Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/60

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The Analyst.

introduced? Is it not to ſhun or rather to palliate the Uſe of Quantities infinitely ſmall? But we have no Notion whereby to conceive and meaſure various Degrees of Velocity, beſide Space and Time, or when the Times are given, beſide Space alone. We have even no Notion of Velocity preſcinded from Time and Space. When therefore a Point is ſuppoſed to move in given Times, we have no Notion of greater or leſſer Velocities or of Proportions between Velocities, but only of longer or ſhorter Lines, and of Proportions between ſuch Lines generated in equal Parts of Time.


XXXI. A Point may be the limit of a Line: A Line may be the limit of a Surface: A Moment may terminate Time. But how can we conceive a Velocity by the help of ſuch Limits? It neceſſarily implies both Time and Space, and cannot be conceived without them. And if the Velocities of naſcent and evaneſcent Quantities, i. e. abſtracted from Time and Space, may not be comprehended, how can we comprehend and demonſtrate their

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