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Maclaurin used Taylor series to characterize maxima, minima, and points of inflection for infinitely differentiable functions in his Treatise of Fluxions. Maclaurin attributed the series to Brook Taylor , though the series was known before to Newton and Gregory , and in special cases to Madhava of Sangamagrama in fourteenth century India. [ 6 ]
Colin Maclaurin's two-volume Treatise of Fluxions published in 1742 also began as a response to Berkeley attacks, intended to show that Newton's calculus was rigorous by reducing it to the methods of Greek geometry. [10]
1736 - Newton's Method of Fluxions posthumously published, 1737 - Thomas Simpson publishes Treatise of Fluxions, 1739 - Leonhard Euler solves the general homogeneous linear ordinary differential equation with constant coefficients, 1742 - Modern definion of logarithm by William Gardiner, 1742 - Colin Maclaurin publishes Treatise on Fluxions,
Maclaurin series , Taylor series ... use of infinitesimals; Gottfried Leibniz; Isaac Newton; Method of Fluxions; Infinitesimal calculus; Brook Taylor; Colin Maclaurin ...
If the fluent is defined as = (where is time) the fluxion (derivative) at = is: ˙ = = (+) (+) = + + + = + Here is an infinitely small amount of time. [6] So, the term is second order infinite small term and according to Newton, we can now ignore because of its second order infinite smallness comparing to first order infinite smallness of . [7]
Colin Maclaurin publishes his Treatise on Fluxions in Great Britain, the first systematic exposition of Newton's methods. Metrology. Anders Celsius publishes his ...
Colin Maclaurin and John Bernoulli, 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 1742, Colin Maclaurin published his treatise on fluxions, in which he showed that the spheroid was an exact solution. If we designate the equatorial radius by r e , {\displaystyle r_{e},} the polar radius by r p , {\displaystyle r_{p},} and the eccentricity by ϵ , {\displaystyle \epsilon ,} with