now began to take its shape.

      Biographers of Sir Isaac Newton make particular mention of five mathematical books which he read while a young student at Cambridge, namely, Euclid’s Elements, Descartes’s Géométrie, Vieta’s Works, Van Schooten’s Miscellanies, and Oughtred’s Clavis mathematicae. The last of these books has been receiving increasing attention from the historians of algebra in recent years. We have prepared this sketch because we felt that there were points of interest in the life and activity of Oughtred which have not received adequate treatment. Historians have discussed his share in the development of symbolic algebra, but some have fallen into errors, due to inability to examine the original editions of Oughtred’s Clavis mathematicae, which are quite rare and inaccessible to most readers. Moreover, historians have failed utterly to recognize his inventions of mathematical instruments, particularly the slide rule; they have completely overlooked his educational views and his ideas on mathematical teaching. The modern reader may pause with profit to consider briefly the career of this interesting man.

      Oughtred was not a professional mathematician. He did not make his livelihood as a teacher of mathematics or as a writer, nor as an engineer who applies mathematics to the control and use of nature’s forces. Oughtred was by profession a minister of the gospel. With him the study of mathematics was a side issue, a pleasure, a recreation. Like the great French algebraist, Vieta, from whom he drew much of his inspiration, he was an amateur mathematician. The word “amateur” must not be taken here in the sense of superficial or unthorough. Great Britain has had many men distinguished in science who pursued science as amateurs. Of such men Oughtred is one of the very earliest.

      CHAPTER I

      OUGHTRED’S LIFE

      AT SCHOOL AND UNIVERSITY

      William Oughtred, or, as he sometimes wrote his name, Owtred, was born at Eton, the seat of Eton College, the year of his birth being variously given as 1573, 1574, and 1575. “His father,” says Aubrey, “taught to write at Eaton, and was a scrivener; and understood common arithmetique, and ’twas no small helpe and furtherance to his son to be instructed in it when a schoole-boy.”1 He was a boy at Eton in the year of the Spanish Armada. At this famous school, which prepared boys for the universities, young Oughtred received thorough training in classical learning.

      According to information received from F. L. Clarke, Bursar and Clerk of King’s College, Cambridge, Oughtred was admitted at King’s a scholar from Eton on September 1, 1592, at the age of seventeen. He was made Fellow at King’s on September 1, 1595, while Elizabeth was still on the throne. He received in 1596 the degree of Bachelor of Arts and in 1600 that of Master of Arts. He vacated his fellowship about the beginning of August, 1603. His career at the University of Cambridge we present in his own words. He says:

      These words describe the struggles which every youth not endowed with the highest genius must make to achieve success. They show, moreover, the kindly feeling toward others and the delight he took throughout life in assisting anyone interested in mathematics. Oughtred’s passion for this study is the more remarkable as neither at Eton nor at Cambridge did it receive emphasis. Even after his time at Cambridge mathematical studies and their applications were neglected there. Jeremiah Horrox was at Cambridge in 1633-35, desiring to make himself an astronomer.

      Some attention was given to Greek mathematicians, but the works of Italian, German, and French algebraists of the latter part of the sixteenth and beginning of the seventeenth century were quite unknown at Cambridge in Oughtred’s day. It was part of his life-work as a mathematician to make algebra, as it was being developed in his time, accessible to English youths.

      At the age of twenty-three Oughtred invented his Easy Way of Delineating Sun-Dials by Geometry, which, though not published until about half a century later, in the first English edition of Oughtred’s Clavis mathematicae in 1647, was in the meantime translated into Latin by Christopher Wren, then a Gentleman Commoner of Wadham College, Oxford, now best known through his architectural creations. In 1600 Oughtred wrote a monograph on the construction of sun-dials upon a plane of any inclination, but that paper was withheld by him from publication until 1632. Sun-dials were interesting objects of study, since watches and pendulum clocks were then still unknown. All sorts of sun-dials, portable and non-portable, were used at that time and long afterward. Several of the college buildings at Oxford and Cambridge have sun-dials even at the present time.

      AS RECTOR AND AMATEUR MATHEMATICIAN

      It was in 1604 that Oughtred entered upon his professional life-work as a preacher, being instituted to the vicarage of Shalford in Surrey. In 1610 he was made rector of Albury, where he spent the remainder of his long life. Since the era of the Reformation two of the rectors of Albury obtained great celebrity from their varied talents and acquirements – our William Oughtred and Samuel Horsley. Oughtred continued to devote his spare time to mathematics, as he had done in college. A great mathematical invention made by a Scotchman soon commanded his attention – the invention of logarithms. An informant writes as follows: