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OF

PRACTICAL MATHEMATICS,

FOR THE USE OF schools.

PART III.

BY JAMES ELLIOT,

AUTHOR OF “A COMPLETE TREATISE ON PRACTICAL GEOMETRY AND MENSURATION,"
A PRACTICAL TREATISE ON THE NATURE AND USE OF LOGARITHMS,

AND ON PLANE TRIGONOMETRY,” ETC.

LOGARITHMS AND PLANE TRIGONOMETE

Tale

EDINBURGH: SUTHERLAND AND KNOX.

LONDON: SIMPKIN, MARSHALL & CO.

MDCCCLI.

In the Press,

KEY
TO THE ELEMENTARY COURSE OF PRACTICAL

MATHEMATICS; Containing Demonstrations of the Rules and Solutions of the Exercises,

MURRAY AND GIBB, PRINTERS, EDINBURGH.

PRACTICAL MATHEMATICS.

PART THIRD.

LOGARITHMS

AND

PLANE TRIGONOMETRY.

LOGARITHMS

AND

PLANE TRIGONOMETRY.

CHAPTER I.

DEFINITIONS AND EXPLANATIONS OF

LOGARITHMS.

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.

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