His manner of teaching was uncommonly clear and engaging to young people, and most of his scholars retained, through life, an affection and reverence for the professor. The college of Glasgow in his time was in great repute, both at home and abroad, to which Dr. Hutcheson, Dr. Moor, Mr. Adam Smith, and himself, much contributed. The resort of students was great, and almost all of them attended Dr. Simson's lectures. The knowledge of the elementary branches of mathematics, and of the most useful applications of them, were thence much diffused in the college, and some taste also for the study of the higher branches was excited; but the early age of the greater number of the students, their short residence in college, and the necessary appropriation of a considerable portion of their time to other sciences, seldom admitted of that long and nearly exclusive cultivation of one particular science, by which alone, especially in mathematics, eminence usually can be attained. Among Dr. Simson's scholars, however, several rose to distinction, as mathematicians. Dr. Matthew Stewart, who alone has applied the metrical method of reasoning to the most complex physical investigations, by universal acknowledgment, is to be named the first; Mr. Williamson, a favourite pupil, from whom he had great expectations, died very young; Dr. Moor, Greek professor at Glasgow, and Professor Robinson of Edinburgh, were all known as mathematicians of superior abilities and at tainments. geo In the year 1758, Dr. Simson, being then seventy-one years of age, found it necessary to employ an assistant in teaching; and in 1761, on his recommendation, the Rev. Dr. Williamson was appointed his assistant and successor. The resignation of Dr. Simson presented an opportunity to the Principal and Professors, of recording in their minutes the affec tion which they felt for the Doctor, and their high admiration of his ge nius. A long paper for this purpose was drawn up by his colleagues, and it is expressed with all the warmth of attachment and respect, which it was natural for them to entertain for the father of the college, from whom the university, had derived so much honour.' pp. 46. The Doctor lived ten years after his resignation, continu ing to enjoy an equable state of good health, and cheerful spirits, excepting as they were now and then interrupted with complaints respecting his loss of memory. He employed himself, principally, in arranging some of his mathematical papers, and in solving such problems as either occurred in the course of his reading, or were suggested to him by his friends for his amusement. He was seriously indisposed only for a few weeks before his death, which happened on the 1st of October, 1768, when he had nearly completed his 81st year. Such are the main particulars furnished by Dr. T. relative to the life of his friend. A few short quotations will make the reader acquainted with his character and his babits. Dr. Simson was originally possessed of great intellectual powers, an accurate and distinguishing understanding, an inventive genius, and a resentive memory; and these powers, being excited by an ardent curiosity, produced a singular capacity for investigating the truths of mathematical science. By such talents, with a correct taste, formed by the study of the Greek geometers, he was also peculiarly qualified for communicating his knowledge, both in his lectures and in his writings, with perspicuity and elegance. He was at the same time modest and unassuming; and though not indifferent to literary fame, he was cautious and even reserved in bringing forward his own discoveries, but always ready to do justice to the merits and inventions of others. Dr. Simson never was married; and the uniform regularity of a long life, spent within the walls of his college, naturally produced fixed and peculiar habits, which, however, with the sincerity of his manners, were unoffending, and became even interesting to those with whom he lived. The strictness of these habits, which indeed pervaded all his occupations, probably had an influence also on the direction and success of some of his scientific pursuits. His hours of study, of amusement, and of exercise, were all regulated with uniform precision. The walks even in the squares or garden of the college were all measured by his steps, and he took his exercise by the hundreds of paces, according to his time or inclination.' pp. 73-75. We suppose the ingenious Professor, on such occasions, walked alone, and that he never indulged himself with looking about him; otherwise we apprehend he would have run great risk of losing his reckoning, and perchance of walking too long. The Doctor, in his disposition, was both cheerful and social; and his conversation, when he was at ease among his friends, was animated and various, enriched with much anecdote, especially of the literary kind, but always unaffected. It was enlivened also by a certain degree of natural humour, and even the slight fits of absence to which in company he was occasionally liable, contributed to the entertainment of his friends, without diminishing their affection and respect, which his excellent qualities were calculated to inspire. One evening in the week he devoted to a club, chiefly of his own selection, which met in a tavern near the college. The first part of the evening was employed in playing the game of whist, of which he was particularly fond; but though he took no small trouble in estimating chances, it was remarked that he was often unsuccessful. The rest of the evening was spent in cheerful conversation, and as he had some taste for music, he did not scruple to amuse his party with a song; and it is said he was rather fond of singing some Greek odes, to which modern music had been adapted. On Saturdays he usually dined in the village of Anderston, then about a mile distant from Glasgow, with some of the members of his regular club, and with a variety of other respectable visitors, who wished to cultivate the acquaintance, and enjoy the society, of so eminent a person. In the progress of time, from his age and character, it became the wish of his company, that every thing in these meetings should be directed by him; and though his authority, growing with his years, was somewhat absolute, yet the good humour with which it was administered, rendered it pleasing to every body. He had his own chair and place at table; he gave instructions about the entertainment, regulated the time of breaking up, and adjusted the expence. These parties, in the years of his severe study, were a desirable and useful relaxation to his mind, and they continued to amuse him till within a few months of his death.' pp. 76, 77. We are thus informed how the learned Professor passed his time on Saturdays, and as his biographer is a clergyman, we read on with some avidity, hoping to learn how his friend employed himself on the days immediately succeeding. We are told, indeed, that he was uniformly reserved in expressing particular opinions on the subject of religion; and, from his sentiments of decorum, he never introduced religion as a subject of conversation in mixed society, and all attempts to do so in his clubs were checked with gravity and decision,' This, to be sure, is natural enough; for it is easy to imagine that a man who wanted to introduce religious conversation at a card-club, would make but an indifferent whist player, and probably a somewhat sorry casuist. Yet Dr. Trail must be aware, that this leaves the main point undecided; although it is a point which, as he has introduced the topic of religion, in reference to his friend, every reader will be anxious to see placed beyond controversy. Dr. T. doubtless knows, that Simson has always been classed among deists, and described as one who, when he entered on the professorship, being asked if the bible contained all the articles of his faith, replied with the usual accompaniment of profane men, "yes, and a great deal more." And he must be aware, that this is not disproved, by telling us how firmly Dr. S. resisted the introduction of religion in mixed society,' or in card parties; or even by writing Deo Optimo Maximo, Benignissimo Servatori, sit laus et gloria,' at the end of a geometrical solution which he completed on his birth-day, in the year 1764. Leaving, then, this matter as we found it, we shall now speak a little of Dr. Simson's performances. The only publications which he sent to the press during his life-time, (besides two papers in the Philosophical Transactions, one on Porisms, and the other containing an investigation of Albert Girard's rule for approximation to the roots of numbers which are not perfect squares) were-his Treatise Sectiorum Conicarum, libri v.' which appeared in 1735; and his excellent edition of Euclid, which appeared both in Latin and English in 1756, and to a second edition of which, in 1762, was annexed the book of Euclid's Data. The treatise on Conic Sections was undertaken by Dr. Simson to correct what he thought the false taste, which then prevailed, of investigating the pro perties of those curves algebraically: he, therefore, assumed the definitions employed by L'Hospital and others in their algebraical treatises, and from them, with the true simplicity and accuracy of the ancient school, he deduced not only the properties of these curves, as given by all preceding writers, but added many new and important propositions of his own, with the generalization and improvement of many, which had been previously discovered.' He deduces the various properties of the curve from their description in plano, in which respect we think his work inferior to the elegant treatises by Dr. Hamilton and Dr. Hutton, both of whom derive their investigations from the properties of the respective sections inferred from their connection with the cone itself. In Simson's edition of 1750, several additions are made, including some valuable communications by Dr. Matthew Stewart. In the preface, Dr. Simson gives a short sketch of the history of this portion of geometry from the age of Menæchmus, who is usually reputed the first inventor. Some omissions have been remarked in this history, which, however, have been supplied by Dr. Abraham Robertson, of Oxford, in the learned history prefixed to his valuable work on the conic sections. But Dr. Simson's grand undertaking is his edition of the first six, with the eleventh and twelfth, books of Euclid's Ele ments. To judge with impartiality of the merits of this work,' says Dr. T., the state of the text in preceding editions must be attended to. Dr. Simson, from his veneration for the ancient Geometers, seems, with an excusable partiality, to have assumed, that the Elements of Euclid, as they came from the author, were nearly without blemish; and he therefore ascribes all the errors and imperfections of the common editions, either to the carelessness of transcribers, or to the blunders of Theon, and other ancient editors. His corrections are numerous and many of them important; and even now, when most of them are adopted, it might be an useful exercise for the young mathematician to study the grounds of his emendations, which exhibit so clearly the precision of his ideas, and the logical accuracy of his understanding. Some animadversions were made on this edition, chiefly by those whose works had been criticised in the Doctor's notes; and to some of these in a second edition, replies and explanations were made; but he had a great aversion to controversy, and his observations on what he had proved to be errors or defects in his predecessors were never calculated to provoke it. Notwithstanding Dr. Simson's valuable corrections, there are still some difficulties in the Elements, which remain to be cleared up by some future editor. The demonstration of the property of parallel lines (29. I. Elem.) is still theoretically defective, requiring the admission of some principle, not strictly belonging to the class of self-evident truths. It has by some been supposed, that the remedy for this difficulty must be sought for in a just definition of a strait line. No definition of a strait line has yet been found, and none perhaps can be found from which all the properties assumed in the Elements to belong to it, can be rigidly de monstrated. There is manifestly also some defect in the definition of a solid angle, since what is given in Dr. Simson's and in all other editions, does not discriminate the solid angle from a number of plain angles, formed at one point, which may exist according to the definition, but without forming the solid angle intended to be defined. The improvements and corrections of the fifth book are also important. His obser vation with respect to solid figures, in the note on Def. 10. xi. Elem. is curious, from remarking an error, which is so obvious when pointed out, but which had escaped the notice of the many learned and acute geometers, who had paid much attention to Euclid's Elements. An observation of a similar kind, and about the same time, was made by Mr. Le Sage which is recorded in the History of the Royal Academy of Sciences at Paris for 1756; and another important correction has been more recently made by Le Gendre, of which a satisfactory history is given by Mr. Playfair, in the second edition of his Elements of Geometry." pp. 31-33. Dr. S. was certainly better qualified, by his singular reverence for his author, by his enthusiastic preference of geometry to the modern analysis, and by his critical acquaintance with the Greek language, to present a correct edition of Euclid, than any other man who has turned his attention to the subject and we, therefore, cannot but regret, that he satisfied himself with giving merely the first six, with the eleventh and twelfth books. His edition, however, though extremely valuable, is not free from blemishes and errors. The most remarkable occur in his attempt to demonstrate the 12th axiom of the first book, where he has fallen into several paralogisms, which render his reasonings completely nuga. tory. Thus in the fifth proposition, in his note to Euclid's 29th, he takes it for granted that, when a line is perpendicular to one of two parallel lines, it may be produced till it meets the other-which is a particular case of the general proposition he was endeavouring to establish. Besides the works already enumerated, Dr. Simson had, long before his death, prepared several others for the press; but the strong impression he often felt respecting the failure of his memory prevented him from publishing them. The copies of these, with a large mass of miscellaneous papers, fell into the hands of his executor, Mr. Clow, Professor of Logic at Glasgow. While Mr. Clow was deliberating what was most expedient to be done with regard to these papers entrusted to his care, the late Earl Stanhope, distinguished in his elevated rank by his ingenious cultivation and liberal patronage of the mathematical sciences, intimated his design of publishing those works of Dr. Simson which he had completed, with any other pieces, which, though unfinished, might without injury to his fame be given to the public. The munificent proposal was most accept |