## Tables of Logarithms of Numbers and of Sines and Tangents for Every Ten Seconds of the Quadrant: With Other Useful Tables |

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35 Degrees 3ioi 47 Degrees 4oio 4ooi 4ooo 56 Degrees 59 Sine 5ioi 5oio 5ooi 5ooo 61 Degrees 62 Degrees 78 Degrees 80 Degrees 9 il i4 analytical geometry arc corresponding arithmic bottom College column headed computed correction corresponding to logarithmic cosecant difference of latitude Dist expressed in seconds fifth figure find the arc find the Logarithm four figures fraction given number i4oi i4oo i5io i5oi i5oo ilOl io5i io5o ioi5 Lat Course Lat Dep leading figures logarithmic cosine logarithmic sine logarithmic tangent LOGARITHMS OF NUMBERS Loomis's Natural Philosophy manner we find Marietta College middle latitude minutes Natural Co-sines Natural Co-tangents natural number natural sines number of seconds o5oo prefixed Prof proportional quadrant radius Required the logarithmic secant Sheep extra sine of 24 Sine or Tangent Sines and Tangents table of natural tabular difference tabular number tivate treatise Vulgar Fraction г1 гг

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Page v - In a system of logarithms all numbers are considered as the powers of some one number, arbitrarily chosen, which is called the base of the system, and the exponent of that power of the base which is equal to any given number, is called the logarithm of that number. Thus, if a be the base of a system of logarithms, N any number, and x such that N = a* then x is called the logarithm of N in the system whose base is a.

Page vi - To find the Logarithm of any Number between 1 and 100. Look on the first page of the table, along the column of numbers under N, for the given number, and against it, in the next column, will be found the logarithm, with its characteristic. Thus, opposite 13 is 1.113943, which is the logarithm of 13 ; " 65 is 1.812913, " " 65. To find tht Logarithm of any Number consisting of three Figures.

Page viii - For, by art. 14, the decimal part of the logarithm of any number is the same, as that of the number multiplied into 10, 100, &c.

Page vi - The characteristic of the logarithm of ANY NUMBER GREATER THAN UNITY, is one less than the number of integral figures in the given number.

Page v - The logarithm of every number between 10 and 100 is some number between 1 and 2, ie, is 1 plus a fraction. The logarithm of every number between 100 and 1000 is some number between 2 and 3, ie, is 2 plus a fraction, and so on.

Page x - The logarithmic cosine of 59° 33' 40" is 9.704682 Proportional part for 7" is 25 Logarithmic cosine of 59° 33' 47

Page xvi - Thus the meridional parts for latitude 12° 23' are 748.9; " " " 57° 42' are 4260.5. TABLE OF CORRECTIONS TO MIDDLE LATITUDE, p. 149. This table is used in Navigation for correcting the middle latitude The given middle latitude is to be found either in the first or last vertical column, opposite to which, and under the given difference of latitude, is inserted the proper correction in minutes, to be added to the middle latitude to obtain the latitude in which the meridian distance is accu rately...

Page vi - N, and their logarithms, or the decimal parts of their logarithms, are opposite on the same line. When the first two figures of the decimal are the same for several successive logarithms, they are not repeated for each, but, being used once, are then left to be supplied. 19. In the column headed D are the mean or average differences of the ten logarithms against which they are placed. To FIND THE LOGARITHM OF ANY NUMBER. 20. When the given number is any integer of ONE or...

Page vi - The characteristic of the logarithm of a decimal fraction is a negative number, and is equal to the number of places by which its first significant figure is removed from the place of units.

Page 1 - In the following Table, the first two figures, in the first column of Logarithms, are to be prefixed to each of the numbers, in the same horizontal line, in the next nine columns; but when a point (•) occurs, a 0 is to be put in its place, and the Itco initial figures are to be taken from the next line below.