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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1906 edition. Excerpt: ...by making the perpendicular b"b" equal to c'b'; hence a"b" is the distance required. (4) Bring the plane (Fig. 177), vertically projecting the line which joins the two points, parallel to V by rabattement around any vertical, preferably that passing through (a', a"). This point remains fixed, and the point (b', b") assumes the position (b/,,") by making the perpendicular b'b/ equal to c'rb"; hence a'b/ is the distance required. 189. PROBLEM.--Upon a given line to measure a given distance from either extremity. Let (a', a") be the extremity from which the measurement is to be made (Figs. 178, 179), and (b', b") any other point of the given line. Fig. 178,5' Fig. Itq Bring the line by any of the preceding four methods parallel to either coordinate plane, and measure upon the projection so determined the required length. By a Counter-rotation restore the dividing point (cx cx") to the primitive projections; (a'c', a"c") is the distance sought. II. DISTANCE OF POINT FROM LINE. 190. Problem.--To determine the perpendicular between a point and a line given by their projections., The point and line fixing the position of a plane, their distance from each other may be found by the rabattement of that plane. (1) Let (a a") be the given point, and (b'c', b"c") the given line (Fig. 180) Bring the plane of these two by rabattement around a horizontal, preferably that which passes through the point (a', a"). During rotation this point remains fixed, and the line be assumes the position (b/'c," b/c) (Art. 183); hence, letting fall a perpendicular (a"ox") upon b"c," a"o" is the horizontal projection of the perpendicular sought....
This book seeks to explore the history of descriptive geometry in relation to its circulation in the 19th century, which had been favoured by the transfers of the model of the École Polytechnique to other countries. The book also covers the diffusion of its teaching from higher instruction to technical and secondary teaching. In relation to that, there is analysis of the role of the institution – similar but definitely not identical in the different countries – in the field under consideration. The book contains chapters focused on different countries, areas, and institutions, written by specialists of the history of the field. Insights on descriptive geometry are provided in the context of the mathematical aspect, the aspect of teaching in particular to non-mathematicians, and the institutions themselves.
Excerpt from An Elementary Course in Descriptive Geoemetry 1. In a limited sense, Descriptive Geometry may be defined to be a conventional method of representing on a plane objects which have three dimensions, so as to admit of an accurate determination of their size, form and position. 2. But position being relative, objects arc in respect of this undeterminable unless referred to other objects, which, for constructive purposes. ought to be of the simplest character and in positions readily conceived and comprehended. In Descriptive Geometry these latter objects arc two or more planes, termed the planes of projection. 3. These two planes intersect at right angles (Fig. t). one being in the position of an ordinary wall and the other in the position of the floor. The upright plane, V. is the vertical plane of projection, and the other plane H. at right angles to it. the horizontal plane of projection. The line GL in which they intersect is termed the ground-line. 4. The planes thus arranged are divided by their line of intersection, GL. into two parts each, and, in turn, divide space into four equal dihedral angles. 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.
Small Hospitals: Establishment and Maintenance by William Atkinson Alfred Worcester, first published in 1894, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it.