GEOMETRIAM

GEOMETRIAM, SUB TYRANNO BARBARO SEVA
SERVITUTE DIU SQUALENTEM, IN LIBERTATEM
ET DECUS ANTIQUUM VINDICAVIT
UNUS.

Yet it must not be understood that Dr Simson's predilection for the geometrical analysis of the ancients did so far mislead him as to make him neglect the symbolical analysis of the present times; on the contrary, he

was completely master of it, as has been already observed, and frequently employed it. In his academical lectures to the students of his upper classes, he used to point out, its proper province (which he by no means limited by a scanty boundary), and in what cases it might be applied with safety and advantage even to questions of pure geometry. He once honoured the writer of this article with the sight of a very short dissertation on this subject (perhaps the one referred to in the preface to his Conic Sections). In this piece he was perhaps more liberal than the most zealous partisans of the symbolical analysis could desire, admitting as a sufficient equation of the Conic

Sections $L\; =\; \backslash frac\{p^2\; c\}\{x^2\}$, where $L$ is the latus rectum, $p$ is the distance of any point of the curve from the focus, $p$ is the perpendicular drawn from the focus to the tangent in the given point, and $c$ is the chord of the equicurve circle drawn through the focus. Unfortunately this dissertation was not found among his papers. He spoke in high terms of the Analytical Works of Mr Cotes, and of the two Bernoullis. He was consulted by Mr McLaurin during the progress of his inestimable Treatise of Fluxions, and contributed not a little to the reputation of that work. The spirit of that most ingenious algebraic demonstration of the fluxions of a rectangle, and the very process of the argument, is the same with Dr Simson's in his dissertation on the limits of quantities. It was therefore from a thorough acquaintance with the subject, and by a just taste, that he was induced to prefer his favourite analysis, or, to speak more properly, to exhort mathematicians to employ it in its own sphere, and not to become ignorant of geometry, while he successfully employed the symbolical analysis in cases which did not require it, and which suffered by its admission. It must be acknowledged, however, that in his later years, the disgust which he felt at the artificial and slovenly employment on subjects of pure geometry, sometimes hindered him from even looking at the most refined and ingenious improvements of the algebraic analysis which occur in the writings of Euler, D'Alembert, and other eminent masters. But, when properly informed of them, he never failed to give them their due praise; and we remember him speaking, in terms of great satisfaction, of an improvement of the infinitesimal calculus, by D'Alembert and De la Grange, in their researches concerning the propagation of sound, and the vibrations of musical cords.

And that Dr Simson not only was master of this calculus and the symbolical calculus in general, but held them in proper esteem, appears from two valuable dissertations to be found in his posthumous works; the one on logarithms, and the other on the limits of ratios. The last, in particular, shows how completely he was satisfied with respect to the solid foundation of the method of fluxions; and it contains an elegant and strict demonstration of all the applications which have been made of the method by its illustrious author to the objects of pure geometry.

We hoped to have given a much more complete and instructive account of this eminent geometer and his works, by the aid of a person fully acquainted with both, and able to appreciate their value; but an accident has deprived us of this assistance, when it was too late to procure an equivalent: and we must request our readers to accept of this very imperfect account, since we cannot do justice to Dr Simson's merit, unless almost equally

equally conversant in all the geometry of the ancient Greeks.

The life of a literary man rarely teems with anecdote; and a mathematician, devoted to his studies, is perhaps more abstracted than any other person from the ordinary occurrences of life, and even the ordinary topics of conversation. Dr Simson was of this class; and, having never married, lived entirely a college life. Having no occasion for the commodious house to which his place in the university entitled him, he contented himself with chambers, good indeed, and spacious enough for his sober accommodation, and for receiving his choice collection of mathematical writers, but without any decoration or commodious furniture. His official servant sufficed for valet, footman, and chambermaid. As this retirement was entirely devoted to study, he entertained no company in his chambers, but in a neighbouring house, where his apartment was faced to him and his guests.

Having in early life devoted himself to the restoration of the works of the ancient geometers, he studied them with unremitting attention; and, retiring from the promiscuous intercourse of the world, he contented himself with a small society of intimate friends, with whom he could lay aside every restraint of ceremony or reserve, and indulge in all the innocent frivolities of life. Every Friday evening was spent in a party at whist, in which he excelled, and took delight in instructing others, till increasing years made him less patient with the dulness of a scholar. The card-party was followed by an hour or two dedicated solely to playful conversation. In like manner, every Saturday he had a less select party to dinner at a house about a mile from town. The Doctor's long life gave him occasion to see the dramatis persone of this little theatre several times completely changed, while he continued to give it a personal identity; so that, without any design or wish of his own, it became, as it were, his own house and his own family, and went by his name. In this state did the present writer first see it, with Dr Simson as its father and head, respected and beloved by every branch; for, as it was for relaxation, and not for the enjoyment of his acknowledged superiority, that he continued this habit of his early youth; and as his notions "of a fine talk" did not consist in the pleasure of having "told and gored a good many to-day," his companions were as much at their ease as he wished to be himself; and it was no small part of their entertainment (and of his too), to smile at those innocent deviations from common forms, and those mistakes with respect to life and manners, which an almost total retirement from the world, and incessant occupation in an abstract science, caused this venerable president frequently to exhibit. These are remembered with a more affecting regret, that they are now "with the days that are past," than the most pithy apophthegms, ushered in with an emphatical, "Why, Sir!" or "No, Sir!" which precludes all reply. Dr Simson never exerted his presiding authority, unless it were to check some infringement of good breeding, or any thing that appeared unfriendly to religion or purity of manners; for these he had the highest reverence. We have twice heard him sing (he had a fine voice and most accurate ear) some lines of a Latin hymn to the Divine Geometer, and each time the rapturous tear flood in his eye.

But we ask the reader's pardon for this digression; it is not however useless, since it paints the man as much as any recital of his studies; and to his acquaintances we are certain that it will be an acceptable memorandum. To them it was often matter of regret, that a person of such eminent talents, which would have made him thine equally in any line of life, should have allowed himself to be so completely devoted to a study which abstracted him from the ordinary pursuits of men, unsuited him for the active enjoyment of life, and kept him out of those walks which they frequented, and where they would have rejoiced to meet him.

Dr Simson was of an advantageous stature, with a fine countenance; and even in his old age had a graceful carriage and manner, and always, except when in mourning, dressed in white cloth. He was of a cheerful disposition; and though he did not make the first advances to acquaintance, had the most affable manner, and strangers were at perfect ease in his company. He enjoyed a long course of uninterrupted health; but towards the close of life suffered from an acute disease, and was obliged to employ an assistant in his professional labours for a few years preceding his death, which happened in 1768, at the age of 81. He left to the university his valuable library, which is now arranged apart from the rest of the books, and the public use of it is limited by particular rules. It is considered as the most choice collection of mathematical books and manuscripts in the kingdom, and many of them are rendered doubly valuable by Dr Simson's notes.