Plane Trigonometry, Vol. 1: With the Use of Logarithms (Classic Reprint) - Softcover

Colenso, J. W.

Softcover

ISBN 10: 1330385772 ISBN 13: 9781330385777

Verlag: Forgotten Books, 2018

Inhaltsangabe

Excerpt from Plane Trigonometry, Vol. 1: With the Use of Logarithms

But the word is now used in a much more extended sense, so as to include all manner of algebraical reason ing about lines and angles, whether parts of a triangle or not, and, particularly, when that reasoning is carried on by means of certain quantities, which are called the trigonometrical Ratios or Functions of an angle.

Of these Ratios we shall speak presently, so far as the subject of plane trigonometry is concerned. But we must first make some remarks upon the mode in which lines and angles are represented for the purposes of algebraical reasoning.

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.

Über diesen Titel

Reseña del editor

Excerpt from Plane Trigonometry, Vol. 1: With the Use of Logarithms

3. Here, however, we have 'unconsciously introduced the idea of a line having a positive or negative value. Fora, we know, means + a; and, if in our reasonings wc should happen to arrive at some negative result as the value of a line, (if, for instance, it came out, at the end of a problem, that the value of a certain line was -b), "What would this (-) sign mean ?

"We shall show that it indicates contrariety of direction to some line which we have before represented by a positive algebraical symbol.

For let AB be a line, containing a units, which we y A c express algebraically by a or+a. Then, if from the end B we measure off in the direction BA a line BC containing b units, the length of the line A C will be a - b units, and, therefore, its algebraical expression will be a-b. Now, if b be less than a, this expression for A C will be positive, and C will also lie to the right of A, that is, AC will be measured in the same direction as AB. But, if b be greater than a, then C will fall to the left of A as at Cy and A C will be measured in the contrary direction to AB, its value in units being b-a ; while, at the same time, the expression a-b will become negative, and may be written - (b - a).

"We infer, then, that, when the algebraical expression for a line is negative, the (-) sign indicates contrariety of direction to a line which has been already assumed to be positive; and, conversely, that if a line drawn in any one direction from a given point, when represented algebraically, be assumed to be positive, then a line drawn from the same point in the opposite direction must be considered negative.

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.

Details zur Ausgabe

• Verlag: Forgotten Books
• Erscheinungsdatum: 2018
• Sprache: Englisch
• ISBN 10: 1330385772
• ISBN 13: 9781330385777
• Einband: Tapa blanda
• Anzahl der Seiten: 160
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar