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PREFACE .

Isaac Newton defines Fluxions to be the Velocitiesof Motions , yet Fie hath Recourse to the Incre-ments, or Moments, generated in equal Particlesof Time, in order to determine those Velocities;which he afterwards teaches us to expound byfinite Magnitudes of other Kinds: Withoutwhich (as is already hinted above) we could havebut very obscure Ideas of the higher Orders ofFluxions: For if Motion in (or at) a Point beso difficult to conceive, that, Some have, even,gone so far as to dispute the very Existence ofMotion, how much more perplexing must it beto form a Conception, not only, of the Velocityof a Motion, but also in infinite Changes and Af-fections of It, in one and the fame Point, whereall the Orders of Fluxions are to be considered ?

Seeing the Notion of a Fluxion, accordingto our Manner of defining It, supposes an uni-form Motion, it may, perhaps, seem a Matterof Difficulty, at first View, how the Fluxionsof Quantities, generated by Means of acceleratedand retarded Motions, can be rightly assigned ;since not any, the least, Time can be taken duringwhich the generating Celerity continues the same :Here, indeed, we cannot express the Fluxion byany Increment or Space, actually, generated in agiven Time (as in uniform Motions.) But,then, we can easily determine, what the contem-porary Increment, or generated Space would be ,if the Acceleration, or Retardation, was to cease

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