Rigorous Thinking and the Use of Instruments 87 Newton’s Comments on Oughtred 94 Index 97 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.