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Trigonometry (from "trigwnon", triangle, and "metrew") is the science of the numerical relations between the sides and angles of triangles.This Treatise is intended to demonstrate, to those who have learned the principal propositions in the first six books of Euclid, so much of Trigonometry as was originally implied in the term, that is, how from given values of some of the sides and angles of a triangle to calculate, in the most convenient way, all the others. A few propositions supplementary to Euclid are premised as introductory to the propositions of Trigonometry as usually understood.This want I have attempted to supply by applying, in the first Chapter, Newton's Method of Limits to the mensuration of circular arcs and areas; choosing that method both because it is the strictest and the easiest, and because I think the Mathematical Student should be early introduced to the method.