Logarithmic and Other Mathematical Tables: With Examples of Their Use and Hints on the Art of Computation |
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9 Prop accuracy algebraic sign arithmetical complement binomial coefficient c. d. L cent co-log column COMMON LOGARITHMS computation consecutive cosine cotangent Cotg Cotgo Diff ences Entering the table equal equation error example EXERCISES fifth find log find the logarithm find the number five places give log given logarithm given number half a unit Hence increase interpolation JUN JIN last figure last two figures log a log log a+b log cot log(a loga logarithms of numbers mantissa natural number number corresponding order of differences places of decimals quotient rate of interest regular law remainder rithms second differences series of numbers side sidereal significant figures sin a sin sine N sine or tangent sixth figure Stirling's formula subtraction logarithms suppose table gives Tang trigonometric functions unity write wwww wwwww Δίν ΙΟ ΙΟΙ ΤΟ
Popular passages
Page 4 - Since the logarithm of 1 is 0 and the logarithm of a quotient is obtained by subtracting the logarithm of the divisor from that of the dividend...
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 34 - To find the trigonometric functions corresponding to an angle between 45° and 90°, we take the degrees at the bottom of the page and the minutes in the right-hand column.
Page 33 - In the case of tangent and cotangent, only one column of differences is necessary for both functions. If we use no fractional parts of minutes, no interpolation is necessary; but if decimals of a minute are employed, we can interpolate precisely as in taking out the logarithms of numbers. Where the differences are very small they are sometimes omitted. Tables of proportional parts are given in the margin, the use oí which is similar to those given with the logarithms of numbers.
Page 50 - Consequently, when the remainder is less than 'twice the part of the root already found, plus unity, the last figure can not be increased. Extract the square root of the following numbers. 1. 4225 Ans.
Page 8 - ... immediately following the decimal point. Thus the characteristic of the logarithm of any number between 1 and 10 is 0, between 10 and 100 1, between 100 and 1000 2, etc. Or let it be asked, " What is the characteristic of the logarithm of 5126 ? " Now this number lies between 1000 and 10000, hence its logarithm lies between 3 and 4, and is, therefore, 3 and some fraction. Again, as to the numerical value of the characteristic of the...
Page 53 - Conventionally the period is divided into 24 hours, each hour into 60 minutes, and each minute into 60 seconds.
Page 32 - If the angle of which a function is sought is less than 45°, we seek the number of degrees at the top of the table and the minutes in the left-hand column.
Page 3 - D 2-56, 7-99 10 and 100 1 and 2 1 +D 11-03, 45-96 100 and 1000 &c. 2 and 3 &c. 2 + D &c. 159, 159-108 &c. Definition. The whole part of a common logarithm, whether positive or negative, is called the characteristic of the logarithm. The decimal part is called the mantissa* We now give some theorems which obviously follow from what precedes. 1. No alteration in the place of the decimal point (in which is included the annexation of ciphers to a whole number) alters the mantissa of the logarithm, but...
Page 26 - Solve by logarithms the problem of the horseshoeing, in which a man agrees to pay 1 cent for the first nail, 2 for the second, and so on, doubling the amount for every nail for 32 nails in all..