Theoretical and Practical Graphics (Classic Reprint)
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| Stand: | 2015-08-04 03:50:33 |
Produktbeschreibung
Excerpt from Theoretical and Practical Graphics 5. Having indicated what projections are and how obtained, it will he well, before giving their grand divisions and sub-divisions, to state the nature and extent of the field in which they may be employed. The mathematical properties of geometrical figures, as also the propositions and problems involving them, are divided into two classes, metrical and descriptive. In the first class the idea of quantity necessarily enters, either directly - as in measurement, or indirectly - as in ratio. In the second or descriptive class, however, we find involved only those properties dependent upon relative position. 6. Descriptive Geometry is that branch of mathematics in which figures are represented and their descriptive properties investigated and demonstrated by means of projection. Divisions Of Projections. 7. All projections may be divided into two general classes. Central and Parallel. If the centre of projection be at a finite distance, as in Figs. 2 and 3, the projection obtained is called a central projection; but if we suppose it to be at infinity, as in Fig. 4, projectors from it will then evidently be parallel, and the resulting figure is called a parallel projection of the original figure. Parallel projection is thus seen to be merely a special case of central projection, yet each has been independently developed to a high degree and has an extensive literature. 8. The terms Conical and Cylindrical are employed by many writers synonymously with central and parallel respectively. Central projections are also occasionally called Radial or Polar. Remark.-A straight line is said to generate a conical surface (see Fig. 5) when it constantly passes through a fixed point (the vertex), and is guided in its motion by a given fixed curve (the directrix). The moving straight line is a generatrix of the surface, and its various positions are called elements of the surface. If the vertex of a conical surface be removed to infinity the elements will become parallel and we shall have a cylindrical, surface, which may be also defined as the surface (see Fig. 6) generated by a straight line that is guided in its motion by a given fixed curve, and is, in any position, parallel to a given fixed straight line. The origin of the terms conical and cylindrical as applied to projection is obvious. We have now to mention the more important sub-divisions of projections, with the sciences based upon them. The names depend in certain cases upon the nature of the centre of projection while in others they are due to some particular application. Under Central (or Conical) projection we have:- 9. Projective Geometry (Geometry of Position). While in its most general sense this science includes all central projections (and therefore those of Articles. 10-13) yet in its ordinary acceptation it may be defined as that branch of mathematics in which - with the centre of projection considered as a mathematical point at a finite distance from the line or plane of projection the descriptive properties of geometrical figures are investigated and established. 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 th
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