Download The Elements of Algerbra and Trigonometry

Download The Elements of Algerbra and Trigonometry

The Elements of Algerbra and Trigonometry.cWilliam N Griffin

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Author: William N Griffin
Page Count: 54 pages
Published Date: 01 Mar 2012
Publisher: Rarebooksclub.com
Publication Country: Miami Fl, United States
Language: Englishhttps://d4rri9bdfuube.cloudfront.net/assets/images/book/large/9781/2865/9781286504741.jpg
ISBN: 9781130007602
File size: 45 Mb
File Name: The.Elements.of.Algerbra.and.Trigonometry.pdf
Download Link: The Elements of Algerbra and Trigonometry
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1885 Excerpt: ...requires for its demonstration higher algebra than this book introduces, that not only has every number a logarithm, but it has an infinite variety of logarithms, constructed, as the term is, on different scales or bases. The base of any system of logarithms is denned by the fact that in that system unity is its logarithm. The base in ordinary use is 10, and hence with this base log 10 = 1. Logarithms to this base are the only ones which will now be considered in their practical use. 3. Whatever the base be, the logarithm of unity is zero. For since, by Art. 1, log a + log b = log ab, let b = 1 and.. ab = a, .. log a + log 1 = oga, .. log 1 = o. 4. Confining ourselves, as has been just premised, to 1o as the base, we have by Art. 1 log 10o = log 1o2 = 2 log 1o = 2, log 10oo = log 103 = 3 log 1o = 3, log 10ooo = 4 log 10 = 4, and generally, if n be any positive integer, log 1o" = n. Again, log = log 1-log 10 =-log 10 log Tis = log x log I0 =-2. and generally, if n be any positive integer, log--=---. 5 10n 5. The same number cannot have two different logarithms to the same base 10. For if it were possible that a had two different logarithms to the base 10, m and n suppose, then log 10- = log 10+log a = 1+n1, also--1+n., '. m and n cannot be different. 6. The same logarithm to the base 1o cannot belong to different numbers. For if it were possible that m were the logarithm of different numbers a and b, log = log a--log b = m--m = o..'. i must be 1, b or a and b are not different. Characteristics of Logarithms. 7. It will be observed on inspection of the tables of logarithms to the base 1o that the logarithms of numbers are larger as the numbers are larger. Since log I is zero and log 10 is 1, the logarithms of all numbers between 1 and 10 are decim...

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