# Maclaurin sentence example

maclaurin

- In it Maclaurin developed several theorems due to Newton, and introduced the method of generating conics which bears his name, and showed that many curves of the third and fourth degrees can be described by the intersection of two movable angles.
- After the death of Newton, in 1728, his nephew, John Conduitt, applied to Maclaurin for his assistance in publishing an.
- This Maclaurin gladly undertook, but the death of Conduitt put a stop to the project.
- Maclaurin was the first to introduce into mechanics, in this discussion, the important conception of surfaces of level; namely, surfaces at each of whose points the total force acts in the normal direction.
- In 1745, when the rebels were marching on Edinburgh, Maclaurin took a most prominent part in preparing trenches and barricades for its defence.Advertisement
- As soon as the rebel army got possession of Edinburgh Maclaurin fled to England, to avoid making submission to the Pretender.
- Maclaurin was married in 1733 to Anne, daughter of Walter Stewart, solicitorgeneral for Scotland.
- After Maclaurin's death his account of Newton's philosophical discoveries was published by Patrick Murdoch, and also his algebra in 1748.
- Of the more immediate successors of Newton in Great Britain Maclaurin is probably the only one who can be placed in competition with the great mathematicians of the continent of Europe at the time.
- C. Maclaurin, Legendre and d'Alembert had furnished partial solutions of the problem, confining their 1 Annales de chimie et de physique (1816), torn.Advertisement
- Legendre, in 1783, extended Maclaurin's theorem concerning ellipsoids of revolution to the case of any spheroid of revolution where the attracted point, instead of being limited to the axis or equator, occupied any position in space; and Laplace, in his treatise Theorie du mouvement et de la figure elliptique des planetes (published in 1784), effected a still further generalization by proving, what had been suspected by Legendre, that the theorem was equally true for any confocal ellipsoids.
- Colin Maclaurin (1698-1746) and John Bernoulli (1667-1748), who were of this opinion, resolved the problem by more direct methods, the one in his Fluxions, published in 1742, and the other in his Hydraulica nunc primum detecta, et demonstrata directe ex fundamentis pure mechanicis, which forms the fourth volume of his works.
- The method employed by Maclaurin has been thought not sufficiently rigorous; and that of John Bernoulli is, in the opinion of Lagrange, defective in clearness and precision.
- The first, for a memoir on the construction of a clepsydra for measuring time exactly at sea, he gained at the age of twenty-four; the second, for one on the physical cause of the inclination of the planetary orbits, he divided with his father; and the third, for a communication on the tides, he shared with Euler, Colin Maclaurin and another competitor.
- Legendre shows that Maclaurin's theorem with respect to confocal ellipsoids is true for any position of the external point when the ellipsoids are solids of revolution.Advertisement
- During forty years the resources of analysis, even in the hands of d'Alembert, Lagrange and Laplace, had not carried the theory of the attraction of ellipsoids beyond the point which the geometry of Maclaurin had reached.
- These curves were investigated by Rene Descartes, Sir Isaac Newton, Colin Maclaurin and others.
- Born at Edinburgh in 1710 and originally educated for the church, Short attracted the attention of Maclaurin, professor of mathematics at the university, who permitted him about 1732 to make use of his rooms in the college buildings for experiments in the construction of telescopes.
- The Academy of Sciences at Paris in 1738 adjudged the prize to his memoir on the nature and properties of fire, and in 1740 his treatise on the tides shared the prize with those of Colin Maclaurin and Daniel Bernoulli - a higher honour than if he had carried it away from inferior rivals.
- With the view of stimulating mathematicians to write annotations on this admirable work, the celebrated 's Gravesande published a tract, entitled Specimen Commentarii in Arithmeticam Universalem; and Maclaurin's Algebra seems to have been drawn up in consequence of this appeal.Advertisement
- Various properties of curves in general, and of cubic curves, are established in Colin Maclaurin's memoir, "De linearum geometricarum proprietatibus generalibus Tractatus " (posthumous, say 1746, published in the 6th edition of his Algebra).
- It may be noticed that the nine inflections of a cubic curve represented by an equation with real coefficients are three real, six imaginary; the three real inflections lie in a line, as was known to Newton and Maclaurin.
- Similar methods were devised by Sir Isaac Newton and Colin Maclaurin.
- In Newton's method, two angles of constant magnitude are caused to revolve about their vertices which are fixed in position, in such a manner that the intersection of two limbs moves along a fixed straight line; then the two remaining limbs envelop a conic. Maclaurin's method, published in his Geometria organica (1719), is based on the proposition that the locus of the vertex of a triangle, the sides of which pass through three fixed points, and the base angles move along two fixed lines, is a conic section.
- Both Newton's and Maclaurin's methods have been developed by Michel Chasles.Advertisement
- Maclaurin's object was to found the doctrine of fluxions on geometrical demonstration, and thus to answer all objections to its method as being founded on false reasoning and full of mystery.
- This work included the "Logometria," the trigonometrical theorem known as "Cotes' Theorem on the Circle" (see TRIGONOMETRY), his theorem on harmonic means, subsequently developed by Colin Maclaurin, and a discussion of the curves known as "Cotes' Spirals," which occur as the path of a particle described under the influence of a central force varying inversely as the cube of the distance.