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Page 137
... Characteristic and Mantissa . It is shown in algebra that every real positive number has a real common logarithm , and that if a and b are any two real positive numbers such that a < b , then log a log b . Neither zero nor any negative ...
... Characteristic and Mantissa . It is shown in algebra that every real positive number has a real common logarithm , and that if a and b are any two real positive numbers such that a < b , then log a log b . Neither zero nor any negative ...
Page 137
... characteristic ; the decimal is called the mantissa . The characteristic of the logarithm of any number greater than 1 may be determined as follows : RULE I. The characteristic of any number greater than 1 is one less than the number of ...
... characteristic ; the decimal is called the mantissa . The characteristic of the logarithm of any number greater than 1 may be determined as follows : RULE I. The characteristic of any number greater than 1 is one less than the number of ...
Page 137
... characteristic , then look in the table for the mantissa . To find the mantissa in the table when the given number ( neglecting the decimal point ) consists of four , or less , digits ( exclusive of ciphers at the beginning or end ) ...
... characteristic , then look in the table for the mantissa . To find the mantissa in the table when the given number ( neglecting the decimal point ) consists of four , or less , digits ( exclusive of ciphers at the beginning or end ) ...
Page 137
... characteristic of the logarithm is positive ( in which case the mantissa is not followed by · 10 ) , begin at the left , count digits one more than the characteristic , and place the decimal point to the right of the last digit counted ...
... characteristic of the logarithm is positive ( in which case the mantissa is not followed by · 10 ) , begin at the left , count digits one more than the characteristic , and place the decimal point to the right of the last digit counted ...
Page 137
... characteristic ) and subtract each digit from 9 , except the last , * which subtract from 10 ; if the logarithm has not - 10 after the mantissa , write 10 after the result ; if the logarithm has - 10 after the mantissa , do not write 10 ...
... characteristic ) and subtract each digit from 9 , except the last , * which subtract from 10 ; if the logarithm has not - 10 after the mantissa , write 10 after the result ; if the logarithm has - 10 after the mantissa , do not write 10 ...
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acute angle angle of elevation angle opposite angular speed Arccos Arcsin Arctan axes called circle colog cologarithm common logarithm congruent angles coördinates cos² cosine law cotangent curve decimal point degrees denoted determine draw equal Example EXERCISES expressions figure Find the angle Find the distance force formulas geometry given angle graph hence hypotenuse included angle law of cosines law of sines law of tangents length Log10 Value Log10 mantissa method negative numerical measure obtuse angle perpendicular plane polar triangle positive angle Proj Prove Quad radian measure radius resultant revolutions revolutions per minute right angle right triangle rotation sec² segment side opposite sin² solution spherical triangle subtends subtract tabular difference terminal side theorem tion trigonometric functions Value Log10 Value velocity vertex whence x-axis y-axis zero
Popular passages
Page 137 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 137 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result. Thus, the characteristic of log...
Page 32 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Page 113 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...
Page 2 - LOGARITHMS ing the proportional part corresponding to the fourth figure to the tabular number corresponding to the first three figures. There may be an error of 1 in the last place. N 0 1 2 3 4 5 6 7 8 9 123 456 789 55...
Page 87 - 1 — cos a 1 + cos a 1 + cos a * 1 + cos a sin a 16. If a numerical value of any function of a is given, all the other functions of a and of a/2 can be found geometrically from Ex. 14. Thus, if sin a = 4/5 is given, lay off OP = 5, BP = 4 ; then 07? = V52 — 4* = 3. Hence, 073 = 8, AB=2; and CP = v
Page xvii - ... duplicates of the preceding fiveplace tables, reduced to four places, and with larger intervals between the tabulations. The value of such four-place tables consists in the greater speed with which they can be used, in case the degree of accuracy they afford is sufficient for the purpose in hand.
Page 42 - The area of a triangle is equal to one half the product of the base and the altitude: A = I bx a.
Page 137 - The logarithm of the root of a number is found by dividing the logarithm of the number by the index of the root. For, \ Therefore, tag tfï = 2 = 6.
Page 137 - In brief : to multiply, add logarithms. II. The logarithm of a fraction is equal to the difference obtained by subtracting the logarithm of the denominator from the logarithm of the numerator : log (a/6) = log a — log 6.