Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/66

56 and conequently the Curve Cc, is coincident with the Tangent CH. In which cae the mixtilinear evanecent Triangle CEc will, in its lat form, be imilar to the Triangle CET: And its evanecent Sides CE, Ec, and Cc will be porportionalproportional [sic] to CE, ET, and CT the Sides of the Triangle CET. And therefore it is concluded, that the Fluxions of the Lines AB, BC, and AC, being in the lat Ratio of their evanecent Increments, are proportional to the Sides of the Triangle CET, or, which is all one, of the Triangle VBC imilar thereunto. It is particularly remarked and inited on by the great Author, that the Points C and c mut not be ditant one from another, by any the leat Interval whatoever: But that, in order to find the ultimate Proportions of the Lines CE, Ec, and Cc (i. e. the Proportions of the Fluxions or Velocities) expreed by the finite Sides of the Triangle VBC, the Points C and c mut be accurately coincident, i. e. one and the ame. A Point therefore is conidered as a Triangle, or a Triangle is uppoed to be formed in a Point. Which to