and conſequently the Curve Cc, is coincident with the Tangent CH. In which caſe the mixtilinear evaneſcent Triangle CEc will, in its laſt form, be ſimilar to the Triangle CET: And its evaneſcent Sides CE, Ec, and Cc will be porportional 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 laſt Ratio of their evaneſcent Increments, are proportional to the Sides of the Triangle CET, or, which is all one, of the Triangle VBC ſimilar thereunto. [1] It is particularly remarked and inſiſted on by the great Author, that the Points C and c muſt not be diſtant one from another, by any the leaſt Interval whatſoever: 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) expreſſed by the finite Sides of the Triangle VBC, the Points C and c muſt be accurately coincident, i. e. one and the ſame. A Point therefore is conſidered as a Triangle, or a Triangle is ſuppoſed to be formed in a Point. Which
- ↑ Introduct. ad Quad. Curv.
