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. 1865 Excerpt: ...numbers. They argue that since E or V(e) has two values which we may call + n and-n, we have therefore + n =, --71 = E, and, from the ordinary definition of logarithms, must be the logarithm both of 4 n and-n. So, indeed, it is, but only when referred to different systems: for, as I maintain, + n and--n are not both ...
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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. 1865 Excerpt: ...numbers. They argue that since E or V(e) has two values which we may call + n and-n, we have therefore + n =, --71 = E, and, from the ordinary definition of logarithms, must be the logarithm both of 4 n and-n. So, indeed, it is, but only when referred to different systems: for, as I maintain, + n and--n are not both values of eJ, but one is the value of (+'e) and the other of (+s), so that is the logarithm of +n in the system whose base is +as, and of--n in the system whose base is +-. The same reasoning may be generally extended to such cases as (+a) which admits of n values, and consequently of n quantities, which have a common logarithm-, but in each case referred to a different base. When n is even, one value will be positive and the other negative, all the others being impossible; and the positive and negative values are the only two of which M. Vincent takes notice when discussing the question. It might, perhaps, have weakened his belief in the correctness of the results, if he had come to the conclusion, as he ought to have done, that the same logarithm corresponded to positive, negative, and impossible quantities. These last he seems quite to have overlooked, which may have arisen from his having adopted, with many other mathematicians, the name of imaginary quantities. I adhere to the name impossible instead of imaginary, because the latter involves an idea which I conceive to be very deleterious in analysis. We may be unable to perform an operation though it be by no means an imaginary one; and indeed all that we can say of those quantities which have this name affixed to them is, that they are uninterpretable in arithmetic. For this reason, if I were permitted to propose a change, I should prefer to call these quantities o...
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Add this copy of The Mathematical Writings of Duncan Farquharson Gregory to cart. $38.52, new condition, Sold by Revaluation Books rated 4.0 out of 5 stars, ships from Exeter, DEVON, UNITED KINGDOM, published 2005 by Scholarly Publishing Office, University of Michigan Library.
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2005, Scholarly Publishing Office, University of Michigan Library
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Add this copy of The Mathematical Writings of Duncan Farquharson Gregory to cart. $58.43, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2007 by Kessinger Publishing.
Add this copy of The Mathematical Writings of Duncan Farquharson Gregory to cart. $93.44, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2010 by Kessinger Publishing.
