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Excerpt from A Treatise on Geometrical Optics In this treatise one of my aims has been to introduce a new method of determining the properties of a symmetrical optical instrument, in which the angle of divergence of a small pencil, rather than any coordinate of its origin, has been adopted as the leading feature. By this method, which is implicitly contained in Cotes's well-known theorem of the apparent distance, all the cardinal properties, notably the power of the system, follow immediately from the application of a simple geometrical formula. Although that theorem dates from the middle of the eighteenth century, yet the present method needs the help of Helmholtz's theorem to render it complete; hence the priority of the proof of the existence of the cardinal points rests with Gauss. But the analytical method adopted by the latter tends, in my opinion, to disguise the essential fact that geometrical foci exist only as a first approximation; and in any particular case a lengthy calculation is necessary to obtain the final convergent of the continued fraction on which his results depend. The simplification that results from the use of the angle of divergence will, I think, be clear on reference to Chapter V. and to the chapter on Aberration. I have attempted to obviate as far as possible the difficulties of sign that arise in connection with the directions in which distances are to be measured by the convention that all lengths on the same straight line are to be treated as algebraical quantities, and, where an origin of light is the origin of measurement, by taking the direction in which the light travels as positive. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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