Tables of Logarithms ...: With Other Tables of Frequent Use in the Study of Mathematics ...

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1854 - 340 pages
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Page 41 - If the number of degrees and minutes falls between 45 and 90, the degrees must be looked for at the bottom of the page, and the minutes on the right...
Page 38 - I 15.314292 6240" + 22".5 = 6262.5 log 3.796748 Am. 11.517544 These two pages may be used in the same way when the given angle lies between 88 and 92, or between 178 and 180; but if the number of degrees be found at the bottom of the page, the title of each column will be found there also; and if the number of degrees be found on the...
Page 13 - The characteristic of the logarithm of a decimal is negative, and is numerically one greater than the number of noughts immediately to the right of the decimal point.
Page 12 - Thus the characteristic of the logarithm of 504.27 is 2, as the integral figures viz. '504 are three in number. And the characteristic of the logarithm of 2.036 is 0, because the number 2.036 has one integral figure. But if the number be only a decimal fraction, the characteristic of its logarithm is negative, and is greater by one than the number of ciphers at the beginning of the decimal. Thus if the number concerned be the decimal .087, the characteristic of its logarithm is —2 or as it should...
Page 14 - Log?ft n — n logm, or the logarithm of any power of a number is obtained by multiplying the logarithm of the number by the index of the power. For r?2 n —( a*)" =="*, and .*. log(m n ) = nz=n logm.
Page 11 - If the number is greater than 1, the characteristic of the logarithm is one less than the number of digits to the left of the decimal point.
Page 13 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 32 - The course is given in degrees or points in the two exterior marginal columns, the distance is found at the top or bottom of the page, according as the course is less or greater than four points or 45?
Page 41 - If the arc, or angle, is less than 45, look for the degrees at the top of the page, and for the minutes in the...
Page 33 - ... something to be wrong. Is it the Formula, the calculation, or the mechanical measurement? You repeat the mechanical measurement and find it correct ; you examine the calculation and find it just. You conclude, then, that the error lies in the Formula, and your conclusion is right. Here is the difficulty: the sine of an angle and that of its supplement are the same. 107 10' is the supplement of 72 50', and 9-9802 is the log sin both of 72 50

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