Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/31

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The Analyst.
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that this reaſoning is not fair or concluſive. For when it is ſaid, let the Increments vaniſh, i. e. let the Increments be nothing, or let there be no Increments, the former Suppoſition that the Increments were ſomething, or that there were Increments, is deſtroyed, and yet a Conſequence of that Suppoſition, i. e. an Expreſſion got by virtue thereof, is retained. Which, by the foregoing Lemma, is a falſe way of reaſoning. Certainly when we ſuppoſe the Increments to vaniſh, we muſt ſuppoſe their Proportions, their Expreſſions, and every thing elſe derived from the Suppoſition of their Exiſtence to vaniſh with them.


XIV. To make this Point plainer, I ſhall unfold the reaſoning, and propoſe it in a fuller light to your View. It amounts therefore to this, or may in other Words be thus expreſſed. I ſuppoſe that the Quantity x flows, and by flowing is increaſed, and its Increment I call o, ſo that by flowing it becomes x + o. And as x increaſeth, it follows that every Power of x is likewiſe increaſed in a due Pro-

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portion.