The Elements of Logarithms: With an Explanation of the Three and Four Place Tables of Logarithmic and Trigonometric FunctionsGinn brothers, 1873 - 83 páginas |
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antilog antilogarithm argument arithmetical complements arithmetical series B₁ bottom characteristic of log colog cologarithm containing the logarithms correction csc and log decimal-figure denary system denotes division division of page divisor example exponent feet find log formulas four places four-place logarithm Four-Place Table fraction given number greater than unity headland Hence incommensurable independent variables integer integral powers interpolation intervals Inverse Trigonometric Functions last figure retained left-hand column less than unity Let the student log cos q log csc log sec log sin log tan loga logarithmic trigonometric function Logarithms of Numbers mant log mantissa method miles minutes multiplier Napier nearest tabulated value number of places observed principle quadrant quantity quotient ratio reciprocal result right-hand column rithm Seaver significant figures small type subtracting system of logarithms table of logarithms table of Proportional theorem theory of logarithms three-place logarithm Three-Place Table tion trigono u₁ value of log
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Página 2 - Corollary. When the base is less than unity, it follows, from art. 3, that the logarithms of all numbers greater than unity are negative, while those of all numbers less than unity are positive. But when, as is almost always the...
Página 45 - The logarithm of a power of a number is found by multiplying the logarithm of the number by the exponent of the power. For, A« = (10°)
Página 82 - S. 40 miles. Find the bear ing and distance of the second ship from the first. Ans. S. 74° 30' E. ; 45.08 miles. 30. An observer from a ship saw two headlands ; the first bearing NE by E., and the second NW After he had sailed NNW 10.25 miles, the first headland bore E. by N., and the second WNW...
Página 28 - A table may be used in two ways : directly and inversely. The direct use of the table consists in finding the value of the function for an assumed value of the argument ; the inverse use, in finding the value of the argument for an assumed value of the function.
Página 27 - E. g. x¿. ^x. log x. sin x. log sin x. are all called functions of x. A mathematical table is an orderly arrangement of the values of some function for certain selected values of the quantity by which it is regarded as determined. The successive values of the latter quantity are assumed arbitrarily. and generally at equal intervals ; and this quantity is called the argument of the table. Some functions require several independent quantities for their determination ; and the...
Página 4 - Changing the sign of either dividend or divisor, changes the siyn of the quotient. II. Changing the signs of both dividend and divisor, does not alter the sign of the quotient. RECIPROCALS, ZERO POWERS, AND NEGATIVE EXPONENTb 86. The Reciprocal of a quantity is the quotient obtained by dividing unity by that quantity. Thus, _ is the reciprocal of x; x is the reciprocal of a — c.
Página 23 - amounts to 603, which probably includes very nearly all that exist ; this cannot be regarded as a great number, when it is considered that the table was the result of an original calculation, and that more than 2,100,000 printed figures are liable to error.
Página 21 - Art. 66 we see that the logarithm of a number which is not an integral power of 10 is an integer plus a decimal.
Página 35 - Whenever figures are neglected at the end of a number. if the figures neglected amount to more than half a unit in the place of the last figure retained. the last figure retained must be increased by 1.
Página 46 - If any three terms of a proportion are known, the fourth can always be found, as follows : — To find one of the extremes.