First Lessons In Geometry Upon The Model Of Colburn S First Lessons In Arithmetic

First Lessons in Geometry

First Lessons in Geometry

Excerpt from First Lessons in Geometry: Upon the Model of Colburn's First Lessons in Arithmetic The following work is stated in the title to be upon the model of Colburn's First Lessons in Arithmetic, because no other method occurred to me of presenting a general view of its plan, which would be at once so brief and so well understood. Without aiming at minute resemblance, and certainly without challenging any comparison in merit, it is an imitation of that admirable work, which has intro duced so entire a revolution in the mode of teaching Arith metic in our country, in the following particulars. 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.

First Lessons in Geometry Upon the Model of Colburn's First Lessons in Arithmetic

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. 1859 edition. Excerpt: ... the several lines proceeding from pG will be represented as follows. 1st Dir. GB (as not departing from the standard) = 0. Dir.GE =e. Dir. GA (as the reverse of GB) = 0 +180 = 180. Dir. GH (as the reverse of GE) = e-L.180. 2d Dir. GB (after an entire revolution) = 360. As CD has the same direction with AB, and EF is a straight line, the directions of the lines proceeding from pH will be represented in like manner; thus, 1st Dir. HD = 0, Dir. HG = e, Dir. HC = 180, Dir. HF = eo _(_ isoo, 2d Dir. HD = 360. b.) As the magnitude of an angle depends simply upon the difference between the directions of its sides ( 9. a), the values of the several angles around G and H may now be obtained by subtraction. Thus, EGB (= Dir. GE--1st Dir. GB), or) 0 _ 0 _ 0 GHD (= Dir. HG--1st Dir. HD), e"' AGH (= Dir. GH-Dir. GA), or j, _ CHF (= Dir. HF--Dir. HC), ( 'ttm AGE (= Dir. GA--Dir. GE), or ) _ _ 0 GHC (= Dir. HC--Dir. HG), '. BGH (=2d Dir.GB--Dir. GH), or) =360--('+18(F) DHF (= 2d Dir. HD--Dir. HF), =180--e. It will be observed, that the four angles, EGB, GHD, AGH, and CHF, have the same value, viz. e; and also, that the four, AGE, GHC, BGH, and DHF, have the same value, viz. 180--e, or, in other words, the supplement of e ( 30. g). c.) Substitute fore a particular number, as 60, and the directions of the several lines will be thus represented: 1st Dir. GB or HD = 0, Dir. GE or HG = 60, Dir. GA or HC = 180, Dir. GH or HF = 60 + 180(c) = 240, 2d Dir. GB or HD = 360. The values of the angles will then be as follows: EGB, or GHD, = G0--0, = 60. i Class I. AGH, or CHF, = 240--180, = 60. ) Acute. AGE, or GHC, = 180--60, = 120. ) Class E. BGH, or DHF, = 360--240, = 120. 5 Obtuse. What will be the direction of each line, and the value.