Both these methods, differing from that now employed, are interesting as preliminary steps towards the method of fluxions and the differential calculus.
His Treatise on Fluxions was published at Edinburgh in 1742, in two volumes.
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.
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.
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.
In his Discourse on the "Residual Analysis," he proposes to avoid the metaphysical difficulties of the method of fluxions by a purely algebraical method.
Xxiv., from which it was copied and reprinted in the Ada Eruditorum (1707), and also in the Memoirs of the Academy of Sciences at Paris; General Laws of Nature and Motion (1705), a work which is commended by Wolfius as illustrating and rendering easy the writings of Galileo and Huygens, and the Principia of Newton; An Institution of Fluxions, containing the First Principles, Operations, and Applications of that admirable Method, as invented by Sir Isaac Newton (1706).
Of less interest nowadays are Robins's more purely mathematical writings, such as his Discourse concerning the Nature and Certainty of Sir Isaac Newton's Methods of Fluxions and of Prime and Ultimate Ratios (1735), "A Demonstration of the Eleventh Proposition of Sir Isaac Newton's Treatise of Quadratures" (Phil.
It is supposed that it was in 1665 that the method of fluxions first occurred to Newton's mind.
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.
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.
Raphson, History of Fluxions, showing in a compendious manner the First Rise of and Various Improvements made in that Incomparable Method (1715); W.