Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/58

From Wikisource
Jump to navigation Jump to search
This page has been validated.
48
The Analyst.

pression of the Increment of the Abſciſs nor of any Power thereof, another which includes the Expreſſion of the Increment it ſelf, and a third including the Expreſſion of the Powers of the Increment. The geometrical Quantity alſo or whole increaſed Area conſiſts of three Parts or Members, the firſt of which is the given Area, the ſecond a Rectangle under the Ordinate and the Increment of the Abſciſs, and the third a curvilinear Space, And, comparing the homologous or correſpondent Members on both Sides, we find that as the firſt Member of the Expreſſion is the Expreſſion of the given Area, ſo the ſecond Member of the Expreſſion will expreſs the Rectangle or ſecond Member of the geometrical Quantity; and the third, containing the Powers of the Increment, will expreſs the curvilinear Space, or third Member of the geometrical Quantity. This hint may, perhaps, be further extended and applied to good purpoſe, by thoſe who have leiſure and curioſity for ſuch Matters. The uſe I make of it is to ſhew, that the Analyſis cannot obtain in Augments or Differences,

but