On Classical Literature Author:Francis William Newman Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: state of this science. These improvements are chiefly due to the two great geometers, Poncelet and Chasles ; both of whom have investigated, by elementary geomet... more »ry, properties of the conic sections and surfaces of the second degree, which can scarcely be accomplished by the aid of the modern analysis in its present state. This has been achieved chiefly by the principle of projections, which is almost equivalent to the method of coordinates. We have lately been informed that the latter has found, by elementary geometry, the attraction of an ellipsoid upon an external point. The resultants of this attraction in the directions of the principal axes contained a radical, which rendered their direct integration impossible by all the known methods. This difficulty was eluded by means of the celebrated theorem of Ivory: but the problem continued for a long time to defy the powers of the integral calculus even in the hands of Laplace and Legendre : and the artifice by which Poisson caused this radical to disappear, has, with considerable justice, been considered as one of the most happy ideas presented to us by the history of analysis. The investigation of these integrals, by elementary geometry, is certainly not the least of the wonders which have been worked by these late discoverers. The next part of the first year's course is elementary Algebra. This course, (in addition to the common rules of algebra and the doctrine of algebraical fractions and surds) comprehends binomial equations, the theory of symmetrical functions of the roots of equations, and the investigations of the principal properties of equations of the first four degrees; with the general solutions of these equations, as far as they can be accomplished in the present state of the science. The theory of-reciprocal equat...« less