# Trigonometry: Analytical, Plane and Spherical: With Logarithmic Tables

J. Wiley & sons, 1885 - 237 pàgines

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Pàgina 122 - The differences in the logarithms due to a change of one second in the arc are given in adjoining columns. To find the log. sin, cos, tan, or cot of a given arc. : Take out from the proper column of the table the logarithm corresponding to the given number of degrees and minutes. If there be any seconds multiply them by the adjoining tabular difference, and apply their product as a correction to the logarithm already taken out. The correction is to be added if the logarithms of the table are increasing...
Pàgina 119 - ... order have the same mantissa, regardless of the position of the decimal point in the number, or of the number of ciphers which precede or follow the significant figures of the number. The value of the characteristic depends entirely on the position of the decimal point in the number. It is always one less than the number of figures in the number to the left of the decimal point. The value is therefore diminished by one every time the decimal point of the number is removed one place to the left,...
Pàgina 122 - The logarithmic sine, tangent, etc., of an arc is the logarithm of the natural sine, tangent, etc., of the same arc, but with 10 added to the characteristic to avoid negatives. This table gives log sines, tangents, cosines, and cotangents for every minute of the quadrant. With the number of degrees at the left side of the page are to be read the minutes in the left-hand column; with the degrees on the right-hand side are to be read the minutes in the right-hand column. When the degrees appear at...
Pàgina 56 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Pàgina 122 - The number derived from a six-place logarithm is not reliable beyond the sixth figure. At the end of table XXIV. is a small table of logarithms of numbers from 1 to 100, with the characteristic prefixed, for easy reference when the given number does not exceed two digits. But the same mantissas may be found in the larger table. TABLE XXV.— The logarithmic sine, tangent, etc.
Pàgina 121 - ... last figure is concerned. The lower part of the page contains a complete list of differences, with their multiples divided by 10. To find the logarithm of a number having six figures ¡—Take out the mantissa for the four superior places directly from the table, and find the difference between this mantissa and the next greater in the table. Add to the mantissa taken out the quantity found in the table of proportional parts, opposite the difference, and in the column headed by the fifth figure...
Pàgina 122 - ... be any seconds multiply them by the adjoining tabular difference, and apply their product as a correction to the logarithm already taken out. The correction is to be added if the logarithms of the table are increasing with the angle, or subtracted if they are decreasing as the angle increases. In the first quadrant the log sines and tangents increase, and the log. cosines and cotangents decrease as the angle increases. Example.— Find the log sin of 9° 28, 20".
Pàgina 123 - ... log sin and the logarithm of the number of seconds in the first column. The first three figures and the characteristic of this logarithm are placed, once for all, at the head of the column. To find the log sin of an arc less than 2° given to seconds.— Reduce the given arc to seconds, and take...
Pàgina 49 - Required the horizontal distance of the vessel, and the height of the hill on which the light-house is placed, the height of the light-house being 60 feet.
Pàgina 121 - The decimals of the corrections are added together to determine the nearest value of the sixth figure of the mantissa. To find the number corresponding to a given logarithm. If the given mantissa is not in the table, find the one next less, and take out the four figures corresponding to it; divide the difference between the two mantissas by the tabular difference in that part of the table, and annex the figures of the quotient to the four figures already taken out. Finally, place the decimal point...