Fluxions sentence example
Both these methods, differing from that now employed, are interesting as preliminary steps towards the method of fluxions and the differential calculus.
In the preface he states that the work was undertaken in consequence of the attack on the method of fluxions made by George Berkeley in 1734.
He also gave in his Fluxions, for the first time, the correct theory for distinguishing between maxima and minima in general, and pointed out the importance of the distinction in the theory of the multiple points of curves.
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.
In this way the principle of continuity, which is the basis of the method of Fluxions and the whole of modern mathematics, may be applied to the analysis of problems connected with material bodies by assuming them, for the purpose of this analysis, to be homogeneous.Advertisement
In his Discourse on the "Residual Analysis," he proposes to avoid the metaphysical difficulties of the method of fluxions by a purely algebraical method.
Napier's original work, the Descriptio Canonis of 1614, contained, not logarithms of numbers, but logarithms of sines, and the relations between the sines and the logarithms were explained by the motions of points in lines, in a manner not unlike that afterwards employed by Newton in the method of fluxions.
There are several papers still existing in Newton's handwriting bearing dates 1665 and 1666 in which the method is described, in some of which dotted or dashed letters are used to represent fluxions, and in some of which the method is explained without the use of dotted letters.
It is known that he purchased prisms and lenses on two or three several occasions, and also chemicals and a furnace, apparently for chemical experiments; but he also employed part of his time on the theory of fluxions and other branches of pure mathematics.
Up to the time of the publication of the Principia in 1687 the method of fluxions which had been invented by Newton, and had been of great assistance to him in his mathematical investigations, was still, except to Newton and his friends, a secret.Advertisement
Newton's admirers in Holland had informed Dr Wallis that Newton's method of fluxions passed there under the name of Leibnitz's Calculus Di fferentialis.
It was therefore thought necessary that an early opportunity should be taken of asserting Newton's claim to be the inventor of the method of fluxions, and this was the reason for this method first appearing in Wallis's works.
The first contains an explanation of the doctrine of fluxions, and of its application to the quadrature of curves; the second, a classification of seventy-two curves of the third order, with an account of their properties.
Newton's desire to have no hand in writing the preface seems. to have proceeded from a knowledge that Cotes was proposing to allude to the dispute about the invention of fluxions.
The second includes a "Method for the Quadrature of Parabolas," and a treatise "on Maxima and Minima, on Tangents, and on Centres of Gravity," containing the same solutions of a variety of problems as were afterwards incorporated into the more extensive method of fluxions by Newton and Leibnitz.Advertisement
He used these fluxions like the scaffold of a building, as things to be laid aside or got rid of.
Newton ' s fluxions produced wonderful mathematical results but many were wary of his use of infinitely small increments.
During the seventeenth century it was becoming clear that fluxions and quadrature were intimately related in fact, that they are inverse processes.
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.
His Treatise on Fluxions was published at Edinburgh in 1742, in two volumes.Advertisement
It is supposed that it was in 1665 that the method of fluxions first occurred to Newton's mind.