*A Treatise of Fluxions,*published in 1801, there has been added a

*Life of the Author*. We give a version of this below:

**Life of the Author**

Mr Maclaurin, a most eminent mathematician and philosopher, was the son of a clergyman, and born at Kilmoddan, in Scotland, in the year 1698. He was sent to the University of Glasgow in 1709; where he continued five years, and applied to his studies in a very intense manner, and particularly to the mathematics. His great genius for mathematical learning discovered itself so early as at twelve years of age; when, having accidentally met with a copy of Euclid's Elements in a friend's chamber, he became in a few days master of the first 6 books without any assistance: and it is certain, that in his 16th year he had invented many of the propositions which were afterwards published as part of his work entitled *Geometria Organica*. In his 15th year he took the degree of Master of Arts; on which occasion he composed and publicly defended a Thesis on the Power of Gravity, with great applause. After this he quitted the University, and retired to a country seat of his uncle, who had the care of his education; his parents being dead some time. Here he spent two or three years in pursuing his favourite studies; but, in 1717, at 19 years of age only, he offered himself a candidate for the Professorship of Mathematics in the Marischal College of Aberdeen, and obtained it after a ten days' trial against a very able competitor.

In 1719, Mr Maclaurin visited London, where he left his *Geometria Organica* to print, and where he became acquainted with Dr Hoadley, then Bishop of Bangor, Dr Clarke, Sir Isaac Newton, and other eminent men; at which time also he was admitted a member of the Royal Society: and in another journey, in 1721, he contracted an intimacy with Martin Folkes, Esq. the President of it, which continued during his whole life.

In 1722, Lord Polwarth, Plenipotentiary of the King of Great Britain at the Congress of Cambray, engaged Maclaurin to go as a tutor and companion to his eldest son, who was then to set out on his travels. After a short stay at Paris, and visiting other towns in France, they fixed in Lorrain; where he wrote his piece, On the Percussion of Bodies, which gained him the prize of the Royal Academy of Sciences for the year 1724. But his pupil dying soon after at Montpelier, he returned immediately to his profession at Aberdeen. He was hardly settled here, when he received an invitation to Edinburgh; the curators of that University being desirous that he should supply the place of Mr James Gregory, whose great age and infirmities had rendered him incapable of teaching. He had here some difficulties to encounter, arising from competitors, who had good interest with the patrons of the University, and also from the want of an additional fund for the new professor; which, however, at length were all surmounted, principally by the means of Sir Isaac Newton. Accordingly, in Nov 1725, he was introduced into the University; as was at the same time his learned colleague and intimate friend Dr Alexander Monro, Professor of Anatomy. After this, the mathematical classes soon became very numerous, there being generally upwards of 100 students attending his Lectures every year; who being of different standings and proficiency, he obliged to divide them into four or five classes, in each of which he employed a full hour every day from the first of November to the first of June. In the first class he taught the first 6 books of Euclid's Elements, Plane Trigonometry, Practical Geometry, the Elements of Fortification, and an to Algebra. The second class studied Algebra, with the 11th and 12th books of Euclid, Spherical Trigonometry, Conic Sections, and the Principles of Astronomy. The third went on in Astronomy and Perspective, read a part of Newton's Principia, and had performed a course of experiments for illustrating them: he afterwards read and demonstrated the Elements of Fluxions. Those in the fourth class read a System of Fluxions, the Doctrine of Chances, and the remainder of Newton's Principia.

In 1734, Dr Berkley, Bishop of Cloyne, published a piece called The Analyst; in which he took occasion, from some disputes that had arisen concerning the grounds of the fluxionary method, to explode the method itself; and also to charge mathematicians in general with infidelity in religion. Maclaurin thought himself included in this charge, and began an answer to Berkley's book: but other answers coming out, and, as he proceeded, so many discoveries, so many new theories and problems occurred to him, that instead of a vindicatory pamphlet, he produced a Complete System of Fluxions, with their application to the most considerable problems in Geometry and Natural Philosophy. This work was published at Edinburgh in 1742, 2 vols. 4to.; and as it cost him infinite pains, so it is the most considerable of all his works, and will do him immortal honour, being indeed the most complete treatise on that science that has yet appeared.

In the mean time, he was continually obliging the public with some observation or performance of his own, several of which were published in the 5th and 6th volumes of the Medical Essays at Edinburgh. Many of them were likewise published in the Philosophical Transactions; as the following:

- On the Construction and Measure of Curves, vol. 30.
- A New Method of describing all Kinds of Curves, vol. 30.
- On Equations with impossible Roots, vol. 34.
- On the Roots of Equations, &c. vol. 34.
- On the Description of Curve Lines, vol. 39.
- Continuation of the same, vol. 39.
- Observations on a Solar Eclipse, vol. 40.
- A Rule for finding the Meridional Parts of a Spheroid with the same Exactness as in a Sphere, vol. 41.
- An Account of the Treatise of Fluxions, vol. 42.
- On the Bases of the Cells where the Bees deposit their Honey, vol. 42.

Mr Maclaurin had still another scheme for the improvement of geography and navigation, of a more extensive nature; which was the opening of a passage from Greenland to the South Sea by the North Pole. That such a passage might be found, he was so fully persuaded, that he used to say, if his situation could admit of such adventures, he would undertake the voyage even at his own charge. But when schemes for finding it were laid before the Parliament in 1741, and he was consulted by several persons of high rank concerning them, and before he could finish the memorials he proposed to send, the premium was limited to the discovery of a North West passage: and he used to regret that the word West was inserted, because he thought that passage, if at all to be found, must lie not far from the Pole.

In 1745, having been very active in fortifying the city of Edinburgh against the rebel army, he was obliged to fly from thence into England, where he was invited by Dr Herring, Archbishop of York, to reside with him during his stay in this country. In this expedition, however, being exposed to cold and hardships, and naturally of a weak and tender constitution, which had been much more enfeebled by close application to study, he laid the foundation of an illness which put an end to his life, in June 1746, at 48 years of age, leaving his widow with two and three daughters.

Mr Maclaurin was a very good as well as a great man, and worthy of love as well as admiration. His peculiar merit as a philosopher was, that all studies were accommodated to general utility; and find, in many places of his works, an even of the most abstruse theories to the of mechanical arts. For the same purpose, he resolved to compose a course of Practical Mathematics, and to rescue several useful branches of science from the ill treatment they often met with less skilful hands. These intentions, however, were prevented by his death; unless we may reckon, as part of his intended work, the translation of Dr David Gregory's Practical Geometry, which he revised, and published with additions, in 1745.

In his life time, however, he had frequent opportunities of serving his friends and his country by his great skill. Whatever difficulty occurred concerning the constructing or perfecting of machines, the working of mines, the improving of manufactures, the conveying of water, or the execution of any public work, he was always ready to resolve it. He was employed to terminate some disputes of consequence that had arisen at Glasgow concerning the gauging of vessels; and for that purpose, presented to the commissioners of the excise two elaborate memorials, with their demonstrations, containing rules by which the officers now act. He made also calculations relating to the provision, now established by law, for the children and widows of the Scotch clergy, and of the professors in the Universities, entitling them to certain annuities and sums upon the voluntary annual payment of a certain sum by the incumbent. In contriving and adjusting this wise and useful scheme he bestowed a great deal of labour, and contributed not a little towards bringing it to perfection.

Of his works, we have mentioned his *Geometria Organica,* in which he treats of the description of curve lines by continued motion; as also of his Piece which gained the prize of the Royal Academy of Sciences in 1724. In 1740, he likewise shared the prize of the same Academy with the celebrated D Bernoulli and Euler, for resolving the problem relating to the motion of the tides from the theory of gravity; a question which had been given out the former year without receiving any solution. He had only ten days to draw up this paper in, and could not find leisure to transcribe a fair copy; so that the Paris edition of it is incorrect. He afterwards revised the whole, and inserted it in his Treatise of Fluxions; as he did also the substance of the former Piece. These, with the Treatise of Fluxions, and the Pieces printed in the Medical Essays and the Philosophical Transactions, a list of which will be found in page xvi, are all the writings which our Author lived to publish. Since his death, however, two more volumes have appeared; his *Algebra*, and his *Account of Sir Isaac Newton's Philosophical Discoveries*. The Algebra, though not finished by himself, is yet allowed to be excellent in its kind; containing, in no large volume, a complete elementary treatise of that science, as far as it has hitherto been carried; besides some neat analytical papers on curve lines. His Account of Newton's Philosophy was occasioned in the following manner: --- Sir Isaac dying in the beginning of 1728, his nephew, Mr Conduitt, proposed to publish an Account of his Life, and desired Mr Maclaurin's assistance. The latter, out of gratitude to his great benefactor, cheerfully undertook, and soon finished, the History of the Progress which Philosophy had made before Newton's time; and this was the first draught of the work in hand, which, not going forward on account of Mr Conduitt's death, was returned to Mr Maclaurin. To this he afterwards made great additions, and left it in the state in which it now appears. His main design seems to have been to explain only those parts of Newton's Philosophy which have been controverted: and this is supposed to be the reason why his grand discoveries concerning light and colours, are but transiently and generally touched upon; for it is known, that whenever the experiments, on which his doctrine of light and colours is founded, had been repeated with due care, this doctrine had not been contested; while his accounting for the celestial motions, and the other great appearances of nature, from gravity, had been misunderstood, and even attempted to be ridiculed.