Source on Colin Maclaurin

“Colin Maclaurin was descended of an ancient family, which had been long in possession of the island of Tirrie, upon the coast of Argyleshire. His grandfather, Daniel, removing to Inverara, greatly contributed to restore that town, after it had teen almost entirely ruined in the time of the civil wars; and, by some memoirs which he wrote of his own times, appears to have been a person of worth and superior abilities. John, the son of Daniel, and father of our author, was minister of Glenderule; where he not only distinguished himself by all the virtues of a faithful and diligent pastor, but has left, in the register of his provincial synod, lasting monuments of his talents for business, and of his public spirit. He was likewise employed by that synod in Completing the version of the Psalms into Irish, which, is still used in those parts of the country where divine service is performed in that language. He married a gentlewoman of the family of Cameron, by whom he had three sons; John, who is still living, a learned and pious divine, one of the ministers of the city of Glasgow; Daniel, who died young, after having given proofs of a most extraordinary genius; and Colin born at Kilmoddan in the tnonth of February 1698.”

“His father died six weeks after; but that loss was in a good measure supplied to the orphan family, by the affectionate care of their uncle Mr. Daniel Maclaurin, minister of Kilfinnan, and by the virtue and prudent œconomy of Mrs. Maclaurin. After some stay in Argyleshire, where her sisters and she had a small patrimonial estate, she removed to Dumbarton, for the more convenient education of her children: but dying in 1707, the care of them devolved entirely to their uncle.”

“Had the celebrated Author lived to publish his own Work, his Name would, alone, have been sufficient to recommend it to the Notice of the Publick: But that Task having, by his lamented premature Death, devolved to the Gentlemen whom he left entrusted with his Papers, the Reader may reasonably expect some Account of the Materials of which it consists, and of the Care that has been taken in collecting and disposing them, so as best to answer the Author's Intension, and fill up the Plan he had designed.”

“1. To give the general Principles and Rules of the Science, in the shortest, and at the same time, the most clear and cemprehensive Manner that was possible. Agreeable to this, though every Rule is properly exemplified, yet he does not launch out into what we may call, a Tautology of Examples. He rejects some Applications of Algebra, that are commonly to be met with in other Writers; because the Number of such Applications is endless: And, however usefull they may be in Practice, they cannot, by the Rules of good Method, have place in an Elementary Treatise. He has likewise omitted the Algebraical Solution of particular Geometrical Problems, as requiring the Knowledge of the Elements of Geometry; from which those of Algebra ought to be kept, as they really are, entirely distinct; reserving to himself to treat of the mutual Relation of the two Sciences in his Third Part, and, more generally still, in the Appendix. He might think too, that such an Application was the less necessary, that Sir Isaac Newton's excellent Collection of Examples is in every body's Hands, and that there are few Mathematical Writers, who do not furnish numbers of the same kind.”

“2. Sir Isaac Newton's Rules, in his Arithmetica Universalis, concerning the Resolution of the higher Equations, and the Affectations of their Roots, being, for the most part, delivered without any Demonstration, Mr. MacLaurin had designed, that his Treatise should serve as a Commentary on that Work. For we here find all those difficult Passages in Sir Isaac's Book, which have so long perplexed the Students of Algebra, clearly explained and demonstrated. How much such a Commentary was wanted, we may learn from the Words of the late eminent Author.The ablest Mathematicians of the last Age (says he) did not disdain to write Notes on the Geometry of Des Cartes; and surely Sir Isaac Newton's Arithmetic no less deserves that Honour. To excite some one of the many skilful Hands that our Times afford to undertake this Work, and to shew the Necessity of it, I give this Specimen, in an Explication of two Passages of the Arithmetica Universalis; which, however, are not the most difficult in that Book.What this learned Professor so earnestly wished for, we at last see executed; not separately nor in the loose disagreeable Form which such Commentaries generally take, but in a Manner equally natural and convenient; every Demonstration being aptly inserted into the Body of the Work, as a necessary and inseparable Member; an Advantage which, with some others, obvious enough to an attentive Reader, will, 'tis hoped, distinguish this Performance from every other, of the Kind, that has hitherto appeared.”

“3. After having fully explained the Nature of Equations, and the Methods of finding their Roots, either in finite Expressions, when it can be done, or in infinite converging Series; it remained only to consider the Relation of Equations involving two variable Quantities, and of Geometrical Lines to each other; the Doctrine of the Loci; and the Construction of Equations. These make the Subject of the Third Part.”

“Upon this Plan Mr. Mac-Laurin composed a System of Algebra, soon after his being chosen Professor of Mathematics in the University of Edinburgh; which he, thenceforth, made use of in his ordinary Course of Lectures, and was occasionally improving to the Perfection he intended it should have, before he committed it to the Press.”

“And the best Copies of his Manuscript having been transmitted to the Publisher, it was easy, by comparing them, to establish a correct and genuine Text. There were, besides, several detached Papers, some of which were quite finished, and wanted only to be inserted in their proper Places. In a few others, the Demonstrations were so concisely expressed, and couched in Algebraical Characters, that it was necessary to write them out at more Length, to make them of a piece with the rest. And this is the only Liberty the Publisher has allowed himself to take; excepting a few inconsiderable Additions, that seemed necessary to render the Book more compleat within itself, and to save the Trouble of consulting others who have written on the same Subject.”

“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 17Q9; where he continued five years, and applied to his studies in a very intense manner, and particulariy to the mathematics.”

“His great genius for mathematical learning discovered itself... 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... assistance: and... 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... 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... Maclaurin visited London... where he became acquainted with Dr. Hoadley... Bishop of Bangor, Dr. Clarke, Sir Isaac Newton, and other eminent men; at which time... he was admitted... [to] the Royal Society...”

“In 172S, Lord Polwarth... engaged Maclaurin to go as a tutor and companion to his eldest son... on his travels. After... Paris, and... other towns in France, they fixed in Lorrain; where he wrote his piece, On the Percussion of Bodies, which gained... the prize of the Royal Academy of Sciences... 1724. But his pupil dying soon after at Montpelier, he returned... to his profession at Aberdeen.”

“He was hardly settled... when he received an invitation to Edinburgh... University... 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... and... from the want of an additional fund... which, however, at length were all surmmounted, principally by the means of Sir Isaac Newton.”

“[M]athematical classes soon became very numerous... generally upwards of 100 students attending his Lectures... who being of different standings and proficiency, he was obliged to divide them into four or five classes...”

“In the first class he taught the first 6 books of Euclid's Elements, Plane Trigonometry, Practical Geometry, the Elements of Fortification, and an Introduction to Algebra. The second class studied Algebra, with the 11th and 12th books of Euclid, Spherical Trigonometry, Conic Sections, and the General Principles of Astronomy. The third... in Astronomy and Perspective... a part of Newton's Principia, and... experiments... illustrating them: he afterwards... 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... which he took occasion, from... disputes... concerning the grounds of the fluxionary method, to explode the method... and... charge mathematicians... with infidelity in religion.”

“Maclaurin thought himself included in this charge, and began an answer to Berkley's book: but [so many] other answers... discoveries... 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 vol. 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... yet...”

“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... were... published in the Philosophical Transactions; as the following: 1. On the Construction and Measure of Curves, vol. 30.---2. A New Method of describing all Kinds of Curves, vol. 30.---3. On Equations with impossible Roots, vol. 34.---4. On the Roots of Equations, &c. vol. 34.---5. On the Description of Curve Lines^ vol. 39.---6. Continuation of the same, vol. 39.---7. Observations on a Solar Eclipse, vol. 40.---8. A Rule for finding the Meridional Parts of a Spheroid with the same Exactness as in a Sphere, vol. 41.---9. An Account of the Treatise of Fluxions, vol. 42.---10. On the Bases of the Cells where the Bees deposit their Honey, vol. 42.”

“[H]e was always ready to lend his assistance in contriving and promoting any scheme which might contribute to the public service.”

“When the Earl of Morton went... 1789, to... his estates in Orkney and Shetland, he requested... Maclaurin to assist him in settling the geography... very erroneous in all our maps; to examine their natural history, to survey the coasts, and to take the measure of a degree of the meridian. ...[F]amily affairs would not permit him to comply... [so] he drew up a memorial of what he thought necessary to be observed, and furnished proper instruments... recommending Mr. Short, the noted optician, as... operator...”

“Mr. Maclaurin had... another scheme for the improvement of geography and navigation... 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... he would undertake the voyage even at his own charge.”

“But when schemes... were laid before the Parliament in 1744, and... before he could finish the memorials he proposed to send, the premium was limited to the... 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... 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... however, being exposed to cold and hardships, and... of a weak and tender constitution... much more enfeebled by close application to study, he laid the foundation of an ilness which put an end to his life in June 1746, at 48 years of age, leaving his widow with two sons and three daughters.”

“Mr. Maclaorin was a very good as well as a very great man, and worthy of love as well as admiration.”

“His... merit as a philosopher was, that all his studies were accommodated to general utility; and we find, in many places of his works, an application even of the most absruse theories to the perfecting of mechanical arts. For the same purpose, he had resolved to compose a course of Practical Mathematics, and to rescue several useful branches of the science from the ill treatment... often met with in less skilful hands. These intentions... were prevented fay his death; unless we... reckon, as a part of his intended work, the translation of... David Gregory's Practical Geometry, which he revised, and published with additions, in 1745.”

“In his life-time..., 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... 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.”

“In 1740, he... shared the prize of the... [Royal] Academy with ... D. Bernoulli and Euler, for resolving the problem relating to the motion of the tides from the theory of gravity... He bad only ten days to draw up this paper in, and could not... transcribe a fair copy; so ... the Paris edition... is incorrect. He afterwards revised the whole, and inserted it in his Treatise of Fluxions.”

“Since his death... two... volumes have appeared; his Algebra, and his Account of Sir Isaac Newton's Philosophical Discoveries.”

“The Algebra, though not finished by himself, is... excellent in its kind; containing, in no large volume, a complete elementary treatise of that science, as far as it has hitherto beea 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 y it now appears.”

“His main design seems to have been to explain only those parts off 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 foimded, 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.”