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FOR THE USE OF schools.
BY JAMES ELLIOT,
AUTHOR OF “A COMPLETE TREATISE ON PRACTICAL GEOMETRY AND MENSURATION,"
AND ON PLANE TRIGONOMETRY,” ETC.
LOGARITHMS AND PLANE TRIGONOMETE
EDINBURGH: SUTHERLAND AND KNOX.
LONDON: SIMPKIN, MARSHALL & CO.
In the Press,
MATHEMATICS; Containing Demonstrations of the Rules and Solutions of the Exercises,
MURRAY AND GIBB, PRINTERS, EDINBURGH.
CONTENTS OF PART III.
DEFINITIONS AND EXPLANATIONS OF
If we take any series of numbers in arithmetical progression, commencing with 0, as 0, 1, 2, 3, &c., and another series in geometrical progression, commencing with 1, as 1, 2, 4, 8, &c.; and if we then place the two series together, thus0, 1, 2, 3, 4, 5,
6, &c. 1, 2, 4, 8, 16, 32, 64, &c. then the numbers in the arithmetical series are said to be the Logarithms of the corresponding numbers in the geometrical series—the latter being called the Natural Numbers. Thus, taking the two preceding series, the logarithm of 64 is 6; the logarithm of 32 is 5; while the natural number corresponding to the logarithm 6 is 64; and so on.
In the specimen just exhibited we have taken two ascending progressions; but they might, equally well, have been two descending progressions, or the one descending and the other ascending. Logarithms, however, as now* used in practice, are limited to the case of two progressions, either both ascending or both descending ;—the former giving the logarithms of integers,—the latter, of fractional numbers.
• It was not so in the table of logarithms first given to the world by their inventor.